CS1371 Teaching Outlines

Summary

Homework 1 due week 1: Getting Started

Homework 2 due week 2: Basic Vectors

Homework 3 due week 3: Conditionals, Iteration and Vector Operations

Homework 4 due week 4: Functions and Cell Arrays

Week 5: Test 1

Homework 5 due week 6: Structures, Arrays

Homework 6 due week 7: File I/O and recursion

Homework 7 due week 8: Plotting

Homework 8 due week 9: Advanced Plotting

Week 10: Test 2

Week 11: Spring Break

Homework 9 due week 12: Matrices, Images

Homework 10 due week 13: Numerical Methods

Homework 11 due week 14: Advanced Numerical Methods, Sorting

Week 15: Test 3

Philosophy

Philosophical Notes:

with a text book containing all the students should know, we are free to explain the difficult parts of a chapter, but expect the students to dig around for the rest of it.
Having said that, many of the chapters push just a bit further than the students really need to go, thereby challenging the top flight students. We might have to make clear which parts are "beyond the pale."

Lecture 1

Objective: Introduce Matlab (Ch 1 & 2)

Introductions

Show of hands by major
Show of hands by class year
Introduce yourself

Course Overview

Slide presentation
Open class Web site
Point them to Syllabus page

Concept: variables and assignment

Difference between algebraic = and assignment.
Encourage useful variable names

Lecture 2

Objective: Scripts (Ch 3)

Problem Solving

Discuss Space Ship One (or some other problem type)
- X prize
- Carried to 50,000 ft on mother ship
- Rocket motor gives vertical velocity V
- Outer space defined as above 100 km altitude
- How would you calculate the required velocity? (v² = u² + 2 a s)
- $15,000 for ride into outer space
- If you had some velocity V₁ (> V), how long would you get in outer space for your money? (s = u t + 1/2 a t² ) -> quadratic equation

Matlab Introduction

Enter some stuff into the Matlab Command Window.
Show the variables appearing in the Workspace.
Do the velocity problem
- 1 km = 3281 ft
- g = -9.81 m/sec²

Writing a Script

Talk about the Current Directory (I usually work from my Acme account)
Open the empty script provided in the Matlab editor
Demonstrate do-a-bit / test-a-bit strategy using the Debug/Save and Run menu item (F5) with the velocity and time above 100 km problems
Solve the quadratic equation in the script explicitly as shown in the finished solution

Lecture 3

Objective: How to do and turn in homework

Introduction to T-Square

Show the links to T-Square
Have a student volunteer:
- go through the registration process
- submit your script as his/her HW1
- retrieve and verify the HW1

Homework Mechanics

Walk through the following steps for doing Homework 1.

Discuss file storage and a working directory:
- On your own computer, store files in the default Matlab working directory Matlabr7/work.
- On a campus computer, either use the Y drive that should be mapped to your gt account, or a floppy disk, or a memory stick.
Retrieving the homework file:
- Open the class web site
- Scroll down to Homework 1
- Right click on Homework 1
- Choose Save target As ...
- Navigate to your working directory (see above)
- Make sure the file has the name hw1.m
- Accept that location and let the system download the file
- Decline the offer to open the file
Doing the homework
- Start Matlab
- Point the current directory to your working directory
- Double click the file -- this should open the Matlab editor
- Build and test solutions incrementally

Introduce Vectors

Create vectors with [...], linspace(...), zeros(...), ones(...), rand(...).
Access the data by indexing – out of bounds below, above the size
Shorten vectors with [ ]
Write a script to plot sqrt(sin(x)) or something. You assume that functions can accept a vector and produce a vector.

Lecture 4

Objective: Vector Operations (Ch 4)

Arithmetic expression

Two vectors matching size, or at least one a scalar
+, -, .*, ./, .^

Logical expression

Two vectors matching size, or at least one a scalar
>, <, >=, <=, ==

Vector Indexing with integer Vectors

Indexing any vector with another vector -- end, etc.
Examples like keeping the odd or even values, reversing a vector

Vector Indexing with logical Vectors

Indexing any vector with a logical vector
Examples like all the numbers > 10, or all the even numbers (as opposed to even locations)

Applying built-in Functions

size, min, max with multiple return values
ceil, floor, round, fix
expand plotting to things like a spiral: plotting theta .* cos(theta) vs theta .* sin(theta)

Lecture 5

Objective: Conditionals (Ch 5)

Logical expression

Anything that returns a Boolean (true/false) result

If statements

Simple if / else, e.g. weekend vs weekday
elseif e.g. numerical grade -> letter grade
If with vector operations implies all(...)

