ME 350: Lectures

Lectures

Lectures are listed on this page. Click on the lecture heading or the "Continue ..." link to get the full content for the lecture.

Compact List of lectures

Excerpts of lectures, most recent first

Week 9 - Solving First Order ODEs in MATLAB

Learning Objectives

At the end of this class you should be able to

Verify whether a given formula is the analytical solution to a first order ODE with a prescribed initial condition
Algebraically rearrange a first order ODE into a format that can be used by odeEuler or other MATLAB codes for solving ODEs
Use the odeEuler code to solve a first order ODE numerically.
Describe how the error in the numerical solution with Euler's method varies with stepsize, $h$

Lecture Videos on YouTube

These videos cover the material that I present in class.

The screencasts were recorded last fall. The sound level during recording was too low, and I haven't been able to figure out how to fix that without re-recording the screencasts.

Download

Here are the slides for the first two videos

Introduction to numerical solution of ODEs slides
Euler's method slides

Week 8 - Solving Linear Systems in MATLAB

Learning Objectives

At the end of this class you should be able to

Manually compute vector addition, vector multiplication and matrix-vector multiplication for modest size (say $n\le4$ ) matrices and vectors
Use MATLAB to check your manual calculations of vector addition, vector multiplication and matrix-vector multiplication
Manually and with MATLAB compute vector inner products.
Define the formula for, manually compute, and use MATLAB to compute the $L_1$ , $L_2$ and $L_\infty$ vector norms

By "manually" I mean using only a pencil and paper, no MATLAB, no Internet access, no textbook

Reading

Same as Lecture 7: Read Sections 6.1 - 6.3 (pp. 129-145) and section 6.6 - 6.6.2, (pp 152 - 153)

Look at the web pages in the Reference section of the class web site.

In MATLAB, type "help slash" or "doc slash" for additional information about the solution of linear equations.

Download

Download the lecture notes on solving linear systems

Download the lecture slides on solving linear systems and focus on these parts:

Setting up the system of equations, slides 4-12
Requirements for a solution, slides 13-21
The backslash operator, slides 57-58
Limits on the Numerical Solution to Ax=b, slides 59-64
The matrix condition number, the residual, and rules of thumb, slides 72-78

You may want to review the slides on Gaussian Elimination (slides 22-56) We will let MATLAB solve the system and instead focus on (1) setting up the system correctly and (2) interpreting the results.

Week 7 - Linear Algebra Operations in MATLAB

Learning Objectives

At the end of this class you should be able to

Manually compute vector addition, vector multiplication and matrix-vector multiplication for modest size (say $n\le4$ ) matrices and vectors
Use MATLAB to check your manual calculations of vector addition, vector multiplication and matrix-vector multiplication
Manually and with MATLAB compute vector inner products.
Define the formula for, manually compute, and use MATLAB to compute the $L_1$ , $L_2$ and $L_\infty$ vector norms

By "manually" I mean using only a pencil and paper, no MATLAB, no Internet access, no textbook

Reading

Read Sections 6.1 - 6.3 (pp. 129-145) and section 6.6 - 6.6.2, (pp 152 - 153)

Look at the web pages in the Reference section of the class web site.

Download

From the linear algebra review slides (second item, above) focus on these parts:

Vector inner product, slides 12-15
Vector norms, slides 18-24
Compatibility requirement of matrix-vector products, slide 40
Row view of the matrix vector product, slides 42-44

Week 6 - Multiple roots and using `fzero`

Learning Objectives

At the end of this class you should be able to

Write an m-file that uses an embedded function to find roots of $f(x)=0$
Use bisect and fzero interchangeably to find the roots of $f(x)=0$
Describe the differences in performance of bisect and fzero.
Write an m-file function to find multiple roots of $f(x)$ function (that has multiple roots).

Reading

The textbook discusses root-finding in two separate contexts. Newton's method is used as an example of a computational algorithm Chapter 2, section 2.7.1 and then again in Chapter 7, section 7.1 through 7.3 as a practical means of discussing function m-files. Please review those sections.

Root-finding as a generic numerical method is discussed Chapter 14, section 14.1.

