← GATE Mathematics guide GATE Mathematics · Section 9

Partial Differential Equations

First- and second-order PDEs, separation of variables and transform methods — directly covered.

Books that cover Section 9

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M.A. & M.Sc. Mathematics · Dr. H.K. Pathak

Covers: The full section — method of characteristics, classification & canonical forms, separation of variables for Laplace/heat/wave, d’Alembert’s formula and Laplace/Fourier transform methods.

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Full syllabus — Section 9

Method of characteristics for first-order linear and quasilinear PDEs
Second-order PDEs in two variables: classification and canonical forms
Separation of variables for the Laplace equation (Cartesian & polar); maximum principle
Heat and wave equations in one space variable; wave equation Cauchy problem & d’Alembert formula; domains of dependence & influence; heat equation Cauchy problem; Laplace & Fourier transform methods

Section 8: Numerical Analysis Section 10: Topology