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Full Description
Differential equations occur in connection with numerous natural phenomena and much of our understanding of nature comes from our ability to solve such equations. Taking note of importance of differential equations, this text is designed to give a simple, lucid, rigorous and comprehensive account of the subject.
This book includes almost all the methods for finding solution of ordinary differential equations and partial differential equations with applications. The text also contains the topics of Laplace transforms and Fourier transforms and their applications in finding solutions of differential equations.
Divided in three sections the book deals with the following:
Section A deals with ordinary differential equations
Section B is devoted to study of partial differential equations
Section C gives introduction to Laplace and Fourier transforms, Fourier series and their applications in finding solutions of differential equations
Contents
SECTION A: Ordinary Differential Equations
1. Some Basic Concepts
2. Solution of Differential Equations with First Order and First Degree
3. Exact Differential Equations
4. Bernoulli's Linear and Differential Equations
5. First Order Higher Degree Differential Equations
6. Singular Solution and Clairaut's Differential Equations
7. Orthogonal Trajectories
8. Homogeneous Linear Differential Equations
9. Non-homogeneous Linear Differential Equations
10. Method of Variation of Parameters and Undetermined Coefficients
SECTION B: Partial Differential Equations
1. Introduction to Partial Differential Equations
2. Solution of Linear Partial Differential Equations of the First Order
3. Nonlinear Partial Differential Equations of the First Order
4. General Methods of Solution of Nonlinear Partial Differential Equations of the First Order
5. Homogeneous Linear Partial Differential Equations with Constant Coefficients
6. Non-Homogeneous Linear Partial Differential Equations with Constant Coefficients
7. Partial Differential Equations Reducible to Equations with Constant Coefficients
8. Classification of Linear Partial Differential Equations of the Second Order
9. Monge's Methods
10. Applications of Partial Differential Equations
SECTION C: Laplace Transforms, Fourier Transforms and Fourier Series
1. Introduction to Laplace Transforms
2. Laplace Transforms of Derivatives and Integrals
3. First and Second Shifting Theorems
4. Differentiation and Integration of Laplace Transforms
5. Convolution Theorem and Laplace Transform of Periodic Functions
6. Solution of Partial Differential Equations using Laplace Transforms
7. Introduction to Fourier Series
8. Fourier Transforms
9. Solution of Differential Equations using Fourier Transforms
Bibliography
Index
