Mathematical Models for Engineering Problems and Differential Equations (fall,2016): materials

Lecture slides
Lecture slides (2017 course)
Lecture slides (2016 course)
Old Exams
- Midterm: 2010 / 2011 / 2012 / 2013 / 2014 / 2016 / 2017
- Final: 2010 / 2011 / 2012 / 2013 / 2014 / 2016 / 2017
Example scripts
- Solving Nonlinear Equations
  - ch02_p42.m: demo of the example on p.42-43.
  - Wolfram Demonstrations Project (You need to install the CDF player to try the demos.)
    - Bisection Method
    - Finding Roots Using Binary or Interpolation Search: Bisection vs. Regula Falsi
    - Newton's Method
    - Learning Newton's Method
    - Secant Root Finding Method
- Solving a System of Linear Equations
  - JvsGS.m: compares the convergence speed of Jacobi vs. Gauss-Seidel
  - Wolfram Demonstrations Project (You need to install the CDF player to try the demos.)
    - Unit-Norm Vectors under Different p-Norms
    - Matrix Norm and Spectral Norm ‖A‖₂ (2-norm)
    - Maximum Absolute Row Sum Norm: ‖A‖_∞ (infinity-norm)
    - Maximum Absolute Column Sum Norm: ‖A‖₁ (1-norm)
- Curve Fitting and Interpolation
  - plot_p163.m: plots the example on p.163
  - fit_interp.m: Plots and compares four methods in Chap 4. (Press space bar to show the interpolating polynomial.)
    - curve fitting (blue) with a quartic (degree 4) polynomial
    - cubic spline interpolation (red)
    - linear spline interpolation (magenta)
    - interpolating polynomial (green)
  - Splines
    - Introduction to spline functions by Ronald G. Mosier
    - A draftman's spline by Carl de Boor
  - Wolfram Demonstrations Project (You need to install the CDF player to try the demos.)
    - Curve Fitting with polynomials
    - Interactive Curve Fitting
    - Interpolating a Set of Data
    - Interpolating Polynomial
    - Runge's Phenomenon
- Numerical Integration
  - Wolfram Demonstrations Project (You need to install the CDF player to try the demos.)
- Ordinary Differential Equations: Initial-Value Problems
  - DemoODE.m Plots the solutions using three methods (Euler's explicit, modified Euler, and 4-th order Runge-Kutta methods) (requires odeEULER.m, odeModEuler.m, odeRK4.m)
  - DemoErrODE.m Plots how the global truncation errors change according to h for three methods (Euler's explicit, modified Euler, and 4-th order Runge-Kutta methods) (requires odeEULER.m, odeModEuler.m, odeRK4.m)
  - Wolfram Demonstrations Project (You need to install the CDF player to try the demos.)
    - Families of Solutions for ODEs
    - Slope Fields
    - Fundamental Theorem of Calculus and Initial Value Problems
    - Graphic Solution of a First-Order Differential Equation
    - Euler's Method for the Exponential Function
    - Numerical Methods for Differential Equations (explicit Euler, implicit Euler, Heun (modified Euler), classical Runge-Kutta)
    - Comparing Leapfrog Methods with Other Numerical Methods for Differential Equations
    - Graphic Solution of a Second-Order Differential Equation
    - One Step of Runge-Kutta: The classical fourth-order Runge-Kutta method in Section 7.5.3.
    - Understanding Runge-Kutta: The classical fourth-order Runge-Kutta method in Section 7.5.3.
    - Global and Local Errors in Runge-Kutta Methods
    - Two-Step and Four-Step Adams Predictor-Corrector Method
- Oridnary Differential Equations: Boundary-Vaue Problems
  - Wolfram Demonstrations Project (You need to install the CDF player to try the demos.)
    - Shooting Method

Materials