Book Details

PARTIAL DIFFERENTIAL EQUATIONS AND ITS APPLICATIONS

PARTIAL DIFFERENTIAL EQUATIONS AND ITS APPLICATIONS

Published by uLektz

Course Code:ULZ0023

Author:uLektz

University: General for All University

Regulation:2016

Categories:Engineering Mathematics

Format : ico_bookePUB3 (DRM Protected)

Type :eBook

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Topics
1. Introduction- Homogeneous function-Euler’s theorem
2. Total derivative-Chain rule
3. Generalized Mean value theorem for single variable (without proof)
4. Taylor’s and Mc Laurent’s series expansion of functions of two variables- Functional dependence
5. Jacobian
6. Applications: Maxima and Minima of functions of two variables without constraints and Lagrange’s method (with constraints)
7. Limits and Continuity
8. Lagrange‟s method of undetermined multipliers.
9. FIRST ORDER PARTIAL DIFFERENTIAL EQUATIONS: Formation of partial differential equations by elimination of arbitrary constants and arbitrary functions
10. Solutions of first order linear (Lagrange) equation and nonlinear (standard types) equations
11. HIGHER ORDER PARTIAL DIFFERENTIAL EQUATIONS: Solutions of Linear Partial differential equations with constant coefficients.
12. RHS term of the type eax + by,sin(ax + by), cos(ax + by), xm yn - Classification of second order partial differential equations
13. APPLICATIONS: Method of separation of Variables
14. Solution of One dimensional Wave equation
15. Solution of One dimensional Heat equation, One dimensional heat equation with the initial and boundary conditions
16. Two-dimensional Laplace equation
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