# 89 Best Books on Differential Equations

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We have compiled a list of the Best Reference Books on Differential Equations, 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 Differential Equations 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 Differential Equations below.

## 7. Numerical Solution of Ordinary and PDE

 1."Time-dependent Partial Differential Equations and Their Numerical Solution (Lectures in Mathematics. ETH Zürich)" by Heinz-Otto Kreiss and Hedwig Ulmer Busenhart “Time-dependent Partial Differential Equations and Their Numerical Solution (Lectures in Mathematics. ETH Zürich)” Book Review: This book serves as a textbook for graduate students. It studies time-dependent partial differential equations and their numerical solution. This study develops the analytic and the numerical theory in parallel. It emphasizes the discretization of boundary conditions. These theoretical results are put into Newtonian and non-Newtonian flows, two-phase flows and geophysical problems. It is useful to the field for applied mathematicians. 2."Handbook of Sinc Numerical Methods" by Frank Stenger “Handbook of Sinc Numerical Methods” Book Review: This book contains several MATLAB programs for approximating almost every type of operation stemming from calculus. It provides new methods for solving ordinary differential equations. This also presents methods for solving partial differential equations and integral equations. This study makes Sinc methods available to users who want to bypass the complete theory. It also covers sufficient theoretical details for readers who do want a full working understanding of numerical analysis. This book comes along with Sinc-Pack programs that are available on the companion CD-ROM. 3."Introduction to Computation and Modeling for Differential Equations" by Lennart Edsberg “Introduction to Computation and Modeling for Differential Equations” Book Review: This book presents the essential principles and applications of problem solving. This problem solving is in the disciplines such as engineering, physics, and chemistry. This book unites the science of solving differential equations with mathematical, numerical, and programming tools. It is done by using the methods involving ordinary differential equations. It includes numerical methods for initial value problems (IVPs), numerical methods for boundary value problems (BVPs). This book provides partial differential equations (PDEs), numerical methods for parabolic, elliptic, and hyperbolic PDEs. 4."Spatial Patterns: Higher Order Models in Physics and Mechanics (Progress in Nonlinear Differential Equations and Their Applications)" by L A Peletier and W C Troy “Spatial Patterns: Higher Order Models in Physics and Mechanics (Progress in Nonlinear Differential Equations and Their Applications)” Book Review: This book presents challenging questions for physicists and mathematicians. It provides an analysis of model equations one hopes to get understanding of the underlying mechanisms. These mechanisms are responsible for the formation and evolution of complex patterns. This book offers the classical model equations have typically been second-order partial differential equations. It discusses the waves on water, pulses in optical fibers, periodic structures in alloys, folds in rock formations, and cloud patterns in the sky. These patterns are popular in the world around us. 5."p-Laplace Equation in the Heisenberg Group: Regularity of Solutions (SpringerBriefs in Mathematics)" by Diego Ricciotti “p-Laplace Equation in the Heisenberg Group: Regularity of Solutions (SpringerBriefs in Mathematics)” Book Review: This book aims on regularity theory for solutions to the p-Laplace equation in the Heisenberg group. It presents elaborate proofs of smoothness for solutions to the non-degenerate equation. This study covers Lipschitz regularity for solutions to the degenerate one. It provides the basic properties of the Heisenberg group, making the coverage satisfactory. This book focuses on the core of the theory and techniques in the field. It also offers detailed proofs to make the work accessible to students at the graduate level. 6."Notes on the Infinity Laplace Equation (SpringerBriefs in Mathematics)" by Peter Lindqvist 7."Ordinary and Partial Differential Equations" by Victor Henner and Tatyana Belozerova “Ordinary and Partial Differential Equations” Book Review: This book covers both ordinary differential equations (ODEs) and partial differential equations (PDEs). It provides a complete and accessible course on ODEs and PDEs using many examples and exercises. This book presents inborn, easy-to-use software. It discusses the important topics in differential equations. This book covers all the topics that form the core of a modern undergraduate or beginning graduate course in differential equations. It also offers topics like integral equations, fourier series, and special functions. 8."Ode and Pde Solutions: Recipes for Solving Constant Coefficient Linear Ordinary and Partial Differential Equations" by Anglin and Steve M

## 8. Finite Difference Methods for Partial Differential Equations

 1."Scientific Computing and Differential Equations: An Introduction to Numerical Methods" by Gene H Golub and James M Ortega “Scientific Computing and Differential Equations: An Introduction to Numerical Methods” Book Review: This book provides an Introduction to Numerical Methods. It shows the significance of a machine solving differential equations, which constitutes a significant portion of what has come to be called theoretical computing. This book will be useful for upper undergraduate courses in mathematics, electrical engineering, and computer science. 2."Fundamentals of Grid Generation" by P Knupp and S Steinberg “Fundamentals of Grid Generation” Book Review: This book discusses applied mathematics, mechanical engineering and aerospace engineering for organized grid generation. It includes various topics such as planar, surface, generation of 3-D grids, numerical techniques and adaptability of solutions. The finite volume approach to discretization of hosted equations and the transformation of differential operators into general coordination systems are also explained in this book. 3."The Finite Difference Method in Partial Differential Equations" by A R Mitchell and D F Griffiths “The Finite Difference Method in Partial Differential Equations” Book Review: This book discusses the division of operators for parabolic and hyperbolic equations to include Richtmyer and Strang form splittings. It includes examples concerning the treatment of singularities, free and moving boundary problems in elliptic equations. The book also includes new improvements in the dynamics of computational fluids. This book will be beneficial for upper undergraduate courses in mathematics, electrical engineering, and computer science. 4."Finite Difference Schemes and PDEs" by John C Strikwerda “Finite Difference Schemes and PDEs” Book Review: This book discusses the division of operators for parabolic and hyperbolic equations to include Richtmyer and Strang form splittings. It includes examples concerning the treatment of singularities, free and moving boundary problems in elliptic equations. The book also includes new improvements in the dynamics of computational fluids. This book will be beneficial for upper undergraduate courses in mathematics, electrical engineering, and computer science.

## 9. Complex Variables and Partial Differential Equations 