Difference between revisions of "AIM 5113"

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==Course description==
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This course introduces students to mathematical techniques useful in an industrial setting.
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==Topics List==
 
==Topics List==
 
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Introduction to statistical reasoning and random variables 
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Model Fitting, Basis Functions and Applications of the Inner Product
 
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* Uniform, Gaussian and Poisson distributions
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* Interpolation, grid spacing, intro to MATLAB. Basis functions. Numerical integration. Latex and MATLAB basics.
 
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|Week 2
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*  
 
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Introduction to statistical reasoning and random variables (continued)
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Model Fitting, Basis Functions and Applications of the Inner Product
 
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* Taguchi quality control
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* Regression, Least Squares, Inner Products
 
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|Week 3
 
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Monte-Carlo methods
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Model Fitting, Basis Functions and Applications of the Inner Product
 
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* Computing integrals using the Monte-Carlo method
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* Hilbert Space, Trigonometric polynomials
 
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|Week 4
 
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Monte-Carlo methods (continued)
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Statistical Reasoning, Distributions
 
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* Learn to implement Monte-Carlo methods in Python/MATLAB
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* Understanding probabilistic and statistical reasoning, Excel, data visualization
 
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|Week 5
 
|Week 5
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*  
 
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Introduction to Data Acquisition and Manipulation
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Monte Carlo Method
 
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* z-transform, filters, stability, error analysis, aliasing
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* Numerical integration, implementing the Monte-Carlo method
 
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|Week 6
 
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Discrete Fourier transform
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Introduction to ODEs
 
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* Properties of the Fourier transform
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* Statement of basic theorems, higher-order equations
 
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|Week 7
 
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Linear Regression and Optimization Problems
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Boundary conditions, phase portraits, Finite difference methods.
 
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* Learn to implement finite difference methods
 
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|Week 8
 
|Week 8
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Cost-Benefit Analysis
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Frequency domain methods, Laplace transforms
 
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*  
 
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*   
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* Applying transform methods to solve ODEs  
 
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|Week 9
 
|Week 9
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Basic of Economic Analysis
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Control theory
 
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*  
 
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*  
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* Designing and implementing control for systems of ODEs
 
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|Week 10
 
|Week 10
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*  
 
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Introduction to Ordinary Differential Equations
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Introduction to PDEs
 
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Derivatives  
 
Derivatives  
 
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*   
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* Basic PDEs such as Laplace and Wave equation  
 
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|Week 11
 
|Week 11
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*  
 
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Introduction to Partial Differential Equations
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Signal processing and data acquisition
 
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*   
 
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*
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* z-transform, Discrete Fourier Transform
 
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|Week 12
 
|Week 12
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*  
 
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Finite Differences
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Fourier and Laplace transform revisited
 
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*   
 
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*  
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* Using transform methods for signal processing
 
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|Week 13
 
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Writing Technical Reports
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Optimization I
 
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* Linear vs Nonlinear programming
 
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|Week 14
 
|Week 14
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Review, advanced topics
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Optimization II
 
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*   
 
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* Optimal control, Neural Networks
 
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Latest revision as of 08:17, 23 March 2023

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

  • Using transform methods for signal processing
Week 13

Optimization I

  • Linear vs Nonlinear programming
Week 14

Optimization II

  • Optimal control, Neural Networks
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