AIM 5113

Course description

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

Date	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		Using transform methods for signal processing
Week 13	Optimization I		Linear vs Nonlinear programming
Week 14	Optimization II		Optimal control, Neural Networks