We have compiled the list of Best Reference Books on Numerical Methods subject. These books are used by students of top universities, institutes and colleges. Here is the full list of best books on Numerical Methods along with reviews.
Kindly note that we have put a lot of effort into researching the best books on Numerical Methods subject and came out with a recommended list of best books. The table below contains the Name of these best books, their authors, publishers and an unbiased review of books on “Numerical Methods” as well as links to the Amazon website to directly purchase these books. As an Amazon Associate, we earn from qualifying purchases, but this does not impact our reviews, comparisons, and listing of these top books; the table serves as a ready reckoner list of these best books.
List of Numerical Methods Books with author’s names, publishers, and an unbiased review as well as links to the Amazon website to directly purchase these books.
 Introduction to Numerical Methods
 Applied Numerical Methods
 Numerical Methods for Engineering Applications
 Numerical Methods in Fluid Flow Problems
 Numerical Methods for Partial Differential Equations
 Application of Numerical Methods in Structural Engineering
 Statistics and Numerical Methods
 Numerical Methods in Civil Engineering
1. Introduction to Numerical Methods
1. “Elementary Numerical Analysis – An Algorithmic Approach” by S D Conte and Carl de Boor
“Elementary Numerical Analysis – An Algorithmic Approach” Book Review: The book aims at introducing the practical solutions for dealing with the problems on computers. The chapters of this book feature the process of formulation for problem solving. The specific objectives, proper input data, and adequate checks are addressed in this text. The book presents a mathematical model for dealing with several physical situations. This book will be a valuable resource for the students and professionals involved in numerical analysis.


2. “Introduction to Numerical Analysis” by C E Froberg  
3. “Advanced Engineering Mathematics” by E Kreyszig
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“Advanced Engineering Mathematics” Book Review: The book covers important aspects and major topics of Advanced Engineering Mathematics. The chapters of this book revolve around linear algebra, vector calculus, Fourier analysis and partial differential equations, complex analysis, numerical methods, optimization, graphs, and probability and statistics. The content of this book is fully updated, compact, selfcontained, and supported by several exercises. For proving realworld experience to the readers many engineering applications and uses of technology are mentioned in this text. The book will be suitable for the engineers and computer scientists.


4. “An Introduction to Numerical Analysis” by Endre Süli and David F Mayers
“An Introduction to Numerical Analysis” Book Review: The book aims at presenting a theoretical foundation for the numerical algorithms, underlying Numerical Analysis. The methodologies and techniques featured in this text are used for dealing with numerous computational problems in science. Several problems such as the approximation of functions and integrals, approximate solutions of algebraic, transcendental, differential and integral equations are addressed in this book. The numerical algorithms featured in this book are stable, accurate, reliable and efficient. The book will be beneficial for the students in the second year of mathematics.


5. “An Introduction to Numerical Methods and Analysis” by James F Epperson
“An Introduction to Numerical Methods and Analysis” Book Review: The book is an updated and revised piece of writing featuring latest topics and recent developments in the fields of numerical approximation and analysis. The chapters of this book are self contained and ascended from basic to advanced topics. The topics like polynomials, spectral collocation, finite element ideas, and ClenshawCurtis quadrature are discussed in detail. The content of this book is supported by several exercises and applications. The deployment of MATLAB is addressed in this text. The book will be an asset for the advanced undergraduate students of mathematics and engineering, seeking knowledge in numerical methods and numerical analysis.


6. “Introduction to Numerical Analysis” by F B Hildebrand and Mathematics
“Introduction to Numerical Analysis” Book Review: The book focuses on presenting a fair introduction of basic processes involved in numerical analysis. The fundamental operations of computation, approximation, interpolation, numerical differentiation, integration, and numerical solution of equations are addressed in this text. The chapters contain detailed description of interpolation with divided differences, Lagrangian methods, finitedifference interpolation, operations with finite differences, and leastsquares polynomial approximation. The book is an updated edition and also features machine errors, recursive calculation, midpoint rule, Romberg integration, Filon integration, and Hamming’s method. The undergraduate and graduate students interested in theory and analysis of numbers will find this book helpful.


7. “A Friendly Introduction to Numerical Analysis” by Brian Bradie
“A Friendly Introduction to Numerical Analysis” Book Review: The book aims at presenting the basic principles, key concepts, and major techniques of numerical analysis and numerical methods. The featured concepts and techniques are presented in a precise, comprehensive, and reader friendly manner. The topics like root finding, systems of equations, eigenvalues and eigenvectors, interpolation and curve fitting, differentiation, integration, and convectiondiffusion equation are thoroughly explained. The numerical and difference methods for initial value problems of ordinary differential equations, secondorder onedimensional twopoint boundary value problems, elliptic partial differential equations, parabolic partial differential equations, and hyperbolic partial differential equations are mentioned. To give better practical knowledge and relatable content to the readers fullyworked examples and applications of numerical analysis are included. The book will be a good resource for the students and professionals related to numerical analysis and methods.
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8. “An introduction to numerical methods for differential equations” by James M Ortega  
9. “An Introduction to MATLAB® Programming and Numerical Methods for Engineers” by Timmy Siauw and Alexandre Bayen
“An Introduction to MATLAB® Programming and Numerical Methods for Engineers” Book Review: The book will be suitable for the beginners in the field of real and numerical analysis.The initial section of the book reflects basic programming concepts. Moving further, the principles of algorithms and numerical analysis are addressed. Each chapter ends with summaries, key terms, and lists of functions and operators. The exercises dependent on thinking, writing, and coding are included in this book. It enables the readers in developing computational problem solving techniques with the use of numerical methods and the MATLAB programming environment.


