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.
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).
Student Solutions Manual, A Modern Introduction to Differential Equations
Student Solutions Manual, A Modern Introduction to Differential Equations
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.
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.
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.
