Page 5 - DMTH504_DIFFERENTIAL_AND_INTEGRAL_EQUATION

CONTENT

Unit 1: Bessel’s Functions 1
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Unit 2: Legendre’s Polynomials 28
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Unit 3: Hermite Polynomials 57
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Unit 4: Laguerre Polynomials 75
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Unit 5: Differential Equations 89
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Unit 6: Existence Theorem for the Solution of the Equation dy dx = f(x, y) 101
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Unit 7: General Properties of Solutions of Linear Differential Equations of Order n 112
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Unit 8: Total Differential Equations, Simultaneous Equations 133
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Unit 9: Adjoint and Self-Adjoint Equations 158
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Unit 10: Green’s Function Method 166
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Unit 11: Sturm–Liouville’s Boundary Value Problems 182
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Unit 12: Sturm Comparison and Separation Theorems 192
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Unit 13: Orthogonality of Solutions 202
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Unit 14: Classification of Partial Differential Equations 215
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Unit 15: Cauchy’s Problem and Characteristics for First Order Equations 223
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Unit 16: Classifications of Integrals of the First Order Partial Differential Equations 233
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Unit 17: Lagrange’s Methods for Solving Partial Differential Equations 244
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Unit 18: Charpit’s Method for Solving Partial Differential Equations 269
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