author | Puneeth Chaganti <punchagan@fossee.in> |
Wed, 01 Dec 2010 16:51:35 +0530 | |
changeset 522 | d33698326409 |
permissions | -rw-r--r-- |
522
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parents:
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1 |
#+LaTeX_CLASS: beamer |
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parents:
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#+LaTeX_CLASS_OPTIONS: [presentation] |
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parents:
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#+BEAMER_FRAME_LEVEL: 1 |
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parents:
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#+BEAMER_HEADER_EXTRA: \usetheme{Warsaw}\usecolortheme{default}\useoutertheme{infolines}\setbeamercovered{transparent} |
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#+COLUMNS: %45ITEM %10BEAMER_env(Env) %10BEAMER_envargs(Env Args) %4BEAMER_col(Col) %8BEAMER_extra(Extra) |
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parents:
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#+PROPERTY: BEAMER_col_ALL 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 :ETC |
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parents:
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#+LaTeX_CLASS: beamer |
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parents:
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#+LaTeX_CLASS_OPTIONS: [presentation] |
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parents:
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#+LaTeX_HEADER: \usepackage[english]{babel} \usepackage{ae,aecompl} |
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#+LaTeX_HEADER: \usepackage{mathpazo,courier,euler} \usepackage[scaled=.95]{helvet} |
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#+LaTeX_HEADER: \usepackage{listings} |
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#+LaTeX_HEADER:\lstset{language=Python, basicstyle=\ttfamily\bfseries, |
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#+LaTeX_HEADER: commentstyle=\color{red}\itshape, stringstyle=\color{darkgreen}, |
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#+LaTeX_HEADER: showstringspaces=false, keywordstyle=\color{blue}\bfseries} |
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#+TITLE: Getting started with symbolics |
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#+AUTHOR: FOSSEE |
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#+EMAIL: |
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#+DATE: |
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#+DESCRIPTION: |
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#+KEYWORDS: |
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#+LANGUAGE: en |
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#+OPTIONS: H:3 num:nil toc:nil \n:nil @:t ::t |:t ^:t -:t f:t *:t <:t |
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#+OPTIONS: TeX:t LaTeX:nil skip:nil d:nil todo:nil pri:nil tags:not-in-toc |
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|
d33698326409
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* Outline |
d33698326409
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parents:
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33 |
- Defining symbolic expressions in sage. |
d33698326409
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Puneeth Chaganti <punchagan@fossee.in>
parents:
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34 |
- Using built-in constants and functions. |
d33698326409
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parents:
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35 |
- Performing Integration, differentiation using sage. |
d33698326409
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parents:
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36 |
- Defining matrices. |
d33698326409
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Puneeth Chaganti <punchagan@fossee.in>
parents:
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37 |
- Defining Symbolic functions. |
d33698326409
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Puneeth Chaganti <punchagan@fossee.in>
parents:
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38 |
- Simplifying and solving symbolic expressions and functions. |
d33698326409
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Puneeth Chaganti <punchagan@fossee.in>
parents:
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39 |
|
d33698326409
Renamed all LOs to match with their names in progress.org.
Puneeth Chaganti <punchagan@fossee.in>
parents:
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40 |
* Question 1 |
d33698326409
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Puneeth Chaganti <punchagan@fossee.in>
parents:
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41 |
- Define the following expression as symbolic |
d33698326409
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Puneeth Chaganti <punchagan@fossee.in>
parents:
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42 |
expression in sage. |
d33698326409
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Puneeth Chaganti <punchagan@fossee.in>
parents:
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43 |
|
d33698326409
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Puneeth Chaganti <punchagan@fossee.in>
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44 |
- x^2+y^2 |
d33698326409
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Puneeth Chaganti <punchagan@fossee.in>
parents:
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45 |
- y^2-4ax |
d33698326409
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Puneeth Chaganti <punchagan@fossee.in>
parents:
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46 |
|
d33698326409
Renamed all LOs to match with their names in progress.org.
Puneeth Chaganti <punchagan@fossee.in>
parents:
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47 |
* Solution 1 |
d33698326409
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Puneeth Chaganti <punchagan@fossee.in>
parents:
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48 |
#+begin_src python |
d33698326409
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parents:
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49 |
var('x,y') |
d33698326409
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Puneeth Chaganti <punchagan@fossee.in>
parents:
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50 |
x^2+y^2 |
d33698326409
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Puneeth Chaganti <punchagan@fossee.in>
parents:
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|
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parents:
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var('a,x,y') |
d33698326409
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Puneeth Chaganti <punchagan@fossee.in>
parents:
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53 |
y^2-4*a*x |
d33698326409
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parents:
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54 |
#+end_src python |
d33698326409
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Puneeth Chaganti <punchagan@fossee.in>
parents:
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55 |
* Question 2 |
d33698326409
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Puneeth Chaganti <punchagan@fossee.in>
parents:
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56 |
- Find the values of the following constants upto 6 digits precision |
d33698326409
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Puneeth Chaganti <punchagan@fossee.in>
parents:
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|
d33698326409
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Puneeth Chaganti <punchagan@fossee.in>
parents:
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58 |
- pi^2 |
d33698326409
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parents:
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59 |
- euler_gamma^2 |
d33698326409
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|
d33698326409
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|
d33698326409
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Puneeth Chaganti <punchagan@fossee.in>
parents:
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62 |
- Find the value of the following. |
d33698326409
Renamed all LOs to match with their names in progress.org.
