Numerical Methods I - Spring 2019 (3 credits)

Dates 1/25/2019 - 05/22/2019, Friday 2:40PM - 5:10PM
Room: North Building HN 1001G

Instructor: Dr. Yao Chu                        Email: yc904@hunter.cuny.edu (best way to reach me)

Prerequisites:

PHYS121 or 120 and two semesters of calculus. MATH 254 (ordinary differential equations) is NOT a pre-req. MATH 254 is not necessary for the student since the numerical techniques for solving differential equations taught in PHYS 385/685 are quite different from the techniques taught in MATH 254.

Learning Goals:

- Distinguish problems in Physics that can be solved analytically and those cannot be solved analytically
- Learn mathematical tools for solving Physics problems expressed as differential equations numerically
- Learn how to use computer technology (e.g. Mathematica) to implement numerical methods in coding
- Calculate and compare various numerical methods in terms of number of calculations and error limits

Syllabus (Tentative):

The following are tentative topics
1. Introduction to Mathematica
2. Taylor and MacLauren Series
3. Falling Object
4. Numerical Derivative
5. More on Numerical Derivatives
6. Numerical Integration
7. More on Numerical Integration
8. Gauss Integration
9. The Euler Method
10. Simple Harmonic Oscillator
11. The Euler Cromer Method
12. The Physical Pendulum
13. The Midpoint Runge-Kutta Method
14. The Fourth Order Runge-Kutta Method
15. The Verlet Method
16. The Leapfrog Method
17. Least Square Fit
18. Matrix Manipulation
19. Systems of Linear Equations
20. Solving Equations - Bisection Method
21. Solving Equations - Newton's Method
22. Fourier Series
23. Discrete Fourier Series
24. Polynomial Interpolation

Grading:

Attendance (10%), In Class Assignment (20%), Exams 1 and 2, (20% each), Final Exam (30%)
There is no make-up exam. Your other exam will be overweighed if you miss an exam for excusable reason with documentation

No Classes
04/19/2019, 04/26/2019

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