**Best Reference Books on Mathematical Methods**, which are used by students of top universities, and colleges. This will help you choose the right book depending on if you are a beginner or an expert. Here is the complete list of

**Mathematical Methods Books**with their authors, publishers, and an unbiased review of them as well as links to the Amazon website to directly purchase them. If permissible, you can also download the free PDF books on Mathematical Methods below.

- Mathematical Methods
- Mathematical Methods in Engineering
- Mathematical Methods of Materials Engineering

## 1. Mathematical Methods

1."Mathematical Methods" by G Shanker Rao
“Mathematical Method” Book Review: This book provides an overview of all mathematical methods used in different fields. First, the book starts with the basics of matrices, eigenvalues and eigenvectors of a matrix, real and complex matrices, quadratic forms, solution of algebraic and transcendental equations. These topics are then used to explain interpolation, curve fitting, numerical differentiation and integration, numerical solution of Ordinary Differential Equations, Fourier series, Fourier integral transform, Z-transform, and Partial Differential Equations and its applications. Numerous solved examples and exercise sets are also included. This book is designed for students of science and engineering.
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2."Fundamental Methods of Mathematical Economics" by Chiang and Wainwright
“Fundamental Methods of Mathematical Economics” Book Review: This book deals with the basic concepts and methods involved in mathematical economics. Static analysis, comparative statics, and dynamic analysis are discussed in great detail. Applications of the theory presented are also discussed vividly using numerous examples and illustrations. Exercise sets are also provided for a better understanding of the subject.
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3."Mathematical Methods in the Physical Sciences" by Mary L Boas
“Mathematical Methods in the Physical Sciences” Book Review: This book elaborates the essential areas of mathematical physics encountered in advanced courses of physical sciences, with particular emphasis on mathematical methods. The book extensively covers DE, multiple integrals, intuition and computational abilities. Simple applications of such methods are also described. This book is intended for students who have had a two-semester or three-semester introductory calculus course.
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4."Mathematical Methods for Physicists" by Arfken
“Mathematical Methods for Physicists” Book Review: This book presents the mathematical relations and their proofs, crucial for the study of physics and its related fields. The text balances the explanation, theorems, proofs and examples in a lucid manner. The book adopts a problem-solving approach to explain theorems with applications. The exercise set provided has problems of varying levels of difficulty. This book is suitable for students, researchers, scientists, and professionals.
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5."Mathematical Methods for Engineers and Physicists" by A K Mukhopadhyay
“Mathematical Methods for Engineers and Physicists” Book Review: The book introduces the various application-oriented areas of mathematics in technology and general science. It deals with different aspects of differential equations as an effective tool for modeling of physical and engineering systems. Spanning over 17 chapters, the book covers numerical methods for solving differential equations as well as the solution methods to partial differential equations. The theory of functions of complex variables and the variational calculus are discussed along with their applications in engineering and physical systems. Extensive coverage of methods of solving integral equations, Laplace transform and its implementation while solving linear and nonlinear differential equations, Fourier series, Fourier transform, and Z-transform are provided. Subsequent chapters deal with Probability theory, statistics, and solutions of special differential equations viz. the Bessel, Legendre, Hermite, Leguerre and Tschebyscheff. Students studying in B.E., B.Tech, AMIETE and AMIE courses as well as B.Sc.(Hons.) and M.Sc. students of physics and mathematics can refer to this book.
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6."Mathematical Methods" by Potter M C
“Mathematical Methods” Book Review: This book presents a comprehensive treatment of the mathematical concepts, tools, and techniques required in engineering and physical sciences. Theory is explained using a number of physical science and engineering applications and examples. Prerequisite knowledge of differential equations is required. The text is intended for first and second semester courses in applied mathematics.
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7."Mathematical Methods in the Physical Sciences" by Mary L Boas
“Mathematical Methods in the Physical Sciences” Book Review: This book elaborates the essential areas of mathematical physics encountered in advanced courses of physical sciences, with particular emphasis on mathematical methods. The book extensively covers DE, multiple integrals, intuition and computational abilities. Simple applications of such methods are also described. This book is intended for students who have had a two-semester or three-semester introductory calculus course.
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8."Mathematical Methods In Engineering" by J A Tenreiro Machado and D Baleanu
