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APM2616 - Computer Algebra Summary
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This is a summary of the APM2616 - Computer Algebra module from the University of South Africa
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ContentsUnit 2............................................................................................................................................................. 3
Identifiers and assignments ...................................................................................................................... 3
Input and output ....................................................................................................................................... 3
Types ......................................................................................................................................................... 3
Unit 3............................................................................................................................................................. 4
Simplification and substitution ................................................................................................................. 4
Looping and branching.............................................................................................................................. 5
Unit 4............................................................................................................................................................. 6
Functions ................................................................................................................................................... 6
Differentiation........................................................................................................................................... 7
Integration ................................................................................................................................................ 8
Unit 5............................................................................................................................................................. 8
Data types ................................................................................................................................................. 8
Packages.................................................................................................................................................... 9
Unit 6........................................................................................................................................................... 10
Procedures .............................................................................................................................................. 10
Unit 7........................................................................................................................................................... 11
Algebraic equations ................................................................................................................................ 11
Ordinary differential equations .............................................................................................................. 12
Recurrence relations ............................................................................................................................... 13
Unit 8........................................................................................................................................................... 15
Taylor series ............................................................................................................................................ 15
General series ......................................................................................................................................... 17
Extracting the coefficients of a series ..................................................................................................... 18
Unit 9........................................................................................................................................................... 19
The command: collect............................................................................................................................. 19
The command: combine ......................................................................................................................... 19
The command: rewrite ........................................................................................................................... 20
The command: partfrac .......................................................................................................................... 21
The command: rectform ......................................................................................................................... 22
The command: radsimp .......................................................................................................................... 24
, The command: assume ........................................................................................................................... 24
The command: limit ................................................................................................................................ 26
Unit 10......................................................................................................................................................... 27
Numerical Packages ................................................................................................................................ 27
Linear Algebra: .................................................................................................................................... 27
Solutions of Algebraic Equations or System of Equations: ................................................................. 27
Definite Equations:.............................................................................................................................. 29
Ordinary Differential Equations (ODEs): ............................................................................................. 29
Unit 11......................................................................................................................................................... 31
Graphical Packages (2D).......................................................................................................................... 31
Creating a plot of a given function:..................................................................................................... 31
Scene Options: .................................................................................................................................... 32
Parametric and Other Plots: ............................................................................................................... 32
Other 2D Plots: ........................................................................................................................................ 33
Unit 12......................................................................................................................................................... 36
Graphical Packages (3D).......................................................................................................................... 36
Plots of Function in 3D ........................................................................................................................ 36
Customized Graphs: ............................................................................................................................ 38
Unit 13......................................................................................................................................................... 40
LaTeX (Document Structure)................................................................................................................... 40
Commands (in CMD): .......................................................................................................................... 40
Structure: ............................................................................................................................................ 40
Unit 14......................................................................................................................................................... 42
LaTeX (Mathematical Expressions) ..................................................................................................... 42
MuPAD & LaTeX ...................................................................................................................................... 43
Packages:............................................................................................................................................. 43
Unit 15......................................................................................................................................................... 44
LaTeX (Graphics & Tables) ...................................................................................................................... 44
,APM2616
Unit 2
Identifiers and assignments
Input and output
Protocol(“ex.1”); → will save a human readable file but is not readable by MUPAD
Write(“temp.out”); → will save a session file readable by MUPAD and by humans although
it is NOT in prettyprint
Read(“ex.2”); → used to input a file with commands and will be executed, Note
READPATH must be set
Types
Domtype(a); → using this command will tell you what type the parameter <a> is
DOM_IDENT → an identifier not yet set with assignment
DOM_INT → integer
DOM_RAT → rational
DOM_FLOAT → real number (can convert to float by multiplying by
a float like 1.0
DOM_COMPLEX → any real, rational or int with I is complex
, DOM_STRING → characters enclosed in quotes
DOM_BOOL → values of TURE or FALSE
DOM_LIST → x: = [2.0, I,7, x^2];
DOM_SET → a: = {1,2, x^2, x^3, 2, x^2};
DOM_EXPR → y: = 1 + x^2;
DOM_ARRAY →
DOM_TABLE →
DOM_PROC →
DOM_POLY →
Unit 3
Simplification and substitution
Simplify(f,<exp,ln,sin,cos,sqrt,logic>); → used to simplify expressions where
the first parameter is the expression you are trying to simplify and the optional parameter is used to
restrict attention to a special class of simplification
Expand(f); → is used to transform a product of sums into a sum of products
Factor(f); → used for factoring expressions and polynomials
Normal(f); → expands the numerator and denominator of an expression
Subs(a + b*a, a = 4); → used to substitute a value for an identifier in an expression
Hold(sin); → used to substitute system functions such as sin, cos, etc. It stops the system from
evaluating the function
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