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Applied Mathematics Laboratory

Asian Institute of Technology

Handout 11

Tue 7 Sep 2010

1 Course Objectives and Outlines

This course aims to provide students with basic programming skills in using the MATLABsoftware. The instructions will be based on 15 weekly tutorial/laboratory sessions astentatively listed below.

1. Familiarization with MATLAB

Working at the command prompt

Basic arithmetic commands

Basic array and matrix manipulations

Basic statistical analysis

Computation with complex numbers

2. Using functions, script files, and input/output files

Creating functions

Writing script files to perform a series of tasks

Saving data to files and loading data from files Project: Comparing data from different files

3. Relational operators and control flows

Logical operators

if, for, and while statements

Debugging in MATLAB

Project: Computing the moving average, maximum, and minimum

4. Signal generation and function plotting: Part one

Basic functions, e.g. trigonometric, logarithmic, and exponential

Plotting one-variable functions

Configuring plot appearances

Creating multiple subplots

Project: Plotting hyperbolic functions

5. Signal generation and graph plotting: Part two

Plotting discrete-time signals1Prepared by Poompat Saengudomlert, Asian Institute of Technology.

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Basic signal processing commands

Plotting two-variable functions using three-dimensional plots or countour lines

Exporting plots as image files

Project: Lowpass filtering of signals

6. Graph representations and basic properties

Matrix representations of graphs

Computing node degrees

Number of paths between node pairs

Checking for connectedness

Project: Finding Euler paths in connected graphs

7. Graph algorithms

Computing minimum spanning trees

Dijkstra algorithm for shortest path routing

Finding link-disjoint paths

Project: Computing the average internodal distances of graphs

8. Review for mid-semester examination

9. Recursion

Writing recursive functions Computing factorials

Computing Fibonacci numbers

Project: Solving the tower-of-Hanoi problem

10. Searching and sorting

Divide-and-conquer approach in problem solving

Binary search in a sorted list

Merge sort Project: Parity check error control coding

11. Random number generator

Generating uniform random integers

Generating uniform random real numbers

Generating other types of random variables, e.g. Gaussian, exponential, bino-mial, and Poisson

Project: Verifying the central limit theorem

12. Numerical analysis

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Solving linear equations

Regression

Root finding

Project: Curve fitting using polynomials

13. Numerical method

Numerical integration

Numerical differentiation

Numerical solutions to ordinary differential equations

Project: Finding impulse responses of electrical circuits

14. Grapical user interface (GUI)

Creating a tabular form for GUI GUI with function plotting

GUI with geometric drawing

Project: Visualizing graph algorithms

15. Review for final examination

2 Familiarization with MATLAB

After creating example arrays and matrices at the command prompt, you should try thefollowing commands.2

Basic array information

size - Size of matrix.

length - Length of vector.

ndims - Number of dimensions.

numel - Number of elements.

disp - Display matrix or text.

isempty - True for empty matrix.

isequal - True if arrays are identical.isnumeric - True for numeric arrays.

islogical - True for logical array.

logical - Convert numeric values to logical.

2When you need additional information in MATLAB about a specific command, you can use the help

command. For example, you can type help sizeto find out more about the size command. The lists

of all commands can be generated by typing help alone.

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Elementary matrices

zeros - Zeros array.

ones - Ones array.

eye - Identity matrix.

repmat - Replicate and tile array.rand - Uniformly distributed random numbers.

randn - Normally distributed random numbers.

: - Regularly spaced vector and index into matrix.

Matrix manipulation

reshape - Change size.

diag - Diagonal matrices and diagonals of matrix.

tril - Extract lower triangular part.

triu - Extract upper triangular part.

fliplr - Flip matrix in left/right direction.flipud - Flip matrix in up/down direction.

flipdim - Flip matrix along specified dimension.

find - Find indices of nonzero elements.

end - Last index.

Special variables and constants

ans - Most recent answer.

realmax - Largest positive floating point number.

realmin - Smallest positive floating point number.

pi - 3.1415926535897....

i, j - Imaginary unit.

inf - Infinity.

NaN - Not-a-Number.

isnan - True for Not-a-Number.

isinf - True for infinite elements.

isfinite - True for finite elements.

Arithmetic operators

plus - Plus +minus - Minus -

mtimes - Matrix multiply *

times - Array multiply .*

mpower - Matrix power ^

power - Array power .^

mldivide - Backslash or left matrix divide \mrdivide - Slash or right matrix divide /

ldivide - Left array divide .\rdivide - Right array divide ./

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Special characters

colon - Colon :

paren - Parentheses and subscripting ( )

paren - Brackets [ ]

paren - Braces and subscripting { }punct - Structure field access .punct - Continuation ...

punct - Separator ,

punct - Semicolon ;

punct - Comment %

punct - Invoke operating system command !

punct - Assignment =

punct - Quote

transpose - Transpose .

ctranspose - Complex conjugate transpose

horzcat - Horizontal concatenation [,]

vertcat - Vertical concatenation [;]

Relational operators

eq - Equal ==

ne - Not equal ~=

lt - Less than

le - Less than or equal =

Logical operators

and - Logical AND &

or - Logical OR |

not - Logical NOT ~

xor - Logical EXCLUSIVE OR

any - True if any element of vector is nonzero

all - True if all elements of vector are nonzero

Set operators

union - Set union.

unique - Set unique.

intersect - Set intersection.

setdiff - Set difference.

setxor - Set exclusive-or.

ismember - True for set member.

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Basic statistical analysis

max - Largest component.

min - Smallest component.

mean - Average or mean value.

median - Median value.std - Standard deviation.

var - Variance.

sort - Sort in ascending order.

sortrows - Sort rows in ascending order.

sum - Sum of elements.

prod - Product of elements.

hist - Histogram.

histc - Histogram count.

cumsum - Cumulative sum of elements.

cumprod - Cumulative product of elements.

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