Download Maxima

Maxima
For all I care, at this moment…
Spring 2013
1
Content
•
•
•
•
•
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Special keys and symbols
Arithmetic
Algebra
Calculus
Matrix calculations
Plot
Linear algebra
Spring 2013
2
Arithmetic
;
%
‘’
^
end of command
previous output
repeat previous command
power
Exact(rational) arithmetic
Irrational number kept in symbolic form
Expanding …
Convert to floating point numbers …
Setting (system) floating point precision …
Repeat a previous command …
Spring 2013
3
Assignment
Spring 2013
Variable
List
Function specification
4
Expand, factor, solve
Trigexpand, trigreduce, …
Algebra
Spring 2013
5
Expand/reduce for rational terms
Algebra
Spring 2013
6
Polynomials
Gcdex,
Gfactor
allroots
gcd
Spring 2013
p/gcd q/gcd
7
Derivate, partial derivative
Integral: definite, indefinite, improper
inf
Calculus
Spring 2013
8
Taylor series,
limit,
Calculus
Taylor series:
=
x
?
x  0 sin x
lim
f x   lim
h 0
f x  h   f x 
h
Spring 2013
9
ODE
dy
  y, y (0)  2
dx
Ode2: solves 1st and 2nd order ODE
Ic1, ic2, bc: setting conditions
‘ do not evaluate
d 2 x dx
  x  sin t , x(0)  1, x (0)  0
2
dt
dt
Spring 2013
10
Plot2D
• Data points (xi,yi)
• Function curve y = f(x)
• Parametric curve (x(t), y(t))
Spring 2013
11
Plot2D (cont)
Spring 2013
12
Use solve to solve linear systems
Ex: Least Square Fit
Spring 2013
13
Linear Algebra
Matrix
multiplication
Spring 2013
14
Matrix Factorization
1
1
2
1
1
0
2
1
1
0
2
0
2
0
1
1















2
2
c
4 1  2 1 0  1  2 1 0  1 0 1  4  1 0 1

 

 



 

LU(Doolittle)
LU(Crout)
LDU
b 1 2  1 0 1 2  LLT
2 5 2 1 0 1

 


Symmetric matrix A = LLT(Cholesky)
U
L
Spring 2013
15
1 2 
b

2
5


numerical
Eigen Problems
symbolic
Spring 2013
16
Linear Solvers
Compare with general solver: solve
Spring 2013
17
Use Maxima to …
• Study modified Newton on multiple roots
• Derive PCA …
• Solve symbolic linear systems (give 2
points to get algebraic eqn)
Spring 2013
18
Index
. (matrix multiply)
^ (power)
^^ (matrix power)
‘’ (repeat previous cmd)
: (variable assignment)
:= (function specification)
‘ (defer evaluation)
Allroots
Bfloat
Charpoly
Cholesky
Determinant
Diff
Divide
Echelon
Eigenvalues
Eigenvectors
Expand
Ezgcd
Factor
Fpprec
Gfactor
14,15
Ic1
3
Ic2
14
Integrate
3
Invert
4
Limit
4
Linsolve
10
Lu_factor
7
Matrix
3
Ode2
16
Plot2d
15
Quotient
14
Rank
8
Ratexpand
7
Ratsimp
14
Realroots
16
Remainder
16
Solve
3,6
Taylor
7
Transpose
5,7
Trigexpand
3
Trigreduce
7 Spring 2013
Uniteigenvectors
10
10
8
14
9
17
15
14
10
11,12,13
7
14
6
6
7
7
5,16,17
9
14,15
5
5
17 19