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- Intriduction: Some Basic Mathematical Models, Direction Fields; Solutions of Some Differential Equations; Classification of Differential Equations
- First Order Differential Equations: Linear Equations;Separable Equations; Modeling with First Order Equations; Differences Between Linear and Nonlinear Equations; Autonomous Equations and Population Dynamics; Exact Equations and Integrating Factors; Numerical Approximations, Euler Methods; The Existence and Uniqueness Theorem; First Order Difference Equations
- Second Order Linear Equations: Homogeneous Equations with Constant Coefficients; Fundamental Solution of Linear Homogeneous Equations; Linear Independence and the Wronskian; Nonhomogeneous Equations; Mechanical and Electrical Vibrations; Forced Vibrations
- Higher Order Linear Equations: General Theory of nth Order Linear Equations; The Methods of Undetermined Coefficients and Variation of Parameters
- Series Solutions of Second Order Linear Equations: Series Solutions of Euler Equations, Legendre Equation, , Chebyshev Equation and Bessel's Equations
- The Laplace Transform: Solution of Initial Value Problems; Differential Equations with Discontinuous
- System of First Order Linear Equations
- Boundary Value Problems
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- Nonlinear Differential Equations and Stability
- Partial Differential Equations and Fourier Series
- Numerical Methods
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- W. E. Boyce and R. C. DiPrima, Elementary Differential Equations and Boundary Value Problems
- F. John, Partial Differential Equations
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