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diff --git a/using_sage/script.rst b/using_sage/script.rst index 03d12e3..1345370 100644 --- a/using_sage/script.rst +++ b/using_sage/script.rst @@ -13,19 +13,12 @@ .. Getting Started -- Sage -.. Author : Puneeth - Internal Reviewer : Anoop Jacob Thomas<anoop@fossee.in> - External Reviewer : - Language Reviewer : Bhanukiran - Checklist OK? : <06-11-2010, Anand, OK> [2010-10-05] - Script ------ .. L1 -{{{ Show the first slide containing title, name of the production -team along with the logo of MHRD }}} +{{{ Show the title slide }}} .. R1 @@ -33,7 +26,7 @@ Hello Friends and Welcome to the tutorial on 'Using Sage'. .. L2 -{{{ show the slide with objectives }}} +{{{ show the 'objectives' slide }}} .. R2 @@ -45,7 +38,7 @@ At the end of this tutorial, you will be able to, .. L3 -{{{ Switch to the pre-requisite slide }}} +{{{ show the 'pre-requisite' slide }}} .. R3 @@ -66,7 +59,8 @@ start is using the command, ``sage --notebook``. .. R5 -To find the limit of the function x*sin(1/x), at x=0, we say +To begin with, let us find the limit of the function x*sin(1/x), at x=0. +To do this we say .. L5 :: @@ -75,7 +69,7 @@ To find the limit of the function x*sin(1/x), at x=0, we say .. R6 -We get the limit to be 0, as expected. +As expected, we get the limit to be 0. It is also possible to limit a point from one direction. For example, let us find the limit of 1/x at x=0, when approaching from @@ -88,6 +82,7 @@ the positive side. .. R7 +We get the limit from positive side. To find the limit from the negative side, we say, .. L7 @@ -95,14 +90,19 @@ To find the limit from the negative side, we say, lim(1/x, x=0, dir='left') +.. L8 + +{{ Show the 'differential expression' slide }} + .. R8 Let us now see how to perform differentiation, using Sage. We shall find the differential of the expression ``exp(sin(x^2))/x`` w.r.t ``x``. For this, we shall first define the expression, and then use the ``diff`` -function to obtain the differential of the expression. +function to obtain the differential of the expression. So, switch to the sage +notebook and type -.. L8 +.. L9 :: var('x') @@ -111,11 +111,19 @@ function to obtain the differential of the expression. .. R9 -We can also obtain the partial differentiation of an expression w.r.t -one of the variables. Let us differentiate the expression -``exp(sin(y - x^2))/x`` w.r.t x and y. +And we get the expected differential of the expression. -.. L9 +.. L10 + +{{{ Show the slide 'Partial Differentiation' }}} + +.. R10 + +We can also obtain the partial differentiation of an expression with one of the +vriables. Let us differentiate the expression +``exp(sin(y - x^2))/x`` w.r.t x and y. Switch to sage notebook and type + +.. L11 :: var('x y') @@ -125,34 +133,39 @@ one of the variables. Let us differentiate the expression diff(f, y) -.. R10 +.. R11 Thus we get our partial differential solution. + +.. L12 + +{{{ Show the 'integration' slide }}} + Now, let us look at integration. We shall use the expression obtained from the differentiation that we calculated before, ``diff(f, y)`` -which gave us the expression ---``e^(sin(-x^2 + y))*cos(-x^2 + y)/x``. +which gave us the expression ---``cos(-x^2 + y)*e^(sin(-x^2 + y))/x``. The ``integrate`` command is used to obtain the integral of an -expression or function. +expression or function. So, switch to sage notebook and type. -.. L10 +.. L13 :: - integrate(e^(sin(-x^2 + y))*cos(-x^2 + y)/x, y) + integrate(cos(-x^2 + y)*e^(sin(-x^2 + y))/x, y) -.. R11 +.. R13 -As we can see,we get back the correct expression. The minus sign being +As we can see, we get back the correct expression. The minus sign being inside or outside the ``sin`` function doesn't change much. Now, let us find the value of the integral between the limits 0 and pi/2. -.. L11 +.. L14 :: integral(e^(sin(-x^2 + y))*cos(-x^2 + y)/x, y, 0, pi/2) -.. R12 +.. R14 Hence we get our solution for the definite integration. Let us now see how to obtain the Taylor expansion of an expression |