E155A Mathematical and Computational Methods for Engineers
Analytical and numerical methods for solving ordinary differential equations arising in engineering applications. Solution of initial and boundary value problems, series solutions, Laplace transforms, and non-linear equations. Numerical methods for solving ordinary differential equations, accuracy of numerical methods, linear stability theory, finite differences. Introduces MATLAB as a basic tool kit for computations. Problems from various engineering fields. Prerequisite: Math 51 or E154. 5 units
Winter and Spring 2003
First-Order Ordinary Differential Equations
- Direction fields, separation of variables
- Exact equations, integrating factors
- Numerical methods, Euler method
- Accuracy, Runge-Kutta methods, multi-step methods
- Numerical solutions with MATLAB
- Numerical stability
Second-Order Ordinary Differential Equations
- Equations with constant coefficients
- Existence, uniqueness, Wronskian
- Euler-Cauchy equation, change of variables
- Method of undetermined coefficients
- Numerical methods for second-order ODEs and systems
- Variation of parameters
- Power series solution, Frobenius method
- Laplace transforms
- Nonlinear ODEs, Chaos, sensitivity to initial conditions