E77: INTRODUCTION TO COMPUTER PROGRAMMING FOR SCIENTISTS AND ENGINEERS

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E77 INTRODUCTION TO COMPUTER PROGRAMMING FOR
SCIENTISTS AND ENGINEERS

• Lecture Outline
• 1. The concept of a function
• 2. MATLAB functions
• 3. User-defined functions in MATLAB

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The concept of a function

• 1. The concept of a function
• A broad definition of a function a rule which
  assigns a set
• of known quantities (the input data) to a set
  of outcomes
• (the output data).

3
The concept of a function

• 1. The concept of a function
• A broad definition of a function a rule which
  assigns a set
• of known quantities (the input data) to a set
  of outcomes
• (the output data).
• Symbolically

4
The concept of a function

• 1. The concept of a function
• A broad definition of a function a rule which
  assigns a set
• of known quantities (the input data) to a set
  of outcomes
• (the output data).
• Symbolically

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The concept of a function

• Pictorially
• Input/output data can be of various types, e.g.,
  numbers,
• strings, arrays, etc.

x1
y1
x2
y2
FUNCTION
.
.
.
.
xn
ym
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MATLAB functions

• 2. MATLAB functions
• MATLAB contains a number of useful functions,
  such as
• Simple mathematical functions (e.g., sin, atan,
• log, exp, sqrt, abs)
• Array functions (e.g., size, sort, sum, max)
• String functions (e.g., strmatch, upper)
• Cell functions (e.g., celldisp, cellplot)
• Structure functions (e.g., fieldnames, rmfield)

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MATLAB functions

• Existing MATLAB functions are distinguished into
  two
• categories
• Built-in functions (i.e., implemented in a
  programming
• language other than MATLAB)
• MATLAB-programmed functions
• MATLAB-programmed functions are contained in
  M-files
• which include a description of the function and
  all MATLAB
• instructions needed to perform the requisite
  operations.
• Use the type command to access the M-file that
  contains
• a MATLAB-programmed function.

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User-defined functions in MATLAB

• 3. User-defined functions in MATLAB
• One of the most powerful features in MATLAB is
  the ability
• to create user functions. Some important rules
• Function files must always possess the extension
  .m
• (function M-files)
• Functions can call other functions!
• Unlike script files, all variables in a function
  file are by
• default local, namely they are neither
  recognized nor
• stored in the MATLAB workspace.

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User-defined functions in MATLAB

• There exist several efficient ways to evaluate an
  existing or
• user-defined function xyz123, where x1,x2,...,xn
• are the input arguments
• Simply type xyz123(x1,x2,...,xn).
• Type feval('xyz123',x1,x2,...,xn),
• where the function is identified by the
  character string
• 'xyz123'.
• Type feval(_at_xyz123,x1,x2,...,xn),
• where the function is identified by the function
  handle
• _at_xyz123. Function handles are MATLAB data types
• used in referencing functions.

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User-defined functions in MATLAB

• Example 1 A function fun1 that evaluates
• INSERT EQN
• for any given real number x.
• Example 2 A function fun2 that prints
• I LIKE X BECAUSE IT IS Y
• on the screen, for any given strings X and Y.
• Example 3 A function fun3 that inputs a
  two-dimensional
• array A and outputs the maximum and minimum
  values
• over all of its elements.
• Example 4 A function fun4 plotting the motion of
  a
• projectile.

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Summary

• What did we learn today?
• Functions are understood as rules that use
  existing
• information (input) to produce new information
  (output).
• A large number of scientific problems can be cast
  in
• the form of function development and evaluation.
• MATLAB already contains a large number of useful
• functions, both built-in and MATLAB-programmed.
• User-defined functions can be easily written in
• MATLAB and constitute a powerful programming
  tool.
• All variables inside a MATLAB function are
  treated by
• default as local.