# HG changeset patch # User Amit Sethi # Date 1289390118 -19800 # Node ID 79a7ca3073d4bd51addb4f889ed001213255d8d1 # Parent a9b71932cbfaf8d1aea641feb24163dde9feb2bf# Parent b2e8522839f00b7c2e3debae667e2e1d7648f651 Merging heads diff -r b2e8522839f0 -r 79a7ca3073d4 getting-started-with-lists/script.rst --- a/getting-started-with-lists/script.rst Wed Nov 10 14:02:46 2010 +0530 +++ b/getting-started-with-lists/script.rst Wed Nov 10 17:25:18 2010 +0530 @@ -46,7 +46,7 @@ List is a compound data type, it can contain data of other data types. List is also a sequence data type, all the elements are in -order and there order has a meaning. +order and the order has a meaning. .. #[[Anoop: "all the elements are in order and **there** order has a meaning." - I guess something is wrong here, I am not able to @@ -75,15 +75,14 @@ As we can see lists can contain different kinds of data. In the previous example 'spam' and 'eggs' are strings and 100 and 1.234 are integer and float. Thus we can put elements of heterogenous types in -lists. Thus list themselves can be one of the element types possible -in lists. Thus lists can also contain other lists. +lists including list itself. .. #[[Anoop: the sentence "Thus list themselves can be one of the element types possible in lists" is not clear, rephrase it.]] Example :: - list_in_list=[[4,2,3,4],'and', 1, 2, 3, 4] + listinlist=[[4,2,3,4],'and', 1, 2, 3, 4] We access list elements using the index. The index begins from 0. So for list nonempty, nonempty[0] gives the first element, nonempty[1] @@ -93,11 +92,20 @@ nonempty[1] nonempty[3] +Following is an exercise that you must do. + +%% %% What happens when you do nonempty[-1]. + +Please, pause the video here. Do the exercise and then continue. + .. #[[Anoop: was negative indices introduced earlier, if not may be we can ask them to try out nonempty[-1] and see what happens and then tell that it gives the last element in the list.]] -We can also access the elememts from the end using negative indices :: +As you can see you get the last element which is 1.234. + + +In python negative indices are used to access elements from the end:: nonempty[-1] nonempty[-2] @@ -113,6 +121,19 @@ nonempty.append(6) nonempty +Following are exercises that you must do. + +%% %% What is the syntax to get the element 'and' +in the list,listinlist ? + + +%% %% How would you get 'and' using negative indices? + +Please, pause the video here. Do the exercise and then continue. + +The solution is on your screen + + As we can see non empty appends 'onemore' and 6 at the end. Using len function we can check the number of elements in the list @@ -148,20 +169,34 @@ but what if there were two 100's. To check that lets do a small experiment. :: - nonempty.append('python') + nonempty.append('spam') nonempty - nonempty.remove('python') + nonempty.remove('spam') nonempty If we check now we will see that the first occurence 'spam' is removed thus remove removes the first occurence of the element in the sequence and leaves others untouched. + + + + .. #[[Anoop: does it have two spams or two pythons?]] .. #[[Anoop: there are no exercises/solved problems in this script, add them]] +Following are exercises that you must do. + +%% %% Remove the third element from the list, listinlist. + +%% %% Remove 'and' from the list, listinlist. + +Please, pause the video here. Do the exercise and then continue. + + + {{{Slide for Summary }}} diff -r b2e8522839f0 -r 79a7ca3073d4 getting-started-with-lists/script.rst.orig --- a/getting-started-with-lists/script.rst.orig Wed Nov 10 14:02:46 2010 +0530 +++ b/getting-started-with-lists/script.rst.orig Wed Nov 10 17:25:18 2010 +0530 @@ -1,361 +1,224 @@ - - - - - - - - - - -
+As you can see you get the last element which is 1.234. -
-

Objective Questions

- -
    -

  1. How do you create an empty list?

    -
    -empty=[]
-
    -
    2. -

  2. What is the most important property of sequence data types like lists?

    -

    The elements are in order and can be accessed by index numbers.

    -
    3. -

  3. Can you have a list inside a list ?

    -

    Yes,List can contain all the other data types, including list.

    -

    Example: -list_in_list=[2.3,[2,4,6],'string,'all datatypes can be there']

    -
    4. -

  4. What is the index number of the first element in a list?

    -

    0 -nonempty = ['spam', 'eggs', 100, 1.234] -nonempty[0]

    -
    5. -

  5. How would you access the end of a list without finding its length?

    -

    Using negative indices. We can the list from the end using negative indices.