10. “Introduction to Numerical Analysis” by Kendall Atkinson
“Introduction to Numerical Analysis” Book Review: The book is an updated and revised piece of writing featuring latest topics and recent developments of numerical analysis. The book covers all the major aspects of root finding for nonlinear equations, interpolation theory, approximation of functions, numerical integration, numerical methods for ordinary differential equations, linear algebra, and numerical solution of systems of linear equations. The topics like optimization, trigonometric interpolation, fast Fourier transform, numerical differentiation, method of lines, , conjugate gradient method, and the least squares solutions of systems of linear equations are thoroughly explained. The chapters based on error along with its sources, propagation, and analysis are included in this text. The book also highlights the problems faced in numerical analysis namely, boundary value problems and matrix eigenvalue problems are featured in this book


11. “An Introduction to Numerical Methods: A MATLAB Approach, Second Edition” by Abdelwahab Kharab and Ronald B Guenther
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“An Introduction to Numerical Methods: A MATLAB Approach, Second Edition” Book Review: The book is designed for researchers and professionals of mathematics, scientific and engineering disciplines. It contains the latest version details of MATLAB. It contains topics like theory and applications of commonly used techniques for solving numerical problems. It also consists iof wide range of useful algorithms in full details.


12. “Numerical Methods for Nonlinear Variational Problems” by Roland Glowinski
“Numerical Methods for Nonlinear Variational Problems” Book Review: This book has useful text describing the mathematical background and reviews the techniques for solving problems, including those that require large computations such as transonic flows for compressible fluids and the NavierStokes equations for incompressible viscous fluids. The book covers topics in details like Finite element approximations and nonlinear relaxation, and nonlinear least square methods and Some Illustrations from an Industrial Application. This book is for applied mathematics and computational physics and engineering and is valuable for practitioners in industry and physics and for advanced students.


2. Applied Numerical Methods
1. “Applied Numerical Methods W/MATLAB” by Steven C Chapra
“Applied Numerical Methods W/MATLAB” Book Review: This book is designed for engineering and science students who want to study numerical problem solving. It also explains key concepts with applications which are demonstrated in MATLAB. This book is also useful for first semester undergraduate courses in numerical methods. The new edition of this book includes new chapters on Eigenvalues and Fourier Analysis with different sets of mfiles and instructor materials.


2. “Numerical Methods in Engineering and Science: with Programs in C and C++” by B S Grewal  
3. “Numerical Methods for Scientists and Engineers” by Rao and Sankara
“Numerical Methods for Scientists and Engineers” Book Review: The new edition of the book contains a complete course on numerical methods for undergraduate students in all branches in engineering. It is also useful for postgraduate students in mathematics and physics, and students studying courses in Master of Computer Applications (MCA). It explains the basics in computing, errors in computation. It also illustrates direct and iterative methods for solving algebraic and transcendental equations and a method for solving a system of nonlinear equations. Thebook also demonstrates a linear system of equations, matrix inversion and computation of eigenvalues and eigenvectors of a matrix. It provides indepth discussion on curve fitting, interpolation and cubic spline interpolation, numerical differentiation and integration.


4. “Applied Numerical Methods Using Matlab” by Dukipati R
“Applied Numerical Methods Using Matlab” Book Review: This book is designed for undergraduate or graduate courses for Science and engineering students of all branches. It covers all important concepts of applied numerical methods, including numerical computations, solution of algebraic and transcendental equations. It also explains finite differences and interpolation, curve fitting, correlation and Regression, numerical differentiation and integration, matrices and linear system of equations. The book maintains a simple and studentfriendly language with numerical problem solving approach. The main goal of the book is to illustrate the major concepts of numerical methods to student learning. It provides numerous examples with exercises problems to clear the concept thoroughly.


5. “Applied Numerical Methods for Engineers” by Terrence J Akai
“Applied Numerical Methods for Engineers” Book Review: This book is written in a conversational style. It provides a comprehensive introduction to numerical methods for all engineers.


6. “Applied Numerical Methods for Engineers and Scientists” by Singiresu S Rao
“Applied Numerical Methods for Engineers and Scientists” Book Review: This book is useful for courses in numerical methods at the beginning of graduate level. The book explains the reference for numerical methods in engineering.


7. “Applied Numerical Methods with MATLAB for Engineers and Scientists” by Steven Chapra
“Applied Numerical Methods with MATLAB for Engineers and Scientists” Book Review: This book is designed for Engineers and scientists who want to study numerical problem solving. It concentrates on problem solving applications rather than theory using MATLAB. Hence theory is included for understanding important concepts.


8. “Applied Numerical Methods” by Carnahan
“Applied Numerical Methods” Book Review: The book in discussion mainly talks about theoretical and applied numerical methods. It targets students of senior and graduate level courses. The described numerical methods are also illustrated with the help of computer programs. Most of the examples of programs are written in FORTRAN VI language. The readers will be able to understand and comprehend the numerical methods and the implementations in digital programs format.