Puneeth Chaganti <punchagan@fossee.in>
parents:
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|
d33698326409
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Puneeth Chaganti <punchagan@fossee.in>
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- sin(pi/4) |
d33698326409
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parents:
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65 |
- ln(23) |
d33698326409
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Puneeth Chaganti <punchagan@fossee.in>
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66 |
|
d33698326409
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67 |
* Solution 2 |
d33698326409
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parents:
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68 |
#+begin_src python |
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69 |
n(pi^2,digits=6) |
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70 |
n(sin(pi/4)) |
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n(log(23,e)) |
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72 |
#+end_src python |
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73 |
* Question 3 |
d33698326409
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- Define the piecewise function. |
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f(x)=3x+2 |
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when x is in the closed interval 0 to 4. |
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f(x)=4x^2 |
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between 4 to 6. |
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|
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- Sum of 1/(n^2-1) where n ranges from 1 to infinity. |
d33698326409
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|
d33698326409
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82 |
* Solution 3 |
d33698326409
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parents:
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83 |
#+begin_src python |
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84 |
var('x') |
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85 |
h(x)=3*x+2 |
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g(x)= 4*x^2 |
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f=Piecewise([[(0,4),h(x)],[(4,6),g(x)]],x) |
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88 |
f |
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89 |
#+end_src python |
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|
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91 |
#+begin_src python |
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92 |
var('n') |
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93 |
f=1/(n^2-1) |
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94 |
sum(f(n), n, 1, oo) |
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parents:
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95 |
#+end_src python |
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96 |
|
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97 |
* Question 4 |
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parents:
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98 |
- Differentiate the following. |
d33698326409
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Puneeth Chaganti <punchagan@fossee.in>
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99 |
|
d33698326409
Renamed all LOs to match with their names in progress.org.
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100 |
- sin(x^3)+log(3x), to the second order |
d33698326409
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parents:
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101 |
- x^5*log(x^7), to the fourth order |
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102 |
|
d33698326409
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103 |
- Integrate the given expression |
d33698326409
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104 |
|
d33698326409
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105 |
- x*sin(x^2) |
d33698326409
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106 |
|
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107 |
- Find x |
d33698326409
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parents:
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108 |
- cos(x^2)-log(x)=0 |
d33698326409
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parents:
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109 |
- Does the equation have a root between 1,2. |
d33698326409
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110 |
|
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Puneeth Chaganti <punchagan@fossee.in>
parents:
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111 |
* Solution 4 |
d33698326409
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Puneeth Chaganti <punchagan@fossee.in>
parents:
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112 |
#+begin_src python |
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113 |
var('x') |
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f(x)= x^5*log(x^7) |
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115 |
diff(f(x),x,5) |
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116 |
|
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117 |
var('x') |
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118 |
integral(x*sin(x^2),x) |
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119 |
|
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120 |
var('x') |
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f=cos(x^2)-log(x) |
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find_root(f(x)==0,1,2) |
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123 |
#+end_src |
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124 |
|
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125 |
* Question 5 |
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126 |
- Find the determinant and inverse of : |
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127 |
|
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A=[[x,0,1][y,1,0][z,0,y]] |
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129 |
|
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130 |
* Solution 5 |
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131 |
#+begin_src python |
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132 |
var('x,y,z') |
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A=matrix([[x,0,1],[y,1,0],[z,0,y]]) |
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134 |
A.det() |
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A.inverse() |
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136 |
#+end_src |
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137 |
* Summary |
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138 |
- We learnt about defining symbolic expression and functions. |
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139 |
- Using built-in constants and functions. |
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140 |
- Using <Tab> to see the documentation of a function. |
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141 |
- Simple calculus operations . |
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142 |
- Substituting values in expression using substitute function. |
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143 |
- Creating symbolic matrices and performing operation on them . |
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144 |
* Thank you! |
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145 |
#+begin_latex |
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146 |
\begin{block}{} |
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147 |
\begin{center} |
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148 |
This spoken tutorial has been produced by the |
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\textcolor{blue}{FOSSEE} team, which is funded by the |
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150 |
\end{center} |
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151 |
\begin{center} |
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\textcolor{blue}{National Mission on Education through \\ |
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153 |
Information \& Communication Technology \\ |
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154 |
MHRD, Govt. of India}. |
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155 |
\end{center} |
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156 |
\end{block} |
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157 |
#+end_latex |
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158 |
|
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159 |
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160 |