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AMATH 301 A: Beginning Scientific Computing

Summer Term: 
Full-term
Meeting Time: 
MWThF 2:20pm - 3:20pm
Location: 
HCK 132
SLN: 
10061
Joint Sections: 
AMATH 301 B
Instructor:
Trevor Caldwell
Trevor Caldwell

Syllabus Description:

This page describes the topics covered in class and lists assigned videos for each week.  It will be continually updated throughout the course.  All video lectures can be found here. Note that for each week after Week 1, optional supplementary video lectures can be found at the bottom of the required videos page.

Week 1 - Introduction to MATLAB

This week will be a brief introduction to MATLAB, including basic programming concepts like loops and conditional statements as well as the use of matrices and vectors.  

Required Videos

  • Lecture 1: Vectors and Matrices
  • Lecture 2: Logic, Loops, and Iterations
  • Lecture 3: Plotting and Importing/Exporting Data

Supplementary Videos

Week 2 - Linear Systems and Linear Algebra

This week we will discuss direct solution techniques for systems of equations of the form Ax = b.  We will also introduce the notion of computational complexity and talk about how solution techniques scale with the size of the problem.  

Required Videos

  • Lecture 1: Linear Systems of Equations
  • Lecture 2: Gaussian Elimination for Ax = b
  • Lecture 3: LU Matrix Decomposition for Ax = b

Week 3 - Iterative Methods for Linear Systems

This week we will discuss iterative solution techniques for systems of equations of the form Ax = b.  We will also talk about eigenvalues/eigenvectors and how they relate to stability and convergence.  

Required Videos

  • Lecture 1: Iterative Methods for Ax = b
  • Lecture 2: Eigenvalues and Eigenvectors
  • Lecture 3: Eigen-decompositions and Iterations

Week 4 - Curve Fitting

This week, we will discuss how to fit various types of curves to data sets and how to use these fits for extrapolation and interpolation.  We will also discuss how to write/use our own functions. Note: the supplementary video on function handles is highly recommended!

Required Videos

  • Lecture 1: Least-Square Fitting Methods
  • Lecture 2: Polynomial Fits and Splines
  • Lecture 3: Data Fitting with Matlab

Week 5 - Optimization

This week we will discuss how to maximize/minimize functions with various types of constraints. Note that the first listed "required video" is actually optional - there won't be any HW or exam questions about this material.

Required Videos

  • Lecture 1: Unconstrained Optimization (Derivative-Free Methods) - this is OPTIONAL
  • Lecture 2: Unconstrained Optimization (Derivative Methods)
  • Lecture 3: Linear Programming and Genetic Algorithms

 

Week 6 - Numerical Integration and Differentiation

This week we will discuss how to approximate derivatives and integrals numerically.  We will also review Taylor series.  

Required Videos

  • Lecture 1: Numerical Differentiation Methods
  • Lecture 2: Higher-Order Accuracy Schemes for Differentiation and Integration
  • Lecture 3: Higher-Order Integration Schemes

Week 7 - Differential Equations I

This week we will discuss methods for integrating ordinary differential equations.  We will look at both boundary value problems and initial value problems.  

Required Videos

  • Lecture 1: Ordinary Differential Equations and Time-Stepping
  • Lecture 2: Error and Stability of Time-Stepping Schemes
  • Lecture 3: General Time-Stepping and Runge-Kutta Schemes

Week 8 - Differential Equations II

This week we will continue our discussion of ordinary differential equations and use the methods we have introduced to solve some interesting examples.  

Required Videos

  • Lecture 1: Application of Runge-Kutta to the Lorenz Equation
  • Lecture 2: Vectorized Time-Step Integrators
  • Lecture 3: Application of Runge-Kutta to Chaotic Dynamics and the Double Pendulum

Week 9 - Singular Value Decomposition

In this section we will discuss the SVD and some of its applications. 

Required Videos

  • Lecture 1: The Singular Value Decomposition
  • Lecture 2: Principal Component Analysis (PCA)
  • Lecture 3: PCA for Face Recognition

Week 10 - Fast Fourier Transform

In this section we will discuss the FFT and some of its applications.

Required Videos

  • Lecture 1: Theory of the Fourier Transform
  • Lecture 2: Discrete Fourier Transform (DFT) 
  • Lecture 3: FFT and Image Compression
Catalog Description: 
Introduction to the use of computers to solve problems arising in the physical, biological, and engineering sciences. Application of mathematical judgment, programming architecture, and flow control in solving scientific problems. Introduction to MATLAB routines for numerical programming, computation, and visualization. Prerequisite: either MATH 125, Q SCI 292, or MATH 135. Offered: AWSpS.
GE Requirements: 
Natural World (NW)
Credits: 
4.0
Status: 
Active
Last updated: 
April 1, 2018 - 9:00pm
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