9. “Applied Numerical Analysis” by Curtis F Gerald and Patrick O Wheatley
“Applied Numerical Analysis” Book Review: The new edition of this book includes updated content of Computer algebra systems and programming languages. This book includes computer algebra systems such as Matlab and programming languages to show how applied numerical analysis works. It provides different applications to enhance students’ understanding of different methods and analysis of results. This book maintains a perfect balance of theory with various techniques and applications. Every chapter end exercises provide challenging problems and projects to show realworld applications. It also illustrates the use of computer algebra systems such as Maple®, Mathematica®, and MATLAB®, facilitating the integration of technology in the course. The book contains programming materials in FORTRAN and C languages. It covers topics such as partial differential equations, systems of nonlinear equations, and matrix algebra.


10. “Computer Oriented Numerical Methods” by V Rajaraman
“Computer Oriented Numerical Methods” Book Review: This book fundamental overview on computer oriented numerical methods. It covers computational algorithms for solving nonlinear algebraic equations, sets of linear equations, curvefitting, integration, differentiation, solving ordinary differential equations and much more. It contains numerous diagrams, graphical representation, mathematical representation, and theoretical explanation to enhance understanding of the reader. The book is designed focusing on students and teachers who need to use computer aided numerical methods to perform complex mathematical calculations. It provides numerous solved and unsolved examples with detailed explanation.


11. “Computer Programming in FORTRAN 77” by Rajaraman  
12. “Variational Methods for Engineers with Matlab (Numerical Methods in Engineering)” by Eduardo Souza de Cursi
“Variational Methods for Engineers with Matlab (Numerical Methods in Engineering)” Book Review: This book provides a complete, pedagogical and engineeroriented presentation of the foundations of variational methods and of their use in numerical problems of Engineering. It explains applications to linear and nonlinear systems of equations, differential equations, optimization and control. The book contains a MATLAB program which illustrates the implementations which helps readers to understand the concept thoroughly for selfstudy.


13. “Numerical Methods for Scientists and Engineers” by Richard W Hamming
“Numerical Methods for Scientists and Engineers (Dover Books on Mathematics)” Book Review: This book introduces numerical methods and their relevance to computing. It highlights five main ideas including ensuring that in computing there is an intimate connection between the source of the problem and the usability of the answers. The new edition of the book is updated, rearranged and enlarged with extensive material. It highlights the frequency approach and its use in the solution of problems. It covers topics such as fundamentals and algorithms, polynomial approximation and classic theory. It also illustrates fourier approximation modern theory and exponential approximation. It is useful for undergraduate and graduate students of mathematics, science and engineering.


14. “Applied Numerical Methods for Engineers” by R Schilling and S L Harris
Book Review: This book carries out discussion on numerical computing techniques thereby stressing on the practical aspects that occur in the streams of chemical, civil, electrical and mechanical engineering. The book also contains software libraries that implement many algorithms. The book also contains various worked out examples, demonstrations and summaries of numerical techniques. Additionally, the book also provides solutions manual to the problems and examples given in the book.


15. “Applied Numerical Methods for Digital Computations” by M L James
Book Review: This book covers all the basic topics taught to engineers in most numerical courses. The author explains the numerical methods by taking into consideration the basic mathematical concepts with the usage of graphics wherever possible. The book also has numerous examples and problems that reflect real world situations and encompass a range of engineering disciplines. The book also provides a very nice coverage of eigen values and eigen vectors as well as Gaussian quadrature. The book also provides programs and sub programs of important numerical methods.


3. Numerical Methods for Engineering Applications
1. “Numerical Methods” by Kandasamy P
“Numerical Methods” Book Review: This book covers important numerical methods that are required to solve a wide variety of numerical problems. The book comprises chapters on empirical laws and curve fitting, theory of equations, difference equations, finite differences and numerical methods of double integers. In addition, the book consists of model test papers for thorough revision and final practice. This textbook is designed for undergraduate and postgraduate students of mathematics.


2. “Introductory Methods of Numerical Analysis” by Sastry S S
“Introductory Methods of Numerical Analysis” Book Review: This book provides a detailed introduction to the fundamentals of numerical methods required in scientific and technological applications. A chapter on spline functions has been added because of their increasing importance in applications. It includes additional modified illustrative examples and problems in every chapter to aid the students in better understanding of the concepts. The book provides answers to all chapterend exercises. Algorithms, computational steps and flow charts for many numerical methods are also included. This text is designed for undergraduate students of all branches of engineering.


3. “Numerical Methods in Engineering and Science” by Grewal B S
“Numerical Methods in Engineering and Science” Book Review: This book provides a clear and precise explanation of modern numerical techniques. It includes topics like Approximation and Errors in Computation, Solutions of Algebraic and Transcendental Equations,Finite Difference etc. Other topics like Interpolation, Numerical Differentiation and Integration, Empirical Laws and Curvefitting, Linear Programming, Numerical Methods using C, C++, MATLAB are also included. Each method is illustrated by a number of solved examples. It is designed as a textbook for engineering and science students upto the postgraduate level.


