"SYLLABUS- ADVANCED DIFFERENTIAL EQUATIONS, Unit-I Ordinary Differential Equations: Qualitative properties of solution: Oscillation, Wronskian, Sturm separation and comparison theorems. Unit-II Ordinary points, Regular singular points, Frobenius series solution. Unit-III Gauss hyper geometric equation, the point at infinity, Gamma functions, Hermite polynomials. Unit-IV Partial Differential Equations: Origin of first order partial differential equations, Linear equations of the first order, Integral surfaces passing through a given curve, Surface orthogonal to a given system of surface, Non-linear partial differential equations of the first order, Charpits method, Special type of first order equations, Jacobi method. Origin of second order partial differential equation, Linear partial differential equations with constant coefficients, Equations with variable coefficients. Unit-V Problems of Laplace, wave and diffusion equations by the method of separation of variables, Reduction of second order partial differential equation into its canonical form. Non-linear equation of second order. "
Author(s): R.K. Gupta, J.N. Sharma
Publisher: Krishna Prakashan Media P. Ltd.
Year: 2019
Language: English
Pages: 784
Advanced Differential Equations
Dedication
Preface to the Revised Edition
Syllabus
Brief Contents
Detailed Contents 1
Detailed Contents 2
Detailed Contents 3
Detailed Contents 4
Detailed Contents 5
Detailed Contents 6
Unit-I
Chapter 1: Ordinary Differential Equations and Wronskian
Chapter 2: Qualitative Properties of Solutions
Unit-II
Chapter 3: Integration in Series
Unit-III
Chapter 4: Beta and Gamma Functions
Chapter 5: Gauss Hypergeometric Equation
Chapter 6: Hermite Polynomials
Unit-IV
Chapter 7: Partial Differential Equations of the First Order
Chapter 8: Non-Linear Partial Differential Equations of First Order
Chapter 9: Partial Differential Equations of the Second Order with Variable Coefficients
Chapter 10: Linear Partial Differential Equations with Constant Coefficients
Unit-V
Chapter 11: Reduction of Second Order Partial Differential Equation into Canonical Forms
Chapter 12: Wave Equations
Chapter 13: Heat and Diffusion Equations
Chapter 14: Laplace Equations
Index 1
Index 2
Index 3
Index 4
