Differential Equations

1.	Differential Equations of the Form  dx/dt = f(t)
  1.1   The problem
  1.2   Initial value problems
  1.3   Definite integrals
  1.4   Special functions defined by definite integrals

2.	First Order Differential Equations
  2.1   Linear first order equations
             2.1.1   Constant coefficient equations
             2.1.2   General linear first order equations
             2.1.3   Solution using Mathematica
  2.2   Separable equations
             2.2.1   Separable equations
             2.2.2   Solution using Mathematica
  2.3   Change of Variable
  2.4   Qualitative Behavior of Solutions to Differential Equations
  2.5   General first order equations
             2.5.1   General First Order Equations
             2.5.2   Numerical solution of differential equations
  2.6   Nonlinear difference equations

3.	Second Order Linear Differential Equation
  3.1    Linear constant coefficient equations
  3.2    Equal roots
  3.3    Complex roots
  3.4    Electric circuits
  3.5    Euler Equations
  3.6    Homogeneous Linear Equations
  3.7    Second Solution Formula
  3.8    Inhomogeneous Linear Equations
  3.9    Undetermined coefficients
  3.11   Solving linear second order equations with mathematical software

4.	Laplace Transforms
  4.1   Laplace Transforms
  4.2   Solving Differential Equations with Laplace Transforms
  4.3   Laplace transforms in Mathematica
  4.4   Piecewise defined functions
              4.4.2   Piecewise defined functions in Mathematica

5.	Systems of Differential Equations
  5.2   Solving systems with mathematical software
  5.3   A mass-spring example

6.	Power Series Solutions of Differential Equations
  6.1   Power series
  6.2   Graphing the power series obtained by solving Airy's equation
  6.3   Graphing the power series obtained by solving Legendre's equation of order 2

7.	Numerical Solution of Differential Equations
  7.1   Euler's method for the numerical solution of differential equations
  7.2   Euler's method for systems of differential equations

8.   An Introduction to Mathematica

9.   An Introduction to MATLAB

  Mathematics 216 Directory