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SMA 432: Partial Differential Equations

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Summary

Contents:

Purpose of the Module 5
Module Learning Outcomes 5
Course Description 5
LESSON 1 6
CONCEPTS OF PARTIAL DIFFERENTIAL EQUATIONS 6
LESSON 2 12
Formation of Partial Differential Equations 12
LESSON THREE 18
SOLUTION OF FIRST ORDER QUASILINEAR PDEs BY THE LAGRANGE’S METHOD OF TYPE ONE AND TWO 18
LESSON FOUR 23
SOLUTION OF FIRST ORDER QUASILINEAR PDEs BY THE LAGRANGE’S METHOD OF TYPES THREE AND FOUR 23
LESSON FIVE 28
INTEGRAL SURFACES PASSING THROUGH GIVEN CURVES AND SURFACES ORTHOGONAL TO A GIVEN SYSTEM OF SURFACES 28
LESSON SIX 35
THE METHOD OF CANONICAL FORMS 35
LESSON SEVEN 40
THE METHOD OF SEPARATION OF VARIABLES 40
LESSON EIGHT 44
Non-linear Partial Differential Equations of Order One 44
LESSON NINE 53
NON-LINEAR PARTIAL DIFFERENTIAL EQUATIONS OF TYPES THREE AND FOUR 53
LESSON TEN 60
SOLUTION OF NON-LINEAR PDEs USING TRANSFORMATIONS 60
LESSON ELEVEN 66
CHARPIT’S METHOD OF SOLVING FIRST ORDER NON-LINEAR PARTIAL DIFFERENTIAL EQUATIONS 66
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