    -

    :: -nonempty = ['spam', 'eggs', 100, 1.234] -nonempty[-1]

    -
    6. -

  6. What is the function to find the length of a list?

    -

    len

    -
    7. -

  7. Delete the last element from list sq=[5,4,3,2,1,0]

    -

    del(sq[-1])

    -
    8. -

  8. How many will you have to use remove function to remove all 6's from the given list sq=[2,5,6,7,6,4,6]?

    -

    3

    -
    9. -
-
-
-

Larger Questions

- -

1. Add all elemets of seq1=['e','f','g','h'] -to the sequence seq=['a','b','c','d']

-
    -
  1. Delete all elements of seq1=[3,5,6] from sequence -seq=[1,2,3,4,5,6,7,8,9]
    2. -
-
-
- - +In python negative indices are used to access elements from the end:: + + nonempty[-1] + nonempty[-2] + nonempty[-4] + +-1 gives the last element which is the 4th element , -2 second to last +and -4 gives the fourth from last element which is first element. + +We can append elements to the end of a list using append command. :: + + nonempty.append('onemore') + nonempty + nonempty.append(6) + nonempty + +Following are exercises that you must do. + +%% %% What is the syntax to get the element 'and' +in the list,listinlist ? + + +%% %% How would you get 'and' using negative indices? + +Please, pause the video here. Do the exercise and then continue. + +The solution is on your screen + + +As we can see non empty appends 'onemore' and 6 at the end. + +Using len function we can check the number of elements in the list +nonempty. In this case it 6 :: + + len(nonempty) + + + +Just like we can append elements to a list we can also remove them. +There are two ways of doing it. One is by using index. :: + + del(nonempty[1]) + + + +deletes the element at index 1, 'eggs' which is the second element of +the list. The other way is removing element by content. Lets say one +wishes to delete 100 from nonempty list the syntax of the command +should be + +.. #[[Anoop: let x = [1,2,1,3] + now x.remove(x[2]) + still x is [2,1,3] so that is not the way to remove + element by index, it removed first occurrence of 1(by + content) and not based on index, so make necessary + changes]] + +:: + + nonempty.remove(100) + +but what if there were two 100's. To check that lets do a small +experiment. :: + + nonempty.append('spam') + nonempty + nonempty.remove('spam') + nonempty + +If we check now we will see that the first occurence 'spam' is removed +thus remove removes the first occurence of the element in the sequence +and leaves others untouched. + + + + + +.. #[[Anoop: does it have two spams or two pythons?]] + +.. #[[Anoop: there are no exercises/solved problems in this script, + add them]] + +Following are exercises that you must do. + +%% %% Remove the third element from the list, listinlist. + +%% %% Remove 'and' from the list, listinlist. + +Please, pause the video here. Do the exercise and then continue. + + + +{{{Slide for Summary }}} + + +In this tutorial we came across a sequence data type called lists. :: + + * We learned how to create lists. + * How to access lists. + * Append elements to list. + * Delete Element from list. + * And Checking list length. + + + +{{{ show Sponsored by Fossee Slide }}} + +This tutorial was created as a part of FOSSEE project. + +I hope you found this tutorial useful. + +Thank You + +.. + * Author : Amit Sethi + * First Reviewer : + * Second Reviewer : Nishanth diff -r b2e8522839f0 -r 79a7ca3073d4 getting-started-with-lists/slides.org --- a/getting-started-with-lists/slides.org Wed Nov 10 14:02:46 2010 +0530 +++ b/getting-started-with-lists/slides.org Wed Nov 10 17:25:18 2010 +0530 @@ -2,34 +2,99 @@ #+LaTeX_CLASS_OPTIONS: [presentation] #+BEAMER_FRAME_LEVEL: 1 -#+BEAMER_HEADER_EXTRA: \usetheme{Warsaw}\useoutertheme{infolines}\usecolortheme{default}\setbeamercovered{transparent} +#+BEAMER_HEADER_EXTRA: \usetheme{Warsaw}\usecolortheme{default}\useoutertheme{infolines}\setbeamercovered{transparent} #+COLUMNS: %45ITEM %10BEAMER_env(Env) %10BEAMER_envargs(Env Args) %4BEAMER_col(Col) %8BEAMER_extra(Extra) #+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 -#+OPTIONS: H:5 num:t toc:nil \n:nil @:t ::t |:t ^:t -:t f:t *:t <:t + +#+LaTeX_CLASS: beamer +#+LaTeX_CLASS_OPTIONS: [presentation] + +#+LaTeX_HEADER: \usepackage[english]{babel} \usepackage{ae,aecompl} +#+LaTeX_HEADER: \usepackage{mathpazo,courier,euler} \usepackage[scaled=.95]{helvet} + +#+LaTeX_HEADER: \usepackage{listings} + +#+LaTeX_HEADER:\lstset{language=Python, basicstyle=\ttfamily\bfseries, +#+LaTeX_HEADER: commentstyle=\color{red}\itshape, stringstyle=\color{darkgreen}, +#+LaTeX_HEADER: showstringspaces=false, keywordstyle=\color{blue}\bfseries} #+TITLE: Getting started with Lists #+AUTHOR: FOSSEE #+DATE: 2010-09-14 Tue #+EMAIL: info@fossee.in -# \author[FOSSEE] {FOSSEE} +#+DESCRIPTION: +#+KEYWORDS: +#+LANGUAGE: en +#+OPTIONS: H:3 num:nil toc:nil \n:nil @:t ::t |:t ^:t -:t f:t *:t <:t +#+OPTIONS: TeX:t LaTeX:nil skip:nil d:nil todo:nil pri:nil tags:not-in-toc -# \institute[IIT Bombay] {Department of Aerospace Engineering\\IIT Bombay} -# \date{} -* Tutorial Plan -** How to create lists -** Structure of lists -** Access list elements -** Append elements to lists -** Deleting elements from lists +* Outline + - How to create lists + - Structure of lists + - Access list elements + - Append elements to lists + - Deleting elements from lists + + +* Question 1 + - What happens when you do nonempty[-1]. + +* Solution 1 + - It gives the last element , 1.234 + +* Questions + - What is the syntax to get the element 'and' +in the list,listinlist ? + - How would you get 'and' using negative indices? + +* Solutions +#+begin_src python + + listinlist[1] + listinlist[-5] + +#+end_src python +* Questions + + - Remove the third element from the list, listinlist. + + - Remove 'and' from the list, listinlist. + +* Solutions +#+begin_src python + + del(listinlist[2]) + listinlist.remove('and') + +#+end_src python * Summary - +#+begin_src python + l=[1,2,3,4] l[-1] l.append(5) del(l[2]) + l.remove(2) len(l) +#+end_src python +* Thank you! +#+begin_latex + \begin{block}{} + \begin{center} + This spoken tutorial has been produced by the + \textcolor{blue}{FOSSEE} team, which is funded by the + \end{center} + \begin{center} + \textcolor{blue}{National Mission on Education through \\ + Information \& Communication Technology \\ + MHRD, Govt. of India}. + \end{center} + \end{block} +#+end_latex + + diff -r b2e8522839f0 -r 79a7ca3073d4 getting-started-with-lists/slides.tex --- a/getting-started-with-lists/slides.tex Wed Nov 10 14:02:46 2010 +0530 +++ b/getting-started-with-lists/slides.tex Wed Nov 10 17:25:18 2010 +0530 @@ -1,4 +1,4 @@ -% Created 2010-11-09 Tue 17:41 +% Created 2010-11-10 Wed 12:22 \documentclass[presentation]{beamer} \usepackage[latin1]{inputenc} \usepackage[T1]{fontenc} @@ -16,13 +16,19 @@ \usepackage{amssymb} \usepackage{hyperref} \tolerance=1000 +\usepackage[english]{babel} \usepackage{ae,aecompl} +\usepackage{mathpazo,courier,euler} \usepackage[scaled=.95]{helvet} +\usepackage{listings} +\lstset{language=Python, basicstyle=\ttfamily\bfseries, +commentstyle=\color{red}\itshape, stringstyle=\color{darkgreen}, +showstringspaces=false, keywordstyle=\color{blue}\bfseries} \providecommand{\alert}[1]{\textbf{#1}} \title{Getting started with Lists} \author{FOSSEE} \date{2010-09-14 