AIM 5113

From Department of Mathematics at UTSA
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Course description

This course introduces students to mathematical techniques useful in an industrial setting.

Topics List

Date Sections Topics Prerequisite Skills Student Learning Outcomes
Week 1

Model Fitting, Basis Functions and Applications of the Inner Product

  • Interpolation, grid spacing, intro to MATLAB. Basis functions. Numerical integration. Latex and MATLAB basics.
Week 2

Model Fitting, Basis Functions and Applications of the Inner Product

  • Regression, Least Squares, Inner Products
Week 3

Model Fitting, Basis Functions and Applications of the Inner Product

  • Hilbert Space, Trigonometric polynomials
Week 4

Statistical Reasoning, Distributions

  • Understanding probabilistic and statistical reasoning, Excel, data visualization
Week 5

Monte Carlo Method

  • Numerical integration, implementing the Monte-Carlo method
Week 6

Introduction to ODEs

  • Statement of basic theorems, higher-order equations
Week 7

Boundary conditions, phase portraits, Finite difference methods.

  • Learn to implement finite difference methods
Week 8

Frequency domain methods, Laplace transforms

  • Applying transform methods to solve ODEs
Week 9

Control theory

  • Designing and implementing control for systems of ODEs
Week 10

Introduction to PDEs

Derivatives

  • Basic PDEs such as Laplace and Wave equation
Week 11

Signal processing and data acquisition

  • z-transform, Discrete Fourier Transform
Week 12

Fourier and Laplace transform revisited

Week 13

Optimization I

  • Linear vs Nonlinear programming
Week 14

Optimization II

  • Optimal control, Neural Networks