CPE 332 Computer Engineering Mathematics II Part III
- Slides: 54
CPE 332 Computer Engineering Mathematics II Part III, Chapter 11 ODE
Today Topics • Chapter 11 Ordinary Differential Equation • HW 10 Due
Example 1 • Solve for
Example 1 • Solve for
Example 1 • Solve for
Differential Equation • ��� Order ����� Derivative ������� Order ��� Differential Equation – ����� Initial Condition ����������� Order ����
Example 2
Example 2 • ���� Integrate ไมได
Differential Equation • Tools ���������� Differential Equation – Laplace Transform (one side/two side) – Fourier Transform ������� – Z-Transform �������� Discrete Version ��� Differential Equation • ��� Differential Equation ������������ • �������� Difference Equation – ����������� CPE
Differential Equation • ������� Numerical Method ���������� Differential Equation – ��������� First Order ��� Initial Condition ������� – ������ Ordinary Differential Equation • One Independent Variable – ���������� Higher Order ��� – ������ Boundary Condition ��������� • ���������� Reference
Chapter 10 • Ordinary Differential Equation
ODE
ODE
ODE
ODE: One Step Method
ODE: One Step Method
Euler’s Method
Euler’s Method
Euler’s Method
Euler’s Method
Euler’s Method
Euler’s Method
Heun and Polygon Method
Heun Method
Heun Method
Heun Method
Heun and Polygon Method
Heun Method
Heun and Polygon Method
Heun Method
Heun Method
Improved Polygon Method
Improved Polygon Method
Runge-Kutta Method
Runge-Kutta Method
Second Order Runge-Kutta Method
Second Order Runge-Kutta Method
Second Order Runge-Kutta Method
Second Order Runge-Kutta Method
Second Order Runge-Kutta Method
Second Order Runge-Kutta Method
Second Order Runge-Kutta Method
Second Order Runge-Kutta Method
Second Order Runge-Kutta Method
Third Order Runge-Kutta Method
Third Order Runge-Kutta Method
Forth Order Runge-Kutta Method
Forth Order Runge-Kutta Method
Higher Order Runge-Kutta Method
Comparison
Chapter 11 Homework (HW 11) • Download ������� Sheet
End of Chapter 11 • Next Week – Ch. 12 Curve Fitting (������� Text) – HW 12 – Last Chapter • Course ENDs