Switch statements

selecting among finite choices -- days in a month works well as an example
Default use to catch exceptions -- bad form for main thread

Lecture 6

Objective: Iteration (Ch 6)

For loops

Simplest example: finding the max of a vector; use for x = A first, and trace it carefully
Debugging using the stepper
Knowing which value -- needs "usual" form index = 1:length(A) [don't use i or j as the index -- they have values in Matlab]

While loops

Repeat finding the max using while
Build a loop-and-a-half by asking for the radius and computing the area

Lecture 7

Objective: Functions (Ch 7)

Abstraction
Black Box View
Code re-use

Simple Function

Find a root of a quadratic
Building, testing, checking
Illustrate variable scoping

Code Re-use

'th' logic should be encapsulated

More Stuff

Returning Multiple Values
Consuming vectors

Lecture 8

Objective: Character Strings (Ch 6)

Manipulating Strings

As if they were vectors
Doing math on them --casting
Input and output -- sprintf
Comparing strings -- strcmp(...) -- not the same as C
Arrays of Strings must match sizes
char(...) gets you off the hook

Lecture 9

Objectives: Cell Arrays (Ch 7)

Containers

Limited number of operations
Uses.
deal(...)
example: vectors of various lengths
- build one using rand extensively for length and content
- process it for average length, min, max etc.

Lecture 10

Objective: Structures (Ch 7)

Structure for 1 CD

Name fields
Access fields
fieldnames(.....)
rmfield(...)

Lecture 11

Objectives: Using structure arrays as examples of problem solving operations (Ch 10)

Structure Arrays

Array of CD structures
Uniformity of fields

Problem Solving

Identify each of the following and code examples from the CD collection

Build / Insert (implied in makeCD(...))
Traverse -- e.g. save to a file as text – see writeCDs(...) but don’t dig around in it…
Map -- change all of them, like raise the prices or add a field like value
Filter -- choose some of them by name or price
Fold -- summarize the whole collection – count, or total price
Search -- find one particular CD
Sort -- introduce Matlab built-in sort(...) -- prepare data using {CDs.artist} or [CDs.value]

Lecture 12

Objectives: Continue problem solving operations (Ch 10)

TEST 1

Lecture 13

Speech about not giving up:

q changing study habits,

q final grade replacing test average

Objective: Arrays (Ch 3)

Extending vectors to arrays

Creating
Accessing elements
Removing whole rows or columns
Scalar and logical operations
Concatenation
Ranges of indices
Slicing
Linearizing (access as if it were a vector, result of find(...) )

Lecture 14

Objectives: File I/O with Spread Sheets (Ch 8)

File I/O Materials

Types of File I/O:

Save and restore the workspace
Read and Process Excel Spread Sheets
Read and Process Comma Separated Values (numbers only)
General-Purpose File Read and Write

Examples:

Read grades.xls
Computations
Read World_Data.xls

Lecture 15

Objective: Mid-Level File I/O (Ch 8)

q CSV Files

Objective: Low-Level File I/O (Ch 8)

q Open, close

q Get strings

Lecture 16

Objective: Finish up File I/O (Ch 8)

q Tokens

Lecture 17

Objective: Understanding Recursion (Ch 9)

Recursion Materials

q Stacks

q Activation Stack implementation of Function Calls

q Illustrate on the Board using Roots of a Quadratic

q Canonical problem: factorial

o Define the factorial

o Identify 3 parts of recursion:

Clone the function
Terminating condition
Move towards termination

o Write the code

o Run with the Debugger for simple case

q Wrapper functions for setup -- negative or fractional numbers?

q Local functions

q Graphical Root Finding

q Palindromes

q Fibonacci

q Mutual recursion

q Tail recursion (?)

Lecture 18

Objective: Complete discussion of recursion (Ch 9)

Overall, we need to have covered these topics:

q Basic recursion -- factorial -- how it works, and why --activation stack etc.

q Wrapper functions -- preparing the data and checking for errors

q Tree recursion --Fibonacci --a bad idea computationally

q Perhaps Palindromes or other examples

q Not tail recursion or mutual recursion

Lecture 19

Objective: Begin discussion of plotting (Ch 11)

Plotting Materials

q There is an intercepts script to start the discussion if you want

q 2-D plotting -- line color, symbols, titles, etc. [rotate to see the 3-D effect]

q Parametric curves -- circle, random walk

q plot3(...)