4. “Numerical Methods for Engineering Applications (New Perspectives on the Past)” by Joel H Ferziger  
5. “Numerical Methods for Engineers: With Software and Programming Applications” by Steven C Chapra and Raymond P Canale
“Numerical Methods for Engineers: With Software and Programming Applications” Book Review: This book discusses various numerical techniques used in engineering. It Includes application sections with a variety of engineering problems along with softwarebased examples and engineeringoriented problems. In addition, the book gives examples of the codes to be written on the computer. It offers complete coverage of most commonly encountered algebraic, interpolation, and integration problems. This book is a valuable working resource for engineers and applied physicists. It will also benefit physics and engineering students in courses on modern numerical methods.


6. “Ordinary Differential Equations: An Elementary Textbook for Students of Mathematics, Engineering and the Sciences” by M Tenenbaum and H Pollard
“Ordinary Differential Equations: An Elementary Textbook for Students of Mathematics, Engineering and the Sciences” Book Review: This book provides a detailed survey of ordinary differential equations which express the relationship between variables and their derivatives. The book begins with a section that examines the origin of differential equations. It defines basic terms and outlines the general solution of a differential equation. Subsequent sections deal with integrating factors, dilution and accretion problems, the algebra of complex numbers, the linearization of first order systems etc. The book is useful for undergraduate students of mathematics and engineering.


7. “Computational Methods for Electric Power Systems, Second Edition (Electric Power Engineering Series)” by Mariesa L Crow
“Computational Methods for Electric Power Systems, Second Edition (Electric Power Engineering Series)” Book Review: This book is an introductory overview of computational methods used for analytical studies in power systems and other engineering and scientific fields. It analyzes the algorithms used in commercial analysis packages and presents salient examples of their implementation. Most of the examples were produced using MATLAB language. The topics such as Generalized Minimal Residual (GMRES) method, Numerical differentiation, Secant method and Homotopy and continuation methods are included in the book. It will be useful for students and teachers of mathematics and engineering.


8. “Numerical Techniques in Electromagnetics with MATLAB” by Matthew N O Sadiku
“Numerical Techniques in Electromagnetics with MATLAB” Book Review: This book teaches the readers how to pose, numerically analyze, and solve EM problems. It would help the readers and give them the ability to expand their problemsolving skills using a variety of methods to prepare them for research in electromagnetism. It is a comprehensive resource that addresses all of the most useful computation methods for EM problems and includes MATLAB code. The exercises included in the book help the students test their understanding of the subject matter. The book is useful for students studying mathematics, engineering and Bsc.


9. “Partial Differential Equations for Scientists and Engineers” by Stanley J Farlow
“Partial Differential Equations for Scientists and Engineers” Book Review: The book explains how to describe the physical phenomenon in the domain of fluid dynamics, electricity, magnetism, mechanics, optics by partial differential equations. It shows the reader how to formulate a partial differential equation from the physical problem and how to solve the equation. It provides a practical coverage of diffusiontype problems, hyperbolictype problems, elliptictype problems, and numerical and approximate methods. It is written for advanced undergraduate and graduate students as well as professionals working in the applied sciences. This book has a concise exercise along with easy to understand explanations.


10. “Numerical Methods: Algorithms and Applications (Featured Titles for Numerical Analysis)” by Laurene V Fausett
“Numerical Methods: Algorithms and Applications (Featured Titles for Numerical Analysis)” Book Review: This text presents the fundamental numerical techniques used in engineering, applied mathematics, computer science, and the physical and life sciences. Each topic is illustrated by simple and moderate level examples. The topics are explained by geometrical or graphical illustrations wherever needed. Each chapter uses introductory problems from specific applications. Algorithmic ideas are explained with the help of MATLAB codes. The book is useful in undergraduate courses on numerical methods and numerical analysis found in engineering, mathematics & computer science depts.


4. Numerical Methods in Fluid Flow Problems
1. “Numerical Methods in Fluid Dynamics” by M Holt
Book Review: This book is very useful for graduates and researchers who are involved in the numerical solution of fluid dynamics problems. The book is logically presented, well arranged and nicely illustrated. The book also contains many FORTRAN programs that enable the students to experiment upon. The book mainly stresses on methods and its implementation. The book also includes Glimm’s method. The book also solves many problems arising in the field of high speed flow.


2. “Implementation of Finite Element Methods for NavierStokes Equations” by F Thomasset
Book Review: The book deals with the representation of arbitrary complicated boundaries and also deals with the systematic rules for the development of stable numerical schemes along with various types of boundary conditions. The book also supports flexibility with the help of increased programming complexity and additional storage requirement. The book also deals with the approximation of incompressible, viscous, Newtonian fluids and stokes equation. The book also establishes and documents techniques of structured mechanical analysis.


3. “Numerical Methods in Fluid Dynamics” by H J Wirz and J J Smolderen
“Numerical Methods in Fluid Dynamics” Book Review: This book provides various numerical methods that are useful in fluid dynamics. It expects the reader to have fundamental knowledge of different concepts in fluid dynamics. It contains numerous solved and unsolved examples. It provides diagrams, mathematical equations, calculations, graphs which make it easy for readers to understand and implement concepts to realworld problems. The book is designed focusing on students, teachers, and professionals in the field of different streams of engineering and science.


