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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

Introduction to Computation and Modeling for Differential Equations

Uses mathematical, numerical, and programming tools to solve differential equations for physical phenomena and engineering problems Introduction to Computation and Modeling for Differential Equations, Second Edition features the essential principles and applications of problem solving across disciplines such as engineering, physics, and chemistry. The Second Edition integrates the science of solving differential equations with mathematical, numerical, and programming tools, specifically with methods involving ordinary differential equations; numerical methods for initial value problems (IVPs); numerical methods for boundary value problems (BVPs); partial differential equations (PDEs); numerical methods for parabolic, elliptic, and hyperbolic PDEs; mathematical modeling with differential equations; numerical solutions; and finite difference and finite element methods. The author features a unique “Five-M” approach: Modeling, Mathematics, Methods, MATLAB®, and Multiphysics, which facilitates a thorough understanding of how models are created and preprocessed mathematically with scaling, classification, and approximation and also demonstrates how a problem is solved numerically using the appropriate mathematical methods. With numerous real-world examples to aid in the visualization of the solutions, Introduction to Computation and Modeling for Differential Equations, Second Edition includes: New sections on topics including variational formulation, the finite element method, examples of discretization, ansatz methods such as Galerkin’s method for BVPs, parabolic and elliptic PDEs, and finite volume methods Numerous practical examples with applications in mechanics, fluid dynamics, solid mechanics, chemical engineering, heat conduction, electromagnetic field theory, and control theory, some of which are solved with computer programs MATLAB and COMSOL Multiphysics® Additional exercises that introduce new methods, projects, and problems to further illustrate possible applications A related website with select solutions to the exercises, as well as the MATLAB data sets for ordinary differential equations (ODEs) and PDEs Introduction to Computation and Modeling for Differential Equations, Second Edition is a useful textbook for upper-undergraduate and graduate-level courses in scientific computing, differential equations, ordinary differential equations, partial differential equations, and numerical methods. The book is also an excellent self-study guide for mathematics, science, computer science, physics, and engineering students, as well as an excellent reference for practitioners and consultants who use differential equations and numerical methods in everyday situations.

The book is also an excellent self-study guide for mathematics, science, computer science, physics, and engineering students, as well as an excellent reference for practitioners and consultants who use differential equations and numerical ...

Introduction to Partial Differential Equations with Applications

This text explores the essentials of partial differential equations as applied to engineering and the physical sciences. Discusses ordinary differential equations, integral curves and surfaces of vector fields, the Cauchy-Kovalevsky theory, more. Problems and answers.

This text explores the essentials of partial differential equations as applied to engineering and the physical sciences.

An Introduction to Linear Ordinary Differential Equations Using the Impulsive Response Method and Factorization

This book presents a method for solving linear ordinary differential equations based on the factorization of the differential operator. The approach for the case of constant coefficients is elementary, and only requires a basic knowledge of calculus and linear algebra. In particular, the book avoids the use of distribution theory, as well as the other more advanced approaches: Laplace transform, linear systems, the general theory of linear equations with variable coefficients and variation of parameters. The case of variable coefficients is addressed using Mammana’s result for the factorization of a real linear ordinary differential operator into a product of first-order (complex) factors, as well as a recent generalization of this result to the case of complex-valued coefficients.

This book presents a method for solving linear ordinary differential equations based on the factorization of the differential operator.

Introduction to Ordinary Differential Equations, Student Solutions Manual

The Fourth Edition of the best-selling text on the basic concepts, theory, methods, and applications of ordinary differential equations retains the clear, detailed style of the first three editions. Includes new material on matrix methods, numerical methods, the Laplace transform, and an appendix on polynomial equations. Stresses fundamental methods, and features traditional applications and brief introductions to the underlying theory.

From first-order equations and higher-order linear differentials to constant coefficients, series solutions, systems, approximations, and more, this solutions guide clarifies increasingly complex calculus with practical, accessible ...