Lecture 20

Objective: Continue discussion of plotting (Ch 11)

q meshgrid, surf, mesh

q shading, lighting

Lecture 21

Objective: Bodies of Rotation (Ch 11)

q Rotate about X-axis

q Rotate discrete data points

Lecture 22

Objective: Finish up Bodies of Rotation (Ch 11)

q Rotate about the vertical axis

q Using the 4^th parameter to surf

q ...

Objectives: File I/O with CSV files (Ch 8)

Atlanta Data

Process and plot atlanta.txt – the streets
Process and plot ttimes.txt

Lecture 23

Objective: Matrix Multiplication (Ch 12)

Matrix Materials

q Matrix multiply

q Coordinate rotation

q Twinkling stars

Lecture 24

Objective: Matrix Division (Ch 12)

q Basics of division

q Solving Simultaneous equations

q Resistor network

q Chemical Composition

Lecture 25

Objectives: Introduce Images (Ch 13)

Image Materials

Introduce Image formats

Simple image analysis and processing

Read volta.jpg
Plot sections through it
Reshape
Change Colors

Lecture 26

Objective: Second Images lecture (Ch 13)

Use the image Volta.jpg

Stretching / Shrinking Images
- Index vectors created with linspace
Clipping/Mirroring Images
- Index vectors created with linspace

TEST 2

Lecture 27

Objective: Third Images Lecture (Ch 13)

"Green Screen" masking
- Replace the grey sky in Vienna.jpg with blue sky from Witney.jpg
- Plot the color values at row 350 to find the thresholds
- Create a 2-D layer mask
- Build a 3-D mask from this layer
- Make the mask below 700 false
- Copy the Witney image into this masked area of Vienna
- Write the new jpeg
Zoom on the wire and discuss its appearance (artifact of the JPEG compression)

Lecture 28

Objective: Begin Numerical Methods – Ch 15

Numerical Methods Materials

Interpolation
- Linear using interp1(x, y, val) -- supply scalar val for one pt, vector for range
- Extrapolation possible?
- Spline interpolation -- math, useful?

Lecture 29

Objective: Continue Numerical Methods (Ch 15)

Curve Fitting
- Why? Trust the underlying physics more than the data
- Polyfit produces the coefficients
- Polyval produces the curve
Integration and Differentiation
- Cumsum integrates
- Diff(y) / diff(x) differentiates

Lecture 30

Objective: Continue Numerical Methods (Ch 15)

Zero Crossings
- Estimate by shifting and multiplying (P. 261)
- Eyeball actual values by plotting
- Compute by Newton's method or geometry
Differentiation and Integration
- Start with a 6^th order polynomial
- Compute and plot the analytical slope
- Compute the gradient by diff(y) / diff(x)
- Compute and plot the analytical integral
- Compute the integral by cumsum, and by trapezoidal rule and Simpson's Rule

Lecture 31

Objective: Problem Solving

Lecture 32

Objective: Understand Measures of Computing (Ch 16)

Big O as a measure of the work done by an algorithm

Objective: Understand MATLAB sorting (Ch 16)

Using MATLAB internal sort of a vector

Extracting fields from a structure array -- numerical and sorting the array

Extracting fields from a structure array -- strings and sorting the array

o I really minimize this discussion by using as an analogy the area of the space occupied by the steps in the sort algorithms. All are N wide; Insertion Sort is also N deep, where the other two are Log N deep.

Objective: Understand sorting algorithms (Ch 16)

Sort Demo & Sorting Code

Four sorting techniques:

o Bubble Sort

o Insertion Sort

o Merge Sort

o Quick Sort

Circumstances under which last three might be used.

Students should be able to code first three using a vector of numbers

Lecture 33

Objective: Sorting (Ch 16)

- Complete sorting discussion

Lecture 34

Objectives: Introduce Sound (Ch 14)

Sound Materials

Reading and Playing Sound

Changing amplitude and playback frequency

Slicing and concatenating speech.

Lecture 35

Objective: More on Sound (Ch 14)

Instrument sounds:

o The musical scale -- 2^1/12factor between half steps

o Octave doubles the frequency

Playing a tune by changing Fs

o Note duration achieved by pausing

Assembling a tune by stretching / shrinking the note

o Note duration achieved by the number of samples concatenated

Lecture 36

Objective: Finish up Sound (Ch 14)

The FFT -- its parameters
Create a 400 Hz sine wave from scratch
Play it
Perform the FFT
Plot the result including the correct axes
Discuss the results
Add a line to the FFT (both ends)
Perform the ifft
Play the absolute value of the result
Read an instrument
Perform and plot the FFT