A Primer on Scientific Programming with Python by Hans Petter Langtangen

By Hans Petter Langtangen

The e-book serves as a primary advent to laptop programming of medical functions, utilizing the high-level Python language. The exposition is instance- and problem-oriented, the place the purposes are taken from arithmetic, numerical calculus, information, physics, biology, and finance. The booklet teaches "Matlab-style" and procedural programming in addition to object-oriented programming. highschool arithmetic is a required history, and it truly is effective to check classical and numerical one-variable calculus in parallel with analyzing this booklet. along with studying find out how to software pcs, the reader also will the right way to remedy mathematical difficulties, coming up in a variety of branches of technological know-how and engineering, by means of numerical equipment and programming. by way of mixing programming, arithmetic and medical functions, the publication lays a pretty good origin for working towards computational technology.

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Solve an ODE specified on the command line . . Find the body’s position in Exer. 5 . . . . . . Add the effect of air resistance on a ball . . . . Solve an ODE system for an electric circuit . . . 74) . . . Explore predator-prey population interactions . . Formulate a 2nd-order ODE as a system . . . . Solve the system in Exer. 30 in a special case . Enhance the code from Exer. 31 . . . . . . . Make a tool for analyzing oscillatory solutions .

Print ’y(t) is\nthe position of\nour ball’ result in identical output: 13 14 1 Computing with Formulas y(t) is the position of our ball. 2 Computer Science Glossary It is now time to pick up some important words that programmers use when they talk about programming: algorithm, application, assignment, blanks (whitespace), bug, code, code segment, code snippet, debug, debugging, execute, executable, implement, implementation, input, library, operating system, output, statement, syntax, user, verify, and verification.

For this reason, most arithmetic operations involve inaccurate real numbers, resulting in inaccurate calculations. Think of the following two calculations: 1/49 · 49 and 1/51 · 51. 0 as answer in the first case, is because 1/49 is not correctly represented in the computer. Also 1/51 has an inexact representation, but the error does not propagate to the final answer. To summarize, errors21 in floating-point numbers may propagate through mathematical calculations and result in answers that are only approximations to the exact underlying mathematical values.

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