“Mathematical Methods In Engineering” Book Review: The book is mainly designed for students in the prior semesters of engineering and study maths as a subject. It is very helpful as it contains some of the contributions that have been carefully selected and peer-reviewed, which were presented at the International Symposium MME06 Mathematical Methods in Engineering. The book is very well divided into chapters and also follows a logical way to link the chapters. It also tries to give a compilation of formulas at the end of every chapter which is of great help for the students. The book covers topics like fractional mathematics boundary value problems, applications of wavelets, neutrices and generalized functions, dynamical systems and control.
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9."Scattering and Biomedical Engineering" by Dimitrios I Fotiadis and Christos Massalas
“Scattering and Biomedical Engineering” Book Review: The book is mainly designed for the students pursuing engineering. It gives the reader the knowledge for various topics viz. modeling and biomedical engineering, applied mathematics and scattering theory. It also extensively uses charts and tables wherever required. The book uses a very scientific language which is very frequently used in the real industry. It also provides problem statements after the chapters and provides step-by-step solutions for the same. The part covering modelling and biomedical engineering uses pictorial representation so the reader can understand the actual things being explained in the theory.
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10."Advanced Mathematical Methods for Engineering and Science Students" by P M Radmore and G Stephenson
“Advanced Mathematical Methods for Engineering and Science Students” Book Review: The book is mainly designed for students pursuing their engineering. It mainly covers the fundamentals of mathematics and helps the reader to build a solid foundation in numerous topics. The approach is quite simple and direct which focuses on the structure first and then application for the same. The book is self sufficient with theory, solved examples, unsolved examples and solutions to all of them. It can also be used as a reference book by the undergraduates in physics, chemistry and theoretical biology. It also uses a lot of tables and charts for the better understanding of the readers.
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11."Mathematical Methods For Physics And Engineering" by Riley
“Mathematical Methods For Physics And Engineering” Book Review: The book is mainly designed for students pursuing engineering and the faculty of undergraduate colleges. This is the third edition of the book and has stand alone chapters and gives systematic explanation of each and every question. It also includes a lot of theory about the chapters and also gives the step-by step explanation of every question. It contains over 800 exercises on all the topics. It uses a lot of charts and takes for the better understanding of the readers.
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12."Mathematical Methods of Science and Engineering: Aided with MATLAB" by Kanti Bhushan Datta
“Mathematical Methods of Science and Engineering: Aided with MATLAB ” Book Review: The book is mainly designed for students of higher education and students of graduation can be used as a reference book. It includes topics like modeling any physical system, either in science or engineering, and needs a thorough and strong understanding of differential equations. The book is finely divided into chapters which includes a lot of theory and solution to the problem questions. It includes many topics like eigenvalues, eigen numbers, interpolation, roots of equations, integrations, ordinary and partial equations and many more.
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13."Mathematical Methods in Scattering Theory And Biomedical Engineering" by Christos Massalas and Dimitrios I Fotiadis
“Mathematical Methods in Scattering Theory And Biomedical Engineering” Book Review: The book is mainly designed for students of higher education and people who are inclined towards mathematics. The volume comprises case studies of very famous and well known people. It focuses on very famous topics in biomedical technology and scattering theory. It also discusses the real time problems which are faced in the industry. The chapters are backed with the problem statements and also provide solutions to them. It uses tables and charts for better understanding. It also provides a list of formulas used in the chapter at the end.
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14."ADVANCED MATHEMATICAL METHODS IN SCIENCE AND ENGINEERING" by S I Hayek
“ADVANCED MATHEMATICAL METHODS IN SCIENCE AND ENGINEERING” Book Review: The book is mainly designed for students in engineering but can also be used as a reference book by the faculties of mathematics. It is very well distributed in different chapters. The book mainly focuses on the problem solving part and hence provides a lot of solved examples and gives a detailed solution to them. It includes numerous unsolved examples at the end of every chapter and provides solutions to them too. Chapters that cover the edges of value problems contain derivations of the differential equations in various fields of applied physics and engineering, such as wave mechanics, acoustics, heat flow in solids, diffusion of liquids and gases, and fluid flow. It showcases the best method to apply mathematical techniques to the physical world.
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15."Mathematical Methods in Physical Sciences" by M L Boas | |