4. “Robust Numerical Methods for Singularly Perturbed Differential Equations” by Lutz Tobiska and HansGorg Roos
“Robust Numerical Methods for Singularly Perturbed Differential Equations” Book Review: The book is designed keeping in mind students, teachers in the field of different streams of engineering and science. It covers numerical methods required for differential equations. It provides information on differential equations, parabolic and elliptic problems, NavierStokes equation and much more. It covers the theoretical and practical aspects of singularly perturbed differential equations which would help the reader enhance their overall understanding of the subject. The book contains numerous solved and unsolved examples with detailed explanation, equations, and mathematical calculations.


5. “Efficient Numerical Methods to Compute Unsteady Subsonic Flows” by Lucas Dr Peter
“Efficient Numerical Methods to Compute Unsteady Subsonic Flows” Book Review: This book provides a detailed overview on efficient numerical methods to compute unsteady subsonic flows. It talks about different computer aided techniques available to have efficient methods to perform complex calculations. It describes the Jacobianfree NewtonKrylov algorithm in detail. The book contains numerous solved and unsolved examples and provides explanations for mathematical equations and extensive calculations. The book is designed for students and professors in the field of engineering and science. It expects the reader to have basic knowledge on the subject as a prerequisite.


6. “Proceedings of the Third International Conference on Numerical Methods in Fluid Mechanics” by Roger Temam and Henri Cabannes
“Proceedings of the Third International Conference on Numerical Methods in Fluid Mechanics” Book Review: This book provides detailed overview on various topics of fluid mechanics. It provides details on numerical methods to perform complex calculations required in fluid dynamics. It provides a healthy balance of theoretical explanation, mathematical equations, and calculations along with diagrams and graphs to enhance understanding of the reader. It contains numerous solved and unsolved examples which are very useful. The book is focused on students and teachers who are in the field of engineering and sciences who have practical use of fluid mechanics in their day to day activities.


7. “Numerical Methods for the Computation of Inviscid Transonic Flows with Shock Waves” by Arthur Rizzi
“Numerical Methods for the Computation of Inviscid Transonic Flows with Shock Waves” Book Review: This book aims to provide students and teachers with detailed information on numerical methods for the computation of inviscid transonic flows with shock waves. It provides theoretical and mathematical explanation of the different numerical methods available to carry out complex calculations in the field of inviscid transonic flow. It also discusses the Jacobianfree NewtonKrylov algorithm tailored for subsonic flow problems. It is written in easy to apprehend language with numerous solved and unsolved examples to enhance understanding.


8. “Modelling and numerical methods for twophase flow” by Svend Tollak Munkejord
“Modelling and numerical methods for twophase flow” Book Review: This book provides a fundamental overview of modelling techniques and numerical methods for twophase flows. The various available methods are benchmarked against various parameters and comparison between them. It assumes the reader to have basic knowledge on the subject. It contains numerous solved and unsolved examples which can be useful. It is aimed to focus on students, teachers, researchers, and professionals in the field of various streams of engineering and science who deal with these tools on a day to day basis.


9. “Micropolar and Newtonian Fluid Flow Problems” by M Anwar Kamal and Abuzar Abid Siddiqui
“Micropolar and Newtonian Fluid Flow Problems” Book Review: This book covers the dynamics of complex fluids like brain fluids, colloidal suspensions, industrial fluids, and many more which are typically analyzed in the field of fluid dynamics of micropolar fluids. It provides numerous graphical and tabular simulations to enhance understanding of the readers. It discusses various methods in the field like the Modified AdamsBashforth temporal scheme, RungeKutta temporal scheme, AdamBashforth temporal Fourier series method and many more in detail. It is aimed to focus on students and teachers in the field of engineering and science.


10. “Analytical Methods for Heat Transfer and Fluid Flow Problems” by Bernhard Weigand
“Analytical Methods for Heat Transfer and Fluid Flow Problems” Book Review: This book provides detailed explanation on heat transfer and fluid flow problems paying special attention to analytical methods which can be applied in the area. It contains various solved and unsolved problems which help the reader to possess knowledge required to apply the analytical methods in real world problems. It provides theoretical and mathematical explanations of various available methods. It provides data points to compare the available methods and identify the best suitable method for a given condition. It is designed to focus on students and teaches in the field of engineering and science.


11. “Numerical Methods in Geotechnical Engineering” by C S Desai and J T Christian
“Numerical Methods in Geotechnical Engineering” Book Review: The book is an excellent blend of theoretical as well as practical concepts of geotechnical engineering. The numerical methods used in geotechnical engineering are highlighted in this book. The chapters of this book clearly explain finite element method, finite difference method, and integral equations. The techniques and methods featured in this book will enable the readers to analyze and solve complex factors in soil and rock mechanics.


5. Numerical Methods for Partial Differential Equations
1. “Some Topics in Nonlinear Functional Analysis” by M C Joshi and R K Bose
“Some Topics in Nonlinear Functional Analysis” Book Review: This book is clear and presents a stronger concept of complete controllability which we call Trajectory Controllability is introduced in this paper. The book provides a clear study on the Trajectory. It also emphasises Controllability of an abstract nonlinear integrodifferential system in the finite and infinite dimensional space setting. It will discuss how approximations to these problems can be found computationally using finite difference methods and optimization. Examples will be presented in one, two and three dimensions.


