Math 320: Numerical Analysis |
Fall 2018 |
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Faculty: Jerry L. Kazdan

Telephone: (215) 898-5109

email:kazdan AT math.upenn.edu

Office Hours: Wed. 9:30-10:30 (and also by appointment) in DRL 4E15TA: Paul Steven Millington

Telephone: (215) 573-9190

email:paulmill@sas.upenn.edu

Office Hours: Tues, 3:30-4:30 (and also by appointment) in DRL 4E11

IntroductionThis course focuses on finding numerical solutions to mathematics problems for which there are no "simple" solutions. Ultimately, one uses a computer program, which either you write yourself (in some computer language) or from a commercial package such as Maple, Mathematica, and Matlab. To get numerical results you trust, you can't just press a button. You need a fundamental understanding of the,mathematical issues of what can go wrong ("an expert is someone who has made all of the mistakes"). That is what this course is all about.

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Computer Programs:I will assume you already have experience with some computer software. If not, most students can fairly quickly learn enough to manage. Ask your friends. Some possibilities are lower level programs such as C, perl, ..., as well as higher level packages like Maple, Mathematica, and Matlab,. Student versions of many packages are available to Penn studentsNOTE: Maple is available on all our public labs. Also, SAS undergraduates have access to MATLAB (https://www.sas.upenn.edu/computing/matlab-student) and Mathematica (https://www.sas.upenn.edu/computing/mathematica-student) for non-research academic work. Those pages will guide them through the license request and installation process. Wharton and SEAS undergraduates need to acquire licenses through their respective schools, but we include links to the instructions on both pages.

Prerequisites & Review Material:Some experience with calculus, linear algebra, and basic computer programming

To remove rust from your background I suggest doing the problems from recent Final Exams: Math 104, Math 114, Math 240Problems to think about during August.

On the first day of class some students might be invited to present their solutions at the blackboard.

Notes:

Everyonewho writes documents containing mathematics should learn LaTeX. Basic documents are not difficult. Begin now by typing your Math 320 Homework in LaTeX. The software (Windows, Mac, Linux) is free.

TeX/LaTeX Stuff: Create documents having mathematics formulas.- Big Numbers
- Field Axioms
- Real solution of x
^{2}= 2- Square Roots by Newton's Method
- Mathematics and Computation by Avi Wigderson (2019)
- Major Quantum Computing Advance Made Obsolete by Teenager
- Universal Method to Sort Complex Information Found
- Runge's phenomenon in interpolation
- Volcano
- Maple: Linear Equations
- Gaussian Elimination Example 1, Example 2
- LU Decomposition Without Pivoting, With Pivoting
- Vectors - and an Application to Least Squares
- Singular Values and Least Squares
- A Simple Tridiagonal Matrix
- Some Puzzles
- Iteration-Notes from -Nov-15-18.pdf

Homework Assignments:

- Set 0 Discussed by YOU in class on Aug. 28

Before the first week of class review the above Prerequisites & Review Material: . and read both Chapter 1 of the Burden Faires text and Sections 1-5 of the Forsythe article referenced above.- Set 1 Due: Thurs., Sept. 6 in class. [Late papers will be accepted until 1:00 PM Fri.] ky
- Set 2 Due: Thurs., Sept. 13 in class. [Late papers will be accepted until 1:00 PM Fri.]
- Set 3 Due: Thurs., Sept. 20 in class. [Late papers will be accepted until 1:00 PM Fri.]
- Set 4 Due: Thurs., Sept. 27 in class. [Late papers will be accepted until 1:00 PM Fri.]
- Set 5 Due: Thurs., Oct. 11 in class. [Late papers will be accepted until 1:00 PM Fri.]
- Set 6 Due: Thurs., Oct. 25 in class. [Late papers will be accepted until 1:00 PM Fri.]
- Set 7 Due: Thurs., Nov. 1 in class. [Late papers will be accepted until 1:00 PM Fri.]
- Set 8 Due: Thurs., Nov. 8 in class. [Late papers will be accepted until 1:00 PM Fri.]
- Set 9 Due: Thurs., Nov. 15 in class. [Late papers will be accepted until 1:00 PM Fri.]
- Set 10 Due: Thurs., Nov. 29 in class. [Late papers will be accepted until 1:00 PM Fri.]

Exams:There will be two in-class exams, from 1:30-3:00:Tuesday, October 2 Thursday. December 6 [No Final Exam] You may always use one 3"×5" card withhandwrittennotes on both sides

Exam 1: Original, condensed.,