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Introduction to Partial Differential Equations

This textbook is designed for a one year course covering the fundamentals of partial differential equations, geared towards advanced undergraduates and beginning graduate students in mathematics, science, engineering, and elsewhere. The exposition carefully balances solution techniques, mathematical rigor, and significant applications, all illustrated by numerous examples. Extensive exercise sets appear at the end of almost every subsection, and include straightforward computational problems to develop and reinforce new techniques and results, details on theoretical developments and proofs, challenging projects both computational and conceptual, and supplementary material that motivates the student to delve further into the subject. No previous experience with the subject of partial differential equations or Fourier theory is assumed, the main prerequisites being undergraduate calculus, both one- and multi-variable, ordinary differential equations, and basic linear algebra. While the classical topics of separation of variables, Fourier analysis, boundary value problems, Green's functions, and special functions continue to form the core of an introductory course, the inclusion of nonlinear equations, shock wave dynamics, symmetry and similarity, the Maximum Principle, financial models, dispersion and solutions, Huygens' Principle, quantum mechanical systems, and more make this text well attuned to recent developments and trends in this active field of contemporary research. Numerical approximation schemes are an important component of any introductory course, and the text covers the two most basic approaches: finite differences and finite elements.

While the classical topics of separation of variables, Fourier analysis, boundary value problems, Green's functions, and special functions continue to form the core of an introductory course, the inclusion of nonlinear equations, shock wave ...

An introduction to nonlinear partial differential equations

Uses an analytical and techniques-oriented approach to present a concise introduction to the subject focusing on time-evolution problems. Emphasizes hyperbolic and parabolic problems and includes a range of applications--chemistry, porous media, biological problems, traffic flow, reactors, heat transfer and detonation. Packed with exercises, examples and illustrations.

Flexible enough to enable instructors to adapt portions of the book to their own curricula, An Introduction to Nonlinear Partial Differential Equations works effectively in first courses on nonlinear PDEs, second course on PDEs, and in ...

Introduction to Differential Equations Using Sage

David Joyner and Marshall Hampton’s lucid textbook explains differential equations using the free and open-source mathematical software Sage. Since its release in 2005, Sage has acquired a substantial following among mathematicians, but its first user was Joyner, who is credited with helping famed mathematician William Stein turn the program into a usable and popular choice. Introduction to Differential Equations Using Sage extends Stein's work by creating a classroom tool that allows both differential equations and Sage to be taught concurrently. It’s a creative and forward-thinking approach to math instruction. Topics include: • First-Order Differential Equations • Incorporation of Newtonian Mechanics• Second-Order Differential Equations• The Annihilator Method• Using Linear Algebra with Differential Equations• Nonlinear Systems• Partial Differential Equations• Romeo and Juliet

Introduction to Differential Equations Using Sage extends Stein's work by creating a classroom tool that allows both differential equations and Sage to be taught concurrently.

Introduction to Numerical Methods for Time Dependent Differential Equations

Introduces both the fundamentals of time dependent differential equations and their numerical solutions Introduction to Numerical Methods for Time Dependent Differential Equations delves into the underlying mathematical theory needed to solve time dependent differential equations numerically. Written as a self-contained introduction, the book is divided into two parts to emphasize both ordinary differential equations (ODEs) and partial differential equations (PDEs). Beginning with ODEs and their approximations, the authors provide a crucial presentation of fundamental notions, such as the theory of scalar equations, finite difference approximations, and the Explicit Euler method. Next, a discussion on higher order approximations, implicit methods, multistep methods, Fourier interpolation, PDEs in one space dimension as well as their related systems is provided. Introduction to Numerical Methods for Time Dependent Differential Equations features: A step-by-step discussion of the procedures needed to prove the stability of difference approximations Multiple exercises throughout with select answers, providing readers with a practical guide to understanding the approximations of differential equations A simplified approach in a one space dimension Analytical theory for difference approximations that is particularly useful to clarify procedures Introduction to Numerical Methods for Time Dependent Differential Equations is an excellent textbook for upper-undergraduate courses in applied mathematics, engineering, and physics as well as a useful reference for physical scientists, engineers, numerical analysts, and mathematical modelers who use numerical experiments to test designs or predict and investigate phenomena from many disciplines.

Written as a self-contained introduction, the book is divided into two parts to emphasize both ordinary differential equations (ODEs) and partial differential equations (PDEs).

An Introduction to Differential Equations and Their Applications

This introductory text explores 1st- and 2nd-order differential equations, series solutions, the Laplace transform, difference equations, much more. Numerous figures, problems with solutions, notes. 1994 edition. Includes 268 figures and 23 tables.

This introductory text explores 1st- and 2nd-order differential equations, series solutions, the Laplace transform, difference equations, much more.

Introduction to Differential Equations

This book provides students with solid knowledge of the basic principles of differential equations and a clear understanding of the various ways of obtaining their solutions by applying suitable methods. It is primarily intended to serve as a textbook for undergraduate students of mathematics. It will also be useful for undergraduate engineering students of all disciplines as part of their course in engineering mathematics. No book on differential equations is complete without a treatment of special functions and special equations. A chapter in this book has been devoted to the detailed study of special functions such as the gamma function, beta function, hypergeometric function, and Bessel function, as well as special equations such as the Legendre equation, Chebyshev equation, Hermite equation, and Laguerre equation. The general properties of various orthogonal polynomials such as Legendre, Chebyshev, Hermite, and Laguerre have also been covered. A large number of solved examples as well as exercises at the end of many chapter sections help to comprehend as well as to strengthen the grasp of the underlying concepts and principles of the subject. The answers to all the exercises are provided at the end of the book.

This book provides students with solid knowledge of the basic principles of differential equations and a clear understanding of the various ways of obtaining their solutions by applying suitable methods.

Introduction to Partial Differential Equations

From Fourier Series to Boundary-Value Problems

The self-contained treatment covers Fourier series, orthogonal systems, Fourier and Laplace transforms, Bessel functions, and partial differential equations of the first and second orders. 266 exercises with solutions. 1970 edition.

The self-contained treatment covers Fourier series, orthogonal systems, Fourier and Laplace transforms, Bessel functions, and partial differential equations of the first and second orders. 266 exercises with solutions. 1970 edition.

An introduction to differential equations, with difference equations, Fourier series and partial differential equations