2. “Functional Analysis and Applications” by S Kesavan
“Functional Analysis and Applications” Book Review: This book has rigorous and thorough introduction to the foundations of the subject with a clear and concise understanding. This book aims to provide a fairly complete, yet simple, treatment of the techniques from Functional Analysis used in the modern theory of Partial Differential Equations and illustrate their applications via examples. This book covers introduction to the theory of Distributions, Sobolev Spaces and Semi groups and the application of results to the study of weak solutions of elliptic boundary value problems and evolution equations. This book has four appendices at the end of each chapter and with several exercises. The book serves both as a textbook and as a source of reference for research workers in the area.


3. “Numerical Methods for Partial Differential Equations: Finite Difference and Finite Volume Methods” by Sandip Mazumder
“Numerical Methods for Partial Differential Equations: Finite Difference and Finite Volume Methods” Book Review: This book explains the method’s processes and techniques in careful, meticulous prose.The book focuses mainly on deterministic methods for solving partial differential equations (PDEs), namely finite difference and finite volume methods. For practical application most of the problems in the book are solved by using finite element methods in solid mechanics, and covered extensively in various other texts. The book aims to beginning graduate students and early career professionals, although advanced undergraduate students may find it equally useful. This book acts as a prerequisite for students who might go on to take additional courses in computational mechanics, computational fluid dynamics, or computational electromagnetics.


4. “Numerical Methods for Partial Differential Equations” by G Evans and J Blackledge
“Numerical Methods for Partial Differential Equations” Book Review: The book gives a clear introduction of the methods and underlying theories used in the numerical solution of partial differential equations. In this book the concepts are concise to help the students to interpret the topic in their way and to enhance their creativity. The book covers the finite difference method of parabolic or heat equations, hyperbolic or wave equations and elliptic or Laplace equations. The book emphasis is on the practical solution rather than the theoretical background, without sacrificing rigour. It has a number of examples and challenging exercises to check the understanding of the readers. This book is both for professionals and students who want a better understanding for the subject.


5. “Numerical Solution of Partial Differential Equations: Finite Difference Methods” by G D Smith
“Numerical Solution of Partial Differential Equations: Finite Difference Methods” Book Review: This book covers the standard finite difference methods of parabolic, hyperbolic, and elliptic equations, and includes the concomitant theoretical work on consistency, stability, and convergence. It also includes LaxRichtmyer definition, the application of Pade approximants to systems of ordinary differential equations for parabolic and hyperbolic equations, and a considerably improved presentation of iterative methods along with fastpaced introduction to numerical methods. This book is for students of mathematics and engineering, and for postgraduates and professionals who need a clear, concise grounding in this discipline. This book gives a practical approach to the topic.


6. “Ordinary Differential Equations” by Morris Tenenbaum and Harry Pollard
“Ordinary Differential Equations” Book Review: This book is wellwritten, skillfully organized introductory text provides an exhaustive survey of ordinary differential equations. The book is simple and its stepbystep style introduces and explains the complexity of the topic. This book also defines basic terms and outlines the general solution of a differential equationthe solution that actually contains every solution of such an equation. The book deals with topics like integrating factors, dilution and accretion problems, the algebra of complex numbers, the linearization of first order systems, Laplace Transforms, Newton’s Interpolation Formulas, and Picard’s Method of Successive Approximations Legendre Differential Equation, Legendre Functions, Legendre Polynomials, the Bessel Differential Equation, and the Laguerre Differential Equation. The book contains two exceptional chapters one on series methods of solving differential equations, the second on numerical methods of solving differential equations. This book is for undergraduate students of mathematics, engineering and the sciences. It has an abundance of solved problems and practice exercises that enhance the value of the topic.


7. “Numerical Methods for Partial Differential Equations: An Introduction” by Vitoriano Ruas
“Numerical Methods for Partial Differential Equations: An Introduction” Book Review: This book is fully updated on the context and has its own unique features. This book covers the three most popular methods for solving partial differential equations: the finite difference method, the finite element method and the finite volume method. It combines the clear descriptions of the three methods, their reliability, and practical implementation aspects. It also has justification for the methods and how they work. It has a balanced emphasis both on practical considerations and a rigorous mathematical treatment. This book pays attention to low order methods, as practitioner’s overwhelming default options for everyday use along with implementation of new methods along with this can be used as a reference for the research work on numerical PDEs. This book is aimed at students of Engineering, Mathematics, Computer Science, Physics and Chemistry this book offers a substantial insight into the principles numerical methods in this class of problems are based upon.


8. “Numerical Analysis of Partial Differential Equations” by S H Lui
“Numerical Analysis of Partial Differential Equations” Book Review: This book provides a comprehensive, selfcontained treatment of the quantitative methods used to solve elliptic partial differential equations (PDEs), with a focus on the efficiency as well as the error of the presented methods. The book covers the theoretical along with the numerical solution of linear systems and various examples and exercises which provides reader introduction to the essential concepts in the numerical analysis. The book focuses on topics like methods of elliptic PDEs: finite difference, finite elements, and spectral methods. The book also covers topics like the mathematical theory of elliptic PDEs, Numerical linear algebra, Numerical linear algebra, Timedependent PDEs, Multigrid and domain decomposition, PDEs posed on infinite domains. The book concludes with a discussion of the methods for nonlinear problems. Each chapter has well defined theory and problems so as to test the understanding of the reader. This book is for the upperundergraduate and graduate levels. The book is also suitable for students in mathematical sciences and engineering.


