UT Math Dept

 

 

 

 

 

 

 

 

 

 

 

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Course Description: This course is an introduction to using computers to teach and perform mathematics. Students will learn to use and write programs in Matlab, along with using one additional higher level language.

Each session will begin with a lecture focusing on a different topic each week. The remainder of the class time will be used to work on a project which focuses on that week's lesson. Some possible topics will include: solving linear systems of equations, prime numbers, solving nonlinear equations, numerical integration, exploring the number Pi, fractals, cellular automa, random walks and geometric constructions using drawing software.

Course Prerequisite: Calculus

Grading: Your grade will be determined by the average of your weekly project grades.

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WEEK
TOPIC
PROJECT
1
Review linear systems
Intro to matlab
Magic square
2

Programming in matlab

Prime numbers
3
Nonlinear equations
Bisection
Newton's method
Secant method

Zeros of Bessel functions

4
Numerical differentiation
Numerical integratiation
Does the Bessel function J_0(x) satisfy Bessel's differential equation?
5
Arbitrary precision arithmetic
Addition, subtraction
6
Arbitrary precision arithmetic
Multiplication
7
Arbitrary precision arithmetic
Division
8
Calculating Pi Calculating Pi
9
Minimization
Minima of Bessel function J_0(x)
10
Sympolic algebra using Maple
Asymptotic approximation of roots to polynomial equations
11
Cellular automata
Life
12
Julia sets Julia sets
13
Mandelbrot set Mandelbrot set
14
Geometric construction, Splines and drawing programs Construction of pentagon
15
Random Walks
The return problem in 2 and 3 dimensions
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