Tue} -\usetheme{Warsaw}\useoutertheme{infolines}\usecolortheme{default}\setbeamercovered{transparent} +\usetheme{Warsaw}\usecolortheme{default}\useoutertheme{infolines}\setbeamercovered{transparent} \begin{document} \maketitle @@ -32,33 +38,112 @@ + + + + \begin{frame} -\frametitle{Tutorial Plan} +\frametitle{Outline} \label{sec-1} -\begin{itemize} -\item How to create lists\\ -\label{sec-1_1}% -\item Structure of lists\\ -\label{sec-1_2}% -\item Access list elements\\ -\label{sec-1_3}% -\item Append elements to lists\\ -\label{sec-1_4}% -\item Deleting elements from lists\\ -\label{sec-1_5}% -\end{itemize} % ends low level +\begin{itemize} +\item How to create lists +\item Structure of lists +\item Access list elements +\item Append elements to lists +\item Deleting elements from lists +\end{itemize} +\end{frame} +\begin{frame} +\frametitle{Question 1} +\label{sec-2} + +\begin{itemize} +\item What happens when you do nonempty[-1]. +\end{itemize} +\end{frame} +\begin{frame} +\frametitle{Solution 1} +\label{sec-3} + +\begin{itemize} +\item It gives the last element , 1.234 +\end{itemize} \end{frame} \begin{frame} -\frametitle{Summary} -\label{sec-2} +\frametitle{Questions} +\label{sec-4} + +\begin{itemize} +\item What is the syntax to get the element `and' +\end{itemize} + +in the list,listinlist ? + + +\begin{itemize} +\item How would you get `and' using negative indices? +\end{itemize} +\end{frame} +\begin{frame}[fragile] +\frametitle{Solutions} +\label{sec-5} + +\begin{verbatim} + +listinlist[1] +listinlist[-5] +\end{verbatim} +\end{frame} +\begin{frame} +\frametitle{Questions} +\label{sec-6} - l=[1,2,3,4] - l[-1] - l.append(5) - del(l\footnote{FOOTNOTE DEFINITION NOT FOUND: 2 }) - len(l) +\begin{itemize} +\item Remove the third element from the list, listinlist. +\item Remove `and' from the list, listinlist. +\end{itemize} +\end{frame} +\begin{frame}[fragile] +\frametitle{Solutions} +\label{sec-7} + +\begin{verbatim} + +del(listinlist[2]) +listinlist.remove('and') +\end{verbatim} +\end{frame} +\begin{frame}[fragile] +\frametitle{Summary} +\label{sec-8} + +\begin{verbatim} + +l=[1,2,3,4] +l[-1] +l.append(5) +del(l[2]) +l.remove(2) +len(l) +\end{verbatim} +\end{frame} +\begin{frame} +\frametitle{Thank you!} +\label{sec-9} + + \begin{block}{} + \begin{center} + This spoken tutorial has been produced by the + \textcolor{blue}{FOSSEE} team, which is funded by the + \end{center} + \begin{center} + \textcolor{blue}{National Mission on Education through \\ + Information \& Communication Technology \\ + MHRD, Govt. of India}. + \end{center} + \end{block} \end{frame} \end{document} diff -r b2e8522839f0 -r 79a7ca3073d4 getting-started-with-symbolics/script.rst --- a/getting-started-with-symbolics/script.rst Wed Nov 10 14:02:46 2010 +0530 +++ b/getting-started-with-symbolics/script.rst Wed Nov 10 17:25:18 2010 +0530 @@ -4,7 +4,7 @@ .. By the end of this tutorial, you will be able to .. 1. Defining symbolic expressions in sage. -.. # Using built-in costants and functions. +.. # Using built-in constants and functions. .. # Performing Integration, differentiation using sage. .. # Defining matrices. .. # Defining Symbolic functions. @@ -37,7 +37,7 @@ {{{ Show outline slide }}} * Defining symbolic expressions in sage. -* Using built-in costants and functions. +* Using built-in constants and functions. * Performing Integration, differentiation using sage. * Defining matrices. * Defining Symbolic functions. @@ -73,26 +73,32 @@ var('x,alpha,y,beta') x^2/alpha^2+y^2/beta^2 -taking another example +taking another example :: var('theta') - sin^2(theta)+cos^2(theta) - + sin(theta)*sin(theta)+cos(theta)*cos(theta) -Similarly, we can define many algebraic and trigonometric expressions -using sage . +Similarly, we can define many algebraic and trigonometric expressions using sage . -Sage also provides a few built-in constants which are commonly used in -mathematics . +Following is an exercise that you must do. -example : pi,e,infinity , Function n gives the numerical values of all these - constants. +%% %% Define following expressions as symbolic expressions +in sage? + + 1. x^2+y^2 + #. y^2-4ax + +Please, pause the video here. Do the exercise and then continue. -{{{ Type n(pi) - n(e) - n(oo) - On the sage notebook }}} +The solution is on your screen. + + +Sage also provides a few built-in constants which are commonly used in mathematics . + +example : pi,e,infinity , Function n gives the numerical values of all these constants. + +{{{ Type n(pi) n(e) n(oo) On the sage notebook }}} @@ -131,6 +137,24 @@ log(e,e) +Following is are exercises that you must do. + +%% %% Find the values of the following constants upto 6 digits precision + + 1. pi^2 + #. euler_gamma^2 + + +%% %% Find the value of the following. + + 1. sin(pi/4) + #. ln(23) + +Please, pause the video here. Do the exercises and then continue. + +The solutions are on your screen. + + Given that we have defined variables like x,y etc .. , We can define an arbitrary function with desired name in the following way.:: @@ -157,13 +181,16 @@ var('x') - h(x)=x^2 g(x)=1 + h(x)=x^2 + g(x)=1 f=Piecewise( {{{ Show the documentation of Piecewise }}} :: - f=Piecewise([[(0,1),h(x)],[(1,2),g(x)]],x) f + f=Piecewise([[(0,1),h(x)],[(1,2),g(x)]],x) + f + @@ -184,9 +211,7 @@ var('n') function('f', n) - f(n) = 1/n^2 - sum(f(n), n, 1, oo) @@ -200,6 +225,18 @@ This series converges to pi/4. +Following are exercises that you must do. + +%% %% Define the piecewise function. + f(x)=3x+2 + when x is in the closed interval 0 to 4. + f(x)=4x^2 + between 4 to 6. + +%% %% Sum of 1/(n^2-1) where n ranges from 1 to infinity. + +Please, pause the video here. Do the exercise(s) and then continue. + Moving on let us see how to perform simple calculus operations using Sage For example lets try an expression first :: @@ -267,6 +304,22 @@ as we can see when we substitute the value the answer is almost = 0 showing the solution we got was correct. +Following is an (are) exercise(s) that you must do. + +%% %% Differentiate the following. + + 1. sin(x^3)+log(3x) , degree=2 + #. x^5*log(x^7) , degree=4 + +%% %% Integrate the given expression + + sin(x^2)+exp(x^3) + +%% %% Find x + cos(x^2)-log(x)=0 + Does the equation have a root between 1,2. + +Please, pause the video here. Do the exercises and then continue. @@ -286,8 +339,18 @@ A.inverse() +Following is an (are) exercise(s) that you must do. -{{{ Part of the notebook with summary }}} +%% %% Find the determinant and inverse of : + + A=[[x,0,1][y,1,0][z,0,y]] + +Please, pause the video here. Do the exercise(s) and then continue. + + + + +{{{ Show the summary slide }}} So in this tutorial we learnt how to diff -r b2e8522839f0 -r 79a7ca3073d4 getting-started-with-symbolics/slides.org --- /dev/null Thu Jan 01 00:00:00 1970 +0000 +++ b/getting-started-with-symbolics/slides.org Wed Nov 10 17:25:18 2010 +0530 @@ -0,0 +1,166 @@ +#+LaTeX_CLASS: beamer +#+LaTeX_CLASS_OPTIONS: [presentation] +#+BEAMER_FRAME_LEVEL: 1 + +#+BEAMER_HEADER_EXTRA: \usetheme{Warsaw}\usecolortheme{default}\useoutertheme{infolines}\setbeamercovered{transparent} +#+COLUMNS: %45ITEM %10BEAMER_env(Env) %10BEAMER_envargs(Env Args) %4BEAMER_col(Col) %8BEAMER_extra(Extra) +#+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 + +#+LaTeX_CLASS: beamer +#+LaTeX_CLASS_OPTIONS: [presentation] + +#+LaTeX_HEADER: \usepackage[english]{babel} \usepackage{ae,aecompl} +#+LaTeX_HEADER: \usepackage{mathpazo,courier,euler} \usepackage[scaled=.95]{helvet} + +#+LaTeX_HEADER: \usepackage{listings} + +#+LaTeX_HEADER:\lstset{language=Python, basicstyle=\ttfamily\bfseries, +#+LaTeX_HEADER: commentstyle=\color{red}\itshape, stringstyle=\color{darkgreen}, +#+LaTeX_HEADER: showstringspaces=false, keywordstyle=\color{blue}\bfseries} + +#+TITLE: Getting started with symbolics +#+AUTHOR: FOSSEE +#+EMAIL: +#+DATE: + +#+DESCRIPTION: +#+KEYWORDS: +#+LANGUAGE: en +#+OPTIONS: H:3 num:nil toc:nil \n:nil @:t ::t |:t ^:t -:t f:t *:t <:t +#+OPTIONS: TeX:t LaTeX:nil skip:nil d:nil todo:nil pri:nil tags:not-in-toc + +* Outline + - Defining symbolic expressions in sage. + - Using built-in constants and functions. + - Performing Integration, differentiation using sage. + - Defining matrices. + - Defining Symbolic functions. + - Simplifying and solving symbolic expressions and functions. + +* Questions 1 + - Define the following expression as symbolic + expression in sage. + + - x^2+y^2 + - y^2-4ax + +* Solutions 1 +#+begin_src python + var('x,y') + x^2+y^2 + + var('a,x,y') + y^2-4*a*x +#+end_src python +* Questions 2 + - Find the values of the following constants upto 6 digits precision + + - pi^2 + + + - Find the value of the following. + + - sin(pi/4) + - ln(23) + +* Solutions 2 +#+begin_src python + n(pi^2,digits=6) + n(sin(pi/4)) + n(log(23,e)) +#+end_src python +* Question 2 + - Define the piecewise function. + f(x)=3x+2 + when x is in the closed interval 0 to 4. + f(x)=4x^2 + between 4 to 6. + + - Sum of 1/(n^2-1) where n ranges from 1 to infinity. + +* Solution Q1 +#+begin_src python + var('x') + h(x)=3*x+2 + g(x)= 4*x^2 + f=Piecewise([[(0,4),h(x)],[(4,6),g(x)]],x) + f +#+end_src python +* Solution Q2 +#+begin_src python + var('n') + f=1/(n^2-1) + sum(f(n), n, 1, oo) +#+end_src python + + +* Questions 3 + - Differentiate the following. + + - x^5*log(x^7) , degree=4 + + - Integrate the given expression + + - x*sin(x^2) + + - Find x + - cos(x^2)-log(x)=0 + - Does the equation have a root between 1,2. + +* Solutions 3 +#+begin_src python + var('x') + f(x)= x^5*log(x^7) + diff(f(x),x,5) + + var('x') + integral(x*sin(x^2),x) + + var('x') + f=cos(x^2)-log(x) + find_root(f(x)==0,1,2) +#+end_src + +* Question 4 + - Find the determinant and inverse of : + + A=[[x,0,1][y,1,0][z,0,y]] + +* Solution 4 +#+begin_src python + var('x,y,z') + A=matrix([[x,0,1],[y,1,0],[z,0,y]]) + A.det() + A.inverse() +#+end_src +* Summary + - We learnt about defining symbolic + expression and functions. + - Using built-in constants and functions. + - Using to see the documentation of a + function. + +* Summary + - Simple calculus operations . + - Substituting values in expression + using substitute function. + - Creating symbolic matrices and + performing operation on them . + +* Thank you! +#+begin_latex + \begin{block}{} + \begin{center} + This spoken tutorial has been produced by the + \textcolor{blue}{FOSSEE} team, which is funded by the + \end{center} + \begin{center} + \textcolor{blue}{National Mission on Education through \\ + Information \& Communication Technology \\ + MHRD, Govt. of India}. + \end{center} + \end{block} +#+end_latex + + + diff -r b2e8522839f0 -r 79a7ca3073d4 getting-started-with-symbolics/slides.tex --- a/getting-started-with-symbolics/slides.tex Wed Nov 10 14:02:46 2010 +0530 +++ b/getting-started-with-symbolics/slides.tex Wed Nov 10 17:25:18 2010 +0530 @@ -1,21 +1,34 @@ -% Created 2010-10-21 Thu 00:06 +% Created 2010-11-10 Wed 17:18 \documentclass[presentation]{beamer} -\usetheme{Warsaw}\useoutertheme{infolines}\usecolortheme{default}\setbeamercovered{transparent} \usepackage[latin1]{inputenc} \usepackage[T1]{fontenc} +\usepackage{fixltx2e} \usepackage{graphicx} \usepackage{longtable} \usepackage{float} \usepackage{wrapfig} \usepackage{soul} +\usepackage{t1enc} +\usepackage{textcomp} +\usepackage{marvosym} +\usepackage{wasysym} +\usepackage{latexsym} \usepackage{amssymb} \usepackage{hyperref} - +\tolerance=1000 +\usepackage[english]{babel} \usepackage{ae,aecompl} +\usepackage{mathpazo,courier,euler} \usepackage[scaled=.95]{helvet} +\usepackage{listings} +\lstset{language=Python, basicstyle=\ttfamily\bfseries, +commentstyle=\color{red}\itshape, stringstyle=\color{darkgreen}, +showstringspaces=false, keywordstyle=\color{blue}\bfseries} +\providecommand{\alert}[1]{\textbf{#1}} -\title{Plotting Data } +\title{Getting started with symbolics} \author{FOSSEE} -\date{2010-09-14 Tue} +\date{} +\usetheme{Warsaw}\usecolortheme{default}\useoutertheme{infolines}\setbeamercovered{transparent} \begin{document} \maketitle @@ -25,43 +38,222 @@ + + + \begin{frame} -\frametitle{Tutorial Plan} +\frametitle{Outline} \label{sec-1} + \begin{itemize} +\item Defining symbolic expressions in sage. +\item Using built-in constants and functions. +\item Performing Integration, differentiation using sage. +\item Defining matrices. +\item Defining Symbolic functions. +\item Simplifying and solving symbolic expressions and functions. +\end{itemize} +\end{frame} +\begin{frame} +\frametitle{Questions 1} +\label{sec-2} + +\begin{itemize} +\item Define the following expression as symbolic + expression in sage. + +\begin{itemize} +\item x$^2$+y$^2$ +\item y$^2$-4ax +\end{itemize} + +\end{itemize} + + +\end{frame} +\begin{frame}[fragile] +\frametitle{Solutions 1} +\label{sec-3} + +\begin{verbatim} +var('x,y') +x^2+y^2 + +var('a,x,y') +y^2-4*a*x +\end{verbatim} +\end{frame} +\begin{frame} +\frametitle{Questions 2} +\label{sec-4} + +\begin{itemize} +\item Find the values of the following constants upto 6 digits precision + +\begin{itemize} +\item pi$^2$ +\end{itemize} + +\item Find the value of the following. + +\begin{itemize} +\item sin(pi/4) +\item ln(23) +\end{itemize} + +\end{itemize} +\end{frame} +\begin{frame}[fragile] +\frametitle{Solutions 2} +\label{sec-5} + +\begin{verbatim} +n(pi^2,digits=6) +n(sin(pi/4)) +n(log(23,e)) +\end{verbatim} +\end{frame} +\begin{frame} +\frametitle{Question 2} +\label{sec-6} -\item Defining symbolic expressions in sage.\\ -\label{sec-1.1}% -\item Using built-in costants and functions.\\ -\label{sec-1.2}% -\item Performing Integration, differentiation using sage.\\ -\label{sec-1.3}% -\item Defining matrices.\\ -\label{sec-1.4}% -\item Defining Symbolic functions.\\ -\label{sec-1.5}% -\item Simplifying and solving symbolic expressions and functions.\\ -\label{sec-1.6}% -\end{itemize} % ends low level +\begin{itemize} +\item Define the piecewise function. + f(x)=3x+2 + when x is in the closed interval 0 to 4. + f(x)=4x$^2$ + between 4 to 6. +\item Sum of 1/(n$^2$-1) where n ranges from 1 to infinity. +\end{itemize} +\end{frame} +\begin{frame}[fragile] +\frametitle{Solution Q1} +\label{sec-7} + +\begin{verbatim} +var('x') +h(x)=3*x+2 +g(x)= 4*x^2 +f=Piecewise([[(0,4),h(x)],[(4,6),g(x)]],x) +f +\end{verbatim} +\end{frame} +\begin{frame}[fragile] +\frametitle{Solution Q2} +\label{sec-8} + +\begin{verbatim} +var('n') +f=1/(n^2-1) +sum(f(n), n, 1, oo) +\end{verbatim} + +\end{frame} +\begin{frame} +\frametitle{Questions 3} +\label{sec-9} + +\begin{itemize} +\item Differentiate the following. + +\begin{itemize} +\item x$^5$*log(x$^7$) , degree=4 +\end{itemize} + +\item Integrate the given expression + +\begin{itemize} +\item x*sin(x$^2$) +\end{itemize} + +\item Find x + +\begin{itemize} +\item cos(x$^2$)-log(x)=0 +\item Does the equation have a root between 1,2. +\end{itemize} + +\end{itemize} +\end{frame} +\begin{frame}[fragile] +\frametitle{Solutions 3} +\label{sec-10} + +\begin{verbatim} +var('x') +f(x)= x^5*log(x^7) +diff(f(x),x,5) + +var('x') +integral(x*sin(x^2),x) + +var('x') +f=cos(x^2)-log(x) +find_root(f(x)==0,1,2) +\end{verbatim} +\end{frame} +\begin{frame} +\frametitle{Question 4} +\label{sec-11} + +\begin{itemize} +\item Find the determinant and inverse of : + + A=[[x,0,1][y,1,0][z,0,y]] +\end{itemize} +\end{frame} +\begin{frame}[fragile] +\frametitle{Solution 4} +\label{sec-12} + +\begin{verbatim} +var('x,y,z') +A=matrix([[x,0,1],[y,1,0],[z,0,y]]) +A.det() +A.inverse() +\end{verbatim} \end{frame} \begin{frame} \frametitle{Summary} -\label{sec-2} +\label{sec-13} + \begin{itemize} +\item We learnt about defining symbolic + expression and functions. +\item Using built-in constants and functions. +\item Using to see the documentation of a + function. +\end{itemize} + + +\end{frame} +\begin{frame} +\frametitle{Summary} +\label{sec-14} -\item We learnt about defining symbolic expression and functions.\\ -\label{sec-2.1}% -\item Using built-in constants and functions.\\ -\label{sec-2.2}% -\item Using to see the documentation of a function.\\ -\label{sec-2.3}% -\item Simple calculus operations .\\ -\label{sec-2.4}% -\item Substituting values in expression using substitute function.\\ -\label{sec-2.5}% -\item Creating symbolic matrices and performing operation on them .\\ -\label{sec-2.6}% -\end{itemize} % ends low level +\begin{itemize} +\item Simple calculus operations . +\item Substituting values in expression + using substitute function. +\item Creating symbolic matrices and + performing operation on them . +\end{itemize} +\end{frame} +\begin{frame} +\frametitle{Thank you!} +\label{sec-15} + + \begin{block}{} + \begin{center} + This spoken tutorial has been produced by the + \textcolor{blue}{FOSSEE} team, which is funded by the + \end{center} + \begin{center} + \textcolor{blue}{National Mission on Education through \\ + Information \& Communication Technology \\ + MHRD, Govt. of India}. + \end{center} + \end{block} \end{frame} \end{document} diff -r b2e8522839f0 -r 79a7ca3073d4 symbolics/slides.org --- a/symbolics/slides.org Wed Nov 10 14:02:46 2010 +0530 +++ /dev/null Thu Jan 01 00:00:00 1970 +0000 @@ -1,33 +0,0 @@ -#+LaTeX_CLASS: beamer -#+LaTeX_CLASS_OPTIONS: [presentation] -#+BEAMER_FRAME_LEVEL: 1 - -#+BEAMER_HEADER_EXTRA: \usetheme{Warsaw}\useoutertheme{infolines}\usecolortheme{default}\setbeamercovered{transparent} -#+COLUMNS: %45ITEM %10BEAMER_env(Env) %10BEAMER_envargs(Env Args) %4BEAMER_col(Col) %8BEAMER_extra(Extra) -#+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 -#+OPTIONS: H:5 num:t toc:nil \n:nil @:t ::t |:t ^:t -:t f:t *:t <:t - -#+TITLE: Plotting Data -#+AUTHOR: FOSSEE -#+DATE: 2010-09-14 Tue -#+EMAIL: info@fossee.in - -# \author[FOSSEE] {FOSSEE} - -# \institute[IIT Bombay] {Department of Aerospace Engineering\\IIT Bombay} -# \date{} - -* Tutorial Plan -** Defining symbolic expressions in sage. -** Using built-in costants and functions. -** Performing Integration, differentiation using sage. -** Defining matrices. -** Defining Symbolic functions. -** Simplifying and solving symbolic expressions and functions. -* Summary -** We learnt about defining symbolic expression and functions. -** Using built-in constants and functions. -** Using to see the documentation of a function. -** Simple calculus operations . -** Substituting values in expression using substitute function. -** Creating symbolic matrices and performing operation on them .