Download

Download Lecture slides on root-finding and study these slides:
- Slide 45 summarizing basic root-finding methods. Note, we did not cover Newton's method and the secant method, but you should be generally aware of these two methods.
- Slides 46 - 50 on fzero

Week 5 - Review user-defined functions; and introduction to root-finding

Learning Objectives

At the end of this class you should be able to

Recognize a local function in a m-file
Write a local function in a m-file
Recognize an embedded function in an m-file
Write an embedded function in an m-file
Describe how the brackPlot function is used to bracket the roots of $f(x)=0$ .
Describe how the bisect function is used to find the roots of $f(x)=0$ , given a bracket.
Write an m-file function that uses brackPlot and bisect to find the roots of an $f(x)$ function.

Reading

Root-finding as a generic numerical method is discussed Chapter 14, section 14.1.

Download

Download slides on user-defined functions and study slides 19-24
Download Lecture slides on root-finding and study these slides:
- Slides 1 - 16 on the introduction and on bracketing
- Slides 23 - 27 on bisection
- Slides 28 - 31 on convergence criteria

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Week 4 - `if` constructs and `while` loops

Learning Objectives

At the end of this class you should be able to

Recognize the various forms of if-end, if-else-end and if-elseif-else-end constructs
Write the logical expressions necessary for if constructs and while loop constructs
Use if constructs in MATLAB programs
Read and understand the logic of a while loop construct
Use while loops in MATLAB programs

Reading in 5th edition of textbook

Chapter 2, pp. 64 - 76
Chapter 8, pp. 179 - 191

Reading in 6th edition of textbook

Chapter 2, pp. 64 - 72
Chapter 8, pp. 179 - 188

Download

Week 3 - `fprintf`, `for` loops and `if` constructs

Learning Objectives

At the end of this class you should be able to

Use fprintf to display text messages in the command window
Use fprintf for display formatted values of numeric variables in the command window
Write a for loop to traverse a vector
Recognize an if-end construct (more practice later)

Reading

Chapter 2, pp. 57 - 76
Chapter 8, pp. 179 - 182

For a gentle introduction to fprintf, try this screencast by Robert Talbert.

Lecture Slides

Download

Notes on Using fprintf
Large size image of Figure 1 in the "Using fprintf" notes.
Slides on the fprintf command
Slides on for loops
Slides on the if constructs

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Week 2 - MATLAB Functions and Applications in Data Analysis

MATLAB functions allow creation of reusable code that can be assembled into larger and more complex analysis. Even if you are using relatively simple analysis, your code will be easier to write and maintain if you use functions.

In this class meeting we will build skills with creating and using functions. Before getting into functions in detail, we will first review the basic numeric data types used in MATLAB: scalars, vectors and matrices. It's important to understand data types because functions are usually designed to accept specific types of variables as inputs and return specific types of variables as outputs.

Reading

The chapter sections are the same for the 5th and 6th edition of the textbook. There is a slight difference in page numbers in the reading from Chapter 7

Chapter 2, pp. 33 - 51, which is a repeat from week 1 plus pp. 44 - 51
Chapter 7, Sections 7.1 - 7.2.1, pp. 161 - 168 5th edition or pp. 161-171 in 6th edition:

Don't get hung up on the Newton's method script at bottom of p. 162. It uses programming constructs while, if-else-end that we have not discussed yet. We will cover these constructs and it would be good to read and think about that code. At least, write and test the f.m and df.m functions from the middle of page 162. Start reading carefully on page 163.
Chapter 9, pp. 197 - 205, 230 - 231: Sections 9.1.1-9.1.10, 9.8

The material from Chapter 7 focuses on the technical requirements of function input and output parameters. The material from Chapter 9 focuses on plotting.

Lecture Notes and Slides

Summary of Vector variables and expressions
slides on 2D plots
Read slides 1 through 16 in the slides on user-defined functions

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Week 1 - Introduction

Reading

Before class read the following sections of the textbook.

Sixth Edition:

Chapter 1, pp. 1 - 16, 25 - 30
Chapter 2, pp. 33 -40

Fifth Edition:

Chapter 1, pp. 1 - 15, 26 - 31
Chapter 2, pp. 33 - 42

The class meets in the computer lab, EB 325. Refer to the lab exercise for downloads and information related to our in-class activity for today.

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Three Main Ideas in ME 350

ME 350 deals with three main ideas.

MATLAB software
Numerical methods
Computational thinking

These ideas overlap and interact. As we study different problems during the term, the emphasis or perspective on the problem will shift between these three ideas.

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