9. “Student Solutions Manual to Boundary Value Problems, Fifth Edition: and Partial Differential Equations” by David L Powers  
6. Application of Numerical Methods in Structural Engineering
1. “Computational Engineering – Introduction to Numerical Methods” by Michael Schäfer
“Computational Engineering – Introduction to Numerical Methods” Book Review: This book provides a complete introduction to modern numerical methods in engineering. It covers different applications in fluid mechanics, structural mechanics and heat transfer. It is useful for all engineering fields such as computational engineering, mechanical engineering, as well as chemical and civil engineering.


2. “Gallagher Optimum Structural *design* Theory And Applications (Wiley Series in Numerical Methods in Engineering)” by RH GALLAGHER  
3. “Manual of Numerical Methods in Concrete: Modelling and Applications Validated by Experimental and Sitemonitoring Data” by M Y H Bangash
“Manual of Numerical Methods in Concrete: Modelling and Applications Validated by Experimental and Sitemonitoring Data” Book Review: The main goal of this book is to explain a unified approach for the available mathematical models. It also helps to link them to element analysis and to computer programs The book covers creep, temperature, and shrinkage formulations of various concrete constitutive models.


4. “Numerical Methods: For Scientific and Engineering Computation” by Mahinder Kumar Jain
“Numerical Methods: For Scientific and Engineering Computation” Book Review: The new edition of the book covers a new material including more comprehensive content. It includes turbo C programs for several standard methods. The book provides an indepth explanation of spline interpolation. It illustrates detailed solutions of problems FORTRAN and C programs provided in CD. It is designed for Both undergraduate and postgraduate students of various engineering disciplines. It is also useful for B. Sc. (Hons. ) Mathematics/Physics and M. Sc. Mathematics students.


5. “Introductory Methods of Numerical Analysis” by Sastry S S
“Introductory Methods of Numerical Analysis” Book Review: The new edition of the book is fully revised and updated. This revised edition of the book provides a perfect introduction to the basics of numerical methods required in scientific and technological applications. It highlights numerical methods and helps students to build problem solving skills. It provides a comprehensive introduction to the basics of numerical methods needed in scientific and technological applications. It also highlights numerical methods and helps to develop problem solving skills. The book contains references to MATLAB, IMSL, numerical recipes and program libraries for implementing the numerical methods. This book is designed for undergraduate students of all branches of engineering. It provides illustrative examples and problems in each chapter with chapterend exercises. It contains four model question papers at the end of the book.


6. “Numerical Methods – Vol. 4” by Kandasamy  
7. “Numerical Methods” by Balagurusamy
“Numerical Methods” Book Review: This book is designed for the core course of the subject. It provides an introduction to numerical methods to students. It illustrates logical arrangement of topics, clarity of presentation and illustration with examples. It contains a number of unique features which make this book different from other books in this field.


8. “Numerical Methods for Engineers” by Canale Chapra
“Numerical Methods for Engineers” Book Review: The new edition of the book retains the instructional techniques which made the book so successful. It gives a unique approach towards each part of topics with sections such as motivation, mathematical background and orientation. The book provides numerous new problems from actual engineering practice. It covers topics from different areas such as biotechnology and biomedical engineering. It contains different new examples and case studies of different engineering which help students to explore various fields in engineering.


9. “Numerical Methods: Problems and Solutions” by Mahinder Kumar Jain
“Numerical Methods: Problems and Solutions” Book Review: This book contains a brief content numerical solution of transcendental and polynomial equations. It explains a system of linear algebraic equations and eigenvalue problems, interpolation. It also discusses approximation, differentiation and integration, ordinary differential equations. The book provides 300 problems with complete solutions.


10. “Numerical Methods in Engineering and Science: with Programs in C and C++” by B S Grewal
“Numerical Methods in Engineering and Science: with Programs in C and C++” Book Review: This comprehensive book covers the fundamental concepts of numerical analysis based on its construction. It explains routines for solving nonlinear equations, linear and nonlinear systems of equations, and eigenvalue problems. The book concentrates on software development and highlights software tools, OOP techniques for handling vectors, polynomials, and matrices. The bok helps students to solve various software development and programming challenges with actual examples. It is used as practical reference for developers and consultants setting up applications programs for electrical, electronic engineering.


7. Statistics and Numerical Methods
1. “Numerical Methods in Engineering and Science” by Grewal B S and Grewal JS
“Numerical Methods in Engineering and Science” Book Review: This book is meant for engineering students and science students till postgraduate. It provides an introduction to numerical methods with both theoretical and applied topics. It covers concepts like approximations and errors in computation. It explains the numerical differentiation and integration. It also explains numerical solutions of ordinary and partial differential equations. This book provides numerical methods using C, C++, and MATLAB. It includes an appendix which provides answers for the exercises.


2. “Numerical Methods for Engineers” by Chapra S C and Canale R P
“Numerical Methods for Engineers” Book Review: This book contains clear explanations and examples to explain the concept of numerical methods for engineering students. This book shows many applications that cover all engineering disciplines. Each part of the book contains a motivation that motivates students to solve problems. It also contains a mathematical background and orientation. The book closes with an epilogue to show important formulas and additional references. Students can learn new skills from this book to apply in their chosen field. The separate appendices in this book are helpful for students to make references.


