Analysis with Mathematica® : Volume 1: Single Variable Calculus

A computer algebra system such as Mathematica® is able to do much more than just numerics: This text shows how to tackle real mathematical problems from basic analysis. The reader learns how Mathematica® represents domains, qualifiers and limits to implement actual proofs – a requirement to unlock the huge potential of Mathematica® for a variety of applications. * Intertwines knowledge of analysis and Mathematica. * Students learn how to solve mathematical problems with a computer algebra system. * Contains a vast collection of examples and exercises. A Computer Algebra System Such As Mