MTE 204 - Numerical Methods

Errors

• Error Definitions
• Stopping Criterion
• Types of Errors
• Control of Numerical Errors

Roots of Equations

• Graphical Methods (Roots)
• Bracketing Method
• Fixed point iteration
• Newton-Raphson Method
• Secant Method

Systems of Linear Equations

• Systems of Linear Equations

• Graphical Method (Systems)

• Cramer’s Rule

  • Determinant

• Gaussian Elimination

  • Round-off Error for Gaussian Elimination

• Pivoting

• Scaling

• Gauss-Seidel

  • Convergence Criterion (Diagonal Dominant)
  • Gauss-Seidel with Relaxation

Curve Fitting

• Least Squares Regression

• Goodness of Fit

• Least Squares Regression for Nonlinear Equations

• Polynomial Regression

• Polynomial Interpolation

  • Newton’s Divided-Difference

• Spline Interpolation

Numerical Integration

• Numerical Integration
• Trapezoid Rule
  • Composite Trapezoid Rule
• Simpson’s Rule
• Romberg Integration
• Gauss Quadrature

Numerical Differentiation

• Numerical Differentiation
• Numerical Differentiation for 2nd Derivative

Ordinary Differential Equations

• ODEs
• Runge-Kutta Methods Intro
  • Euler’s Method
    • Implicit Euler
  • Heun’s Method
  • Midpoint Method
• Runge-Kutta Method
• Systems of ODEs
• 2nd-order ODEs
• Boundary Value Problems with ODEs
  • Shooting Method
  • Method of Finite Differences

Finite Element Method

• Finite Element Method
  • Finite Element Method - 1D Poisson
• Finite Element Method for Structural Analysis

Partial Differential Equations

• Numerical Partial Differential Equations
• Elliptic Equations
• Parabolic Equations
• Hyperbolic Equations

Problems

• Project 1 - Gauss-Seidel Circuit Solver
• Midterm Problems 204
• MTE 204 Project 2 – Finite Element Analysis