MATH 128 (Section 001)

Objectives: This is the first half of a year-long sequence in applied and computational mathematics for advanced students of applied or natural science. The class places equal emphasis on analytical and numerical techniques for solving differential equations arising from physical or biological phenomena.

Topics:

1. Modeling of physical system: review of preliminary concepts (chap 1-4 in the text)

2. Ordinary differential equation (ODE): initial value problems (chap 5-6 in the text)
   • Laplace transforms
   • Numerical methods: Euler, midpoint, Runge-Kutta methods, and other higher-order methods

3. Two-point boundary value problems (chap 17 in the text)
   • Fourier Series
   • Fourier Transforms
   • Numerical Methods: discrete Fourier transform & FFT, finite difference methods

4. Partial differential equations (PDEs) (chap 18 in the text)
   • Basic concepts of partial differential equations
   • Separation of variables
   • Fourier and Laplace transforms
   • Numerical methods: method of lines and finite-difference methods

Programming: Programming is part of the course; each student will be expected to learn Matlab and use it on some of the homework assignments. Online tutorials are listed on the web page.

Homework: Homework and/or programming projects will be given approximately weekly and posted on the course web site. Collaboration on homework is allowed and encouraged but copying from another person is prohibited. In principle, late homework is NOT accepted.

Exams: There will be two midterm exams and one final exam on the following dates:

• Midterm 1: Thursday, September 23
• Midterm 2: Thursday, October 28
• Final : Thursday, December 16, 9:00 am

Grading

Homework	30%
Midterm 1	20%
Midterm 2	20%
Final	30%
Extra Credit	10%
Total	110%

A 90% will guarantee you an A.

Honor Code: All work is expected to be completed in accordance with the Honor Code. In particular, copying any other person's work is prohibited.

News & update

• 9/7, correction to hw2, pb #3 (a), and solution to hw1 are uploaded.
• 9/9, a sign error is spotted in the solution key for hw #1, 1 (c).
• 9/9 the deadline for hw #2 is extended to Friday (9/10).
• Mathematica is available in the computer lab on the 2nd floor of Phillips Hall (for Physics Majors only.)
• Instruction for accessing your H: Drive and setting up Matlab and Mathematica for your PC.
• Information for AFS client .
• Information for AFS client for Windows
• An example of Mathematica notebook (save this file with extension .nb and open it in Mathematica.)
• 9/13, solution key for hw # 2 is posted.
• An example of Matlab script (save this file with extension .m and run it under Matlab environment: file name only, no extension.)
• Another example of Matlab script ( modify the script for your homework # 4 )
• 9/16, deadline for homework #3 is postponed to next Thursday (9/23)
• 9/25, solution-key to exam1 is posted (see homework section below)
• Mathematica notebook for Gibbs phenomenon (save this file with extension .nb and open it in Mathematica.)
• 9/30, homework # 5 is posted (Using Mathematica for this homework is OK.)
• 10/12 homework # 6 is posted.
• 10/22 homework # 7 is posted.
• 10/26 For exam # 2, you are allowed to bring a piece of size 8.5x11 paper into the exam. You may write whatever you wish on one side of that paper.
• 11/5 homework # 8 is posted (due 11/11).
• 11/17 homework # 9 is posted (due 11/23).
• 11/29 extra credit problems are posted (due 12/10).
• 12/06 sample final is posted.

Homework assignments

Reading assignments

Programming links

Basic concepts:

• University of Florida
• Michigan Tech
• University of Utah
• University of Colorado
• University of New Hampshire

• Solving ODE
• Higher order ODEs and Systems
• Solving Elliptic PDEs with the PDE Toolbox