Multivariable Calculus with Maxima - G. Jay Kerns

1 Multivariable Calculus with MaximaG. Jay KernsDecember 1, 2009 The following is a short guide to Multivariable Calculus with Maxima . It loosely followsthe treatment of Stewart sCalculus, Seventh Edition. Refer there for definitions, theorems,proofs, explanations, and exercises. The simple goal of this guide is to demonstrate how touse Maxima to solve problems in that was originally written for the students in my third semester Calculus class, but onceit grew past twenty pages I thought it might be of interest to awider audience. Here it is. Iam releasing this as a FREE document, and other people are freeto build on this to makeit better.

2 The source for this document is located ~gkerns/ Maxima /It was inspired byMaxima by Exampleby Edwin Woollett,A Maxima Guide for CalculusStudentsby Moses Glasner, andTutorial on Maximaby unknown. I also received help fromthe Maxima mailing list archives and volunteer responses tomy questions. Thanks to all ofthose Getting How to Installimaximafor Microsoft Windowsr.. Install the software.. Configure your system.. 52 Three Dimensional Vectors and Linear algebra .. Lines, Planes, and Quadric Surfaces.. vector Valued Functions.. Arc Length and Curvature.

3 193 Functions of Several Partial Derivatives.. Linear Approximation and Differentials.. Chain Rule and Implicit Differentiation.. Directional Derivatives and the Gradient.. Optimization and Local Extrema.. Lagrange Multipliers.. 324 Multiple Double Integrals.. Integration in Polar Coordinates.. Triple Integrals.. Integrals in Cylindrical and Spherical Coordinates.. Change of Variables.. 365 vector vector Fields.. Line Integrals.. Conservative vector Fields and Finding Scalar Potentials.. 416 Saving your plots.. Saving your Maxima commands.

4 447 GNU Free Documentation License452 Copyrightc 2009 G. Jay KernsPermission is granted to copy, distribute and/or modify this document under the terms ofthe GNU Free Documentation License, Version or any laterversion published by the FreeSoftware Foundation; with no Invariant Sections, no Front-Cover Texts, and no Back-CoverTexts. A copy of the license is included in the section entitled GNU Free DocumentationLicense .31 Getting MaximaThere are many ways to get Maxima , and the choices are governed somewhat by the user soperating system (although Maxima proper is platform independent).

5 The home page forMaxima (which has links to download from SourceForge) document was written with Emaxima on GNU-Emacs. Emacs is a powerful texteditor, and Emaxima uses Emacs to integrate Maxima input/output with LATEX code toproduce documents that look like they could have come from a textbook. That s why themathematical expressions below are so pretty. See the following link to learn more you do not want to write a paper but just want to work with Maxima interactivelythen another option isimaxima, which also works with Emacs and LATEX (and Ghostscript) totypeset Maxima input/output professionally.

6 To learn moreaboutimaximasee the option that exists is TeXmacs, but I do not have much experience with it. Fromwhat I can gather it has a good How to Installimaximafor Microsoft WindowsrThe following instructions are to set upimaximaon a computer with a Microsoft Windowsroperating system (the majority of users). If you are runningMac-OS then instead go ,and if you are running Linux (like me) you can go note that these instructions are NOT needed to install plain-old Maxima . Itis already installed in Cushwa 1062, and you can install it athome with the Maxima instructions in the next Install the softwareIn order to take advantage of the full power ofimaximayou need several (pronounced MICK - teck ) is an up-to-date implementationof TEX andrelated programs for Windowsr.

7 Its official web site You can click theDownloadbutton of theBasic MiKTeX Installeron that page. You may save anywhere,such as the Desktop. Start the installation with a double-click. You need to install itin the default Ghostscript main page for Ghostscript ~ghost/.To download the latest Ghostscript compiled for Windowsr, you go ~ghost/doc/ the middle of the page there there is a link to the file you need. (or the latest release; if you have a 64-bit system then you will ,and if you do not know what I am talking about then you probablydo not need the64-bit version). You can double click the to start theinstallation.

8 You need to install it in the default , and scroll down totheMaxima-Windowssection. (or the latest release) for thedownload of a Windowsrpre-compiled binary installer. Double click the to start installation. You need to install it in the default a very powerful text editor. The very official precompiled release can be However, the distributed pre-compiled binary does NOT support image features, hence it isnot good enough forimaxima, by default. Thanks to Vincent Goulet, however, you can obtain a precom-piled binary installer which has everything you need to useimaxima. Go to the download.

9 Just follow the instructions and install itin the default Configure your systemOnce you have installed all of the above, go to theStart Menuunder GNU Emacs and clickUpdate Site Configuration. In the file that opens add the following single line (and it has tobeexactlyright) to the top of the file and click theSavebutton. Note that there shouldn tbe any line break; it is one, big, long, line.(load "C:/ Program Files/ Maxima share/ Maxima emacs/setup -imaxima ")If you have installed a different version of Maxima then twice inthe above line should be replaced with the version you have quit Emacs and restart.

10 When it opens, type:5M-x imaximaThe symbolMmeans theAltkey (which is also known as theMetakey). Thus, thecommandM-x imaximameans1. Hold down theAltkey and Let go, then typeimaxima, then this is your first time usingimaxima, MikTEX will probably ask you to install themhpackage from CTAN. Please proceed withYesfor installation. This may take some time, sobe , you will see the initial screen of Maxima . Enjoy!!2 Three Dimensional Vectors and Linear AlgebraWe set up vectors in a way which is slightly different from how we do it in Maple.(%i1)a: [1,2,3];(%o1)[1,2,3](%i2)b: [2,-1,4];(%o2)[2, 1,4]We can do the standard addition and scalar multiplication ofvectors.