Calculus & Mathematica : part 1 basics, tutorials, and literacy sheets /
Donald P. Brown, Horacio Porta y J. Jerry Uhl.
- Reading, MA : Addison-Wesley Publishing Company, 1991
- xxi; 426 páginas 21 x 27 cm
- Preliminary Edition .
Numbers and algebra. Functions and plotting. Linear growth. Instantaneous growth rates. Using the chain rule to unlock the secrets of logs and exponentials. Using the logarithm to calculational advantage: powers, products and trigonometics functions. The race track principle. The differential equation. Largest and smallest greatest and least, best and worst, a sampler. Tangent lines. Parameters. Circle and curvatures. Higher derivatives, splines and approximations . Area and the integral. Trying to break the code of the integral. Breaking the code of the integral: the fundamental theorem of calculus. Measurements through integration. Measuremen and the models through separation of variables and integrating. Volume measurement. Integration by parts and integration over an infinite interval. Substitutions. Empirical approximations. Approximations by expansions: quotients of ploynomials. Approximation by expansions : integration. Convergence: the explanation of our observations. Error estimates. Power series. Trustworthy plots. Expansion in powers of (x - a)
In two years, Mathematica has already revolutionized the desk tops of mathematicians and scientists all over the world. Pencils and writing paper have been assigned a new role as more and more scientists begin to rely on Mathematica s their calculating tool of choice. Calculus & Mathematica takes this revolution out of the research laboratories and into the classroom. This package is developed completely with Mathematica notebooks that are flexibly designed for structured, partly supervised, self-paced, or even independent study.