1."Rock Mechanics and the Design of Structures in Rocks" by L Obert and W I Duvall | |

## 2. Mathematical Methods of Materials Engineering

1."Mathematical Methods for Physics and Engineering: a Comprehensive Guide" by K F Riley
Book Review: This book is useful for the subjects of physical sciences and mathematics at the undergraduate levels. The book contains very good description of all the topics and also has many worked examples and exercises. The book also contains many applications related to complex variables and quantum operators. Information on statistics and numerical integration has also been added in the book. Most of the exercise problems in the book have hints and solutions which some others do not have hints and answers. Quantum operators and applications of complex variables are also discussed. The book also provides systematic tabulations related to statistics and numerical integration. Numerous examples and exercises are included out of which half of them are solved or hints have been provided. Undergraduate students and teachers can refer to this book. | |

2."Numerical Methods in Science and Engineering" by Rajasekaran S
“Numerical Methods in Science and Engineering” Book Review: A large number of numerical concepts and applications regarding science and engineering are covered. It is prescribed to students mainly. Strategies for solving large scale equations such as large-scale Eigen-value problems and non-linear algebraic equations are discussed. Interpolation and numerical integration techniques are emphasised. Partial differential equations are described in detail. Readers can also find several computer programs in Basic, FORTRAN and C throughout the text.
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3."Mathematical Methods for Physics and Engineering: A Comprehensive Guide" by K F Riley and M P Hobson
“Mathematical Methods for Physics and Engineering: A Comprehensive Guide” Book Review: The book covers various mathematical concepts of physical sciences. It is prescribed to undergraduate students. Special functions of physical science, complex variables and quantum operators are discussed in the text. Statistics and numerical integration are also presented. Readers can find a plethora of worked out problems and unsolved problems for practice in the text.
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4."Principle of Mathematical Analysis" by Walter Rudin
“Principle of Mathematical Analysis” Book Review: This book explains the fundamentals of mathematical analysis. Major chapters included are real number systems, development of convergence, continuity, differentiation and integration. A brand-new section is added on the gamma function. Multiple exercises are added for students to get the best out of the book. This book is suitable for undergraduate or first year graduate students.
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5."Mathematical Analysis" by T M Apostol
“Mathematical Analysis” Book Review: This book provides Advanced topics on real and complex function theory. Main chapters included are real and complex number systems, set theory, limits and continuity. Other topics mentioned are Derivatives, functions of bounded variation, infinite products, sequences of functions, Riemann-stieltjes integral. All the topics and theorems are described in detail. Numerous problems and their respective solutions are provided for students’ practice. This book is useful for students studying graduate level engineering or advanced level mathematics.
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6."Foundations of Mathematical Analysis" by Richard Johnsonbaugh
“Foundations of Mathematical Analysis” Book Review: This book discusses the foundation of mathematical Analysis. Main chapters covered are infinite series, limits of real valued functions, metric spaces, differential calculus of the real line. Other topics mentioned are sequences and series of functions, transcendental functions, inner product spaces and Fourier series. over 750 exercises are added in this book for students’ practice. It also includes 34 figures to explain methods and equations easily. This book is useful for graduate engineering or applied mathematics students.
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