Animating calculus: Mathematica notebooks for the laboratory, Volume 1
Animating Calculus is designed to help you explore calculus and visualize concepts through the use of computation and animation. This collection of 22 labs, together with the computer algebra system Mathematica, can be used for self-study, demonstration, or as a laboratory supplement to an existing calculus sequence. Standard calculus topics as well as new and unusual extensions and applications are presented, including derivatives and rate of change, calculus and landing airplanes, population dynamics and iteration, the fundamental theorem, The Buffon needle problem, numerical and symbolic integration, rolling wheels (round and square), subtleties of the harmonic series, and more.
Animating Calculus includes exercises and demonstrations that focus on important and fundamental ideas and applications rather than the everyday mechanics of a computer algebra system. Sophisticated animations are used to clarify geometric concepts in calculus. In addition, discussions of numerical and graphical pitfalls help the student to understand the importance of verifying results.
Originally published by W. H. Freeman, this new TELOS edition of Animating Calculus includes the full set of labs for DOS/Windows as well as Macintosh platforms.
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ADDITIONAL EXERCISES Exercise algebraic alternating harmonic series angle animation antiderivative approach path approximation area accumulation function binomial calculus cell compute constant convergence Cos[t curve cycloid defined definite integral denote derivative diagram differential equation digits dominoes error Euler's method evaluate example Exercise 11 Exercise 4(a Exercise 9 explain extrema f[x_ Figure FindRoot fixed point following command formula function f(x fundamental theorem geometric series graph graphic guess H Exercise happens harmonic numbers harmonic stack Hint histogram horizontal ideas improper integral infinite infinity interval iteration l'Hopital's rule limit Log[n logarithm look Mathematica techniques discussed Mathematical movie needle negative NestList Newton's method obtained option orbit output parametric plot partial sums PlotRange->All polar plot probability radians radius real number rearranged rectangles rolling rule shows Sin[t solution Solve speed symbolic Taylor polynomial Taylor series TELOS trapezoidal rule trapezoids true value variable velocity wheel zero