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I. Inroduction
1.3 Classifications of differential equations
1.2 Solutions of some differential equations
2.8 The existence and uniqueness theorem (Picard iterates)
II. First Order Equations
1.1 Direction fields
2.2 Separable equations
2.5 Population dynamics
2.2 Homogenous equations. The method of substitution
2.6 Exact equations and integrating factors
2.1 Linear equations
2.4 Differences between linear and nonlinear equations
2.7 Numerical approximations: Euler's method*
(* sketch only)
III. Second Order Linear
Equations
3.1 Homogeneous equations with constant coefficients
3.2 Fundamental solutions of linear homogeneous equations
3.3 Linear independence and the Wronskian
3.4 Complex roots and the characteristic equation
3.5 Repeated roots; reduction of order
3.6 Nonhomogeneous equations
3.6 The method of undetermined coefficients
3.7 Variation of parameters
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V. Series Solutions of Differential
Equations
5.1 Review of power series
5.2 Series Solution near an OP
5.3 Series Solution near an OP
5.4 Regular singular points
5.5 Euler equation
5.6 Series Solution near a RSP*
5.7 Series Solution near a RSP*
VI. The Laplace Transforms
6.1 Definition of the Laplace transform
6.2 Solution of initial value problems
6.3 Step functions
6.4 Differential equations with discontinuous forcing functions
6.5 Impulse functions
6.6 The convolution integral
VII. Systems of Linear
Equations
7.4 Basic theory of systems of first order linear equations
7.5 Homogeneous linear systems with constant coefficients
7.6 Complex eigenvalues
7.7 Repeated eigenvalues
7.8 Fundamental matrices
7.9 Nonhomogeneous linear systems
VIII. Partial Differential
Equations and Fourier Series
Separation of variables. The Heat equation
Separation of variables. The Wave equation
Separation of variables. The Laplace equation |