3. “Numerical Analysis” by Richard L Burden and J Douglas Faires
“Numerical Analysis” Book Review: This book provides a foundation for modern techniques for numerical approximation. This book explains how techniques work and when they work. The author of this book uses reallife problems to explain the concepts. Numerical methods are applied in many areas such as computer science and biology. This book shows how numerical analysis is applied in these areas. Many exercises are available for students to learn numerical analysis. Students preparing for the Actuaries examination can prepare for it using this book as the author has included examination questions in this book.


4. “Numerical Methods for Engineers and Scientists” by Joe D Hoffman and Steven Frankel
“Numerical Methods for Engineers and Scientists” Book Review: Learn about the methodology for constructing individual computer programs in a systematic manner. This book emphasizes on the finite difference approach to solve differential equations. Get accurate solutions to complex engineering problems in this book. Each chapter has an objective and discusses a representative application. It sums up all the tasks that students should be capable of doing after reading this book. This book is suitable for students to use it as a guide or to do reviews.


5. “Elementary Numerical Analysis” by Kendall Atkinson and Weimin Han
“Elementary Numerical Analysis” Book Review: This book contains MATLAB programs to give a clear understanding of numerical analysis. Students can master numerical analysis techniques and scientific computing using this book. Learn about the approximation of problems using simple methods in this text. This book allows you to learn about the construction of algorithms and iteration methods. It has some topics like error analysis and the effects of machine arithmetic.


8. Numerical Methods in Civil Engineering
1. “The Algebraic Eigenvalue Problem” by J H Wilkinson
Book Review: This is the most widely used book in the field of numerical analysis. The book provides a distillation of author’s famous discoveries in the field of computation of matrix eigen values. The book also stresses more on the transmission of knowledge rather than lengthy proofs. This book is very useful to the numerical analysts, students, researchers, engineers and scientists in the field of numerical analysis and who are dealing with algebraic eigen value problem.


2. “An Introduction to Numerical Analysis” by K E Atkinson
“An Introduction to Numerical Analysis” Book Review: The book is fully updated and revised piece of writing along with some new topics and concepts. The topics like optimization, trigonometric interpolation, fast Fourier transform, numerical differentiation, the method of lines, boundary value problems, the conjugate gradient method, and the least squares solutions of systems of linear equations are thoroughly explained. The book also discusses error along with its sources, propagation, and analysis. Moving on, root finding for nonlinear equations, interpolation theory, approximation of functions, numerical integration, numerical methods for ordinary differential equations, linear algebra, numerical solution of systems of linear equations, the matrix eigenvalue problems are featured. The book consists of both solved and unsolved problems.


3. “Matrix Computations” by G E Golub and C F Van Loan
“Matrix Computations” Book Review: The book focuses on mathematical concepts and algorithmic skills necessary for working on numerical software. The chapters of this book are based on matrix multiplication problems and parallel matrix computations, CS decomposition, floating point arithmetic, and modified GramSchmidt process. Some modern methods and techniques like GMRES and QMR are introduced for dealing with unsymmetric linear system problems. The content of the book is uptodate and compact. The book will be useful for the students interested in matrix computations.


4. “Numerical Recipes in C: The Art of Scientific Computing” by W H Press
“Numerical Recipes in C: The Art of Scientific Computing” Book Review: The book is a wellstructured and updated text majorly based on scientific computing. The theoretical and mathematical concepts given in the book are explained from a practical point of view. The topics like linear algebra, interpolation, special functions, random numbers, nonlinear sets of equations, optimization, eigensystems, Fourier methods and wavelets, statistical tests, ODEs and PDEs, integral equations, and inverse theory are described. The updated section of the book covers linear programming, Monte Carlo Markov Chains, spectral and pseudospectral methods for PDEs, and many new statistical distributions, Gaussian mixture models, HMMs, hierarchical clustering, Support Vector Machines. For better understanding of the readers many numerical routines are featured. The book will be beneficial for scientists and engineers working in scientific computing.


5. “Numerical Methods for Scientific and Engineering Computation” by S R K Iyengar and R K Jain
“Numerical Methods for Scientific and Engineering Computation” Book Review: This book provides a detailed overview on numerical methods for scientific and engineering computation. It covers chapters like introduction, focus on the course, goals, computing with matrices and vectors, direct methods of linear systems of equations, direct methods for linear least squares problems, filtering algorithms, data interpolation and data fitting, approximation functions, numerical quadrature, iterative methods for nonlinear systems of equations, eigenvalues, krylov methods for linear system of equations, numerical integration and much more. Each chapter contains theory, equations, numerical and required diagrams.


6. “Numerical Methods for Stochastic Computations: A Spectral Method Approach” by Dongbin Xiu
“Numerical Methods for Stochastic Computations: A Spectral Method Approach” Book Review: The book reflects various numerical methods used in stochastic computations, based on generalized polynomial chaos (gPC). The chapters of this book describe polynomial approximation theory, probability theory, and fundamental theory of gPC methods. The Galerkin and collocation approaches are discussed for dealing with stochastic equations into and highdimensional problems. The methods and techniques featured in this book are explained efficiently with the help of examples. The book concludes with a chapter based on applications of gPC methods in critical areas like inverse problems and data assimilation. This text will be useful for the graduatelevel students seeking an introduction on the numerical methods for stochastic computations as well as the researchers involved in stochastic computations.


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