The purpose of this tutorial is to introduce students in APMA 0330(Methods of Applied Mathematics - I) to the computer algebra systemSage. Sage is built out of nearly 100 open-source packages that areunited in a single interface. Sage can be used to study elementary andadvanced, pure and applied mathematics. This includes a huge range ofmathematics including basic algebra, calculus, elementary to veryadvanced number theory, cryptography, numerical computation,commutative algebra, group theory, combinatorics, graph theory, exactlinear algebra and much more. It utilizes various software packagesand seamlessly integrates their functionality into a commonexperience.
Maxima can plot functions and data in two and three dimensions. The Maxima source code can be compiled on many systems, including Windows, Linux, and MacOS X. The source code for all systems and precompiled binaries for Windows and Linux are available at the SourceForge file manager. After you install Snow Leopard you will have to download and install the Mac OS X 10.6.8 Update Combo v1.1 to update Snow Leopard to 10.6.8 and give you access to the App Store. You can purchase Lion by contacting Customer Service: Contacting Apple for support and service - this includes international calling numbers.
The goal of this tutorial is two-fold. On one side, it provides tools to assist in solving problems based on an alternate software, that is free of charge---Sage. Therefore, this tutorial contains many scripts written is Sage. You, as the user, are free to use all codes for your needs, and have the right to distribute this tutorial and refer to this tutorial as long as this tutorial is accredited appropriately. On the other side, this tutorial supplements and accompanies the textbookApplied Differential Equations. The Primary Course by Vladimir Dobrushkin, CRC Press, 2015; http://www.crcpress.com/product/isbn/9781439851043. It contains many examples from real world problems that are used for demonstration and clarification of material presented in the textbook.
In this tutorial, the user learns the essential steps in mathematical modeling, including the identification of state variables, assumptions, the invocation of relevant science or empirical laws, the derivation of the governing differential equations, the avalable methods of solutions, the design of a computational algorithm, the generation of computer graphics, and the effect of the system's parameters. Therefore, the tutorial is an introduction to mathematical modeling with differential equations. Any comments and/or contributions for this tutorial are welcome; you can send your remarks to <Vladimir_Dobrushkin@brown.edu>
- Preface
- Introduction
- Part I:Plotting
- Part II:First Order ODEs
- Integrating factors ▼
- Qualitative analysis ▼
- Part III:Numerical Methods and Applications
- Euler's methods ▼
- Runge--Kutta methods▼
- Multistep methods▼
- Part IV:Second and Higher Order Differential Equations
- ▼
Part IV N:Nonlinear ODEs - Spring problems ▼
- Pendulum ▼
- Part V:Series and Recurrences
- ▼
- Part VI:Laplace Transformation
- Part VII:Boundary Value Problems
Return to computing page for the second course APMA0340
Return to Sage tutorial for the second course APMA0340
Return to the main page for the course APMA0330
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Glossary
I need to download the El Capitan to install on my Mac computer. What is the best place to download the El Capitan dmg or El Capitan iso.
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Comments:
I've been looking for El Capitan for weeks and today I finally managed to get it.
Maxima Download Mac Os X 10.11
The Appstore no longer has OS X El Capitan available to download.
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To solve this issue follow this link: http://bit.ly/ElCaptanOriginalOSX
.
Maxima Download Mac Os X 10.13
The Appstore only has updates but not the original OS. So If you did not download El Capitan before it was removed from the App Store then you will not be able to get it from the Appstore anymore. You can now only download it via alternative sources, Just make sure they are trusted sources though. Hence I recommended the link above.
Hope this helps you also.
@Kate smith, They are illegally selling Apples software !
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Find the official installers here
Infographic over the many versions of OSX/macOS
@katemor Its not true that App Store no longer has El Capitan as download. It does not have it as download, if your Apple-ID has never registered a machine with El Capitan. Otherwise they are still there.
And your link points to a place, which charges $20 for Apple software. Not quite legal..