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Topics ·
Step
functions. DE with discontinuous forcing. The convolution integral. ·
Homogeneous
linear systems with constant coefficients. ·
Ch1: Introduction. Basics. Direction fields. Classification of DE. · Ch2: First Order DE. Linear eqns.Separable eqns. Exact eqns. and
integrating factors. The existence and
uniqueness theorem. ·
Ch3: Second Order Linear Equations. Homogeneous
constant-coefficient eqns. ·
Fundamental
solutions. The Wronskian. Complex roots of characteristic eqn. ·
Repeated
roots. Reduction of order. Nonhomogeneous eqns. Method of undetermined cefficients. ·
Variation
of parameters. ·
Ch4: Higher Order Linear Equations. General theory.
Homogeneous constant-coefficient eqns. The method of undetermined
coefficients and variation of parameters revisited. ·
Ch5: Series Solutions of Second Order Linear Equations. Ordinary points. Series solutions about an ordinary point. Regular singular points. Euler's eqn. Series solutions
about a regular singular point. Bessel's eqn. ·
Ch6: The Laplace Transform. Definitions.
Solns of initial value problems. ·
Ch7: Systems of First Order Linear
DE. Introduction.
Basic theory. Complex eigenvalues. Fundamental matrices. Repeated eigenvalues. Nonhomogeneous linear systems. ·
Ch10: Partial Differential Equations and Fourier Series. Two point boundary value problems. Fourier series. ·
The convergence theorem. Separation of variables.
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