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Diffstat (limited to 'getting-started-with-symbolics')
| -rw-r--r-- | getting-started-with-symbolics/script.rst | 101 | ||||
| -rw-r--r-- | getting-started-with-symbolics/slides.org | 166 | ||||
| -rw-r--r-- | getting-started-with-symbolics/slides.tex | 258 |
3 files changed, 473 insertions, 52 deletions
diff --git a/getting-started-with-symbolics/script.rst b/getting-started-with-symbolics/script.rst index b41ab87..e03d85c 100644 --- a/getting-started-with-symbolics/script.rst +++ b/getting-started-with-symbolics/script.rst @@ -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 @@ During the course of the tutorial we will learn {{{ 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 @@ So let us try :: 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 . +Following is an exercise that you must do. -Sage also provides a few built-in constants which are commonly used in -mathematics . +%% %% 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. + +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. +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 }}} +{{{ Type n(pi) n(e) n(oo) On the sage notebook }}} @@ -131,6 +137,24 @@ lets try some of them out on the sage notebook. 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 @@ screen var('x') - h(x)=x^2 g(x)=1 + h(x)=x^2 + g(x)=1 f=Piecewise(<Tab> {{{ 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 @@ For a convergent series , f(n)=1/n^2 we can say :: var('n') function('f', n) - f(n) = 1/n^2 - sum(f(n), n, 1, oo) @@ -200,6 +225,18 @@ Lets us now try another series :: 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 @@ correct :: 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 @@ Now lets do some of the matrix operations on this matrix A.inverse() +Following is an (are) exercise(s) that you must do. + +%% %% 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. + + + -{{{ Part of the notebook with summary }}} +{{{ Show the summary slide }}} So in this tutorial we learnt how to diff --git a/getting-started-with-symbolics/slides.org b/getting-started-with-symbolics/slides.org new file mode 100644 index 0000000..5ac2471 --- /dev/null +++ b/getting-started-with-symbolics/slides.org @@ -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 <Tab> 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 --git a/getting-started-with-symbolics/slides.tex b/getting-started-with-symbolics/slides.tex index 4fc3634..6ae2851 100644 --- a/getting-started-with-symbolics/slides.tex +++ b/getting-started-with-symbolics/slides.tex @@ -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} + +\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) -\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 +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 <Tab> to see the documentation of a + function. +\end{itemize} + + +\end{frame} +\begin{frame} +\frametitle{Summary} +\label{sec-14} + +\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} -\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 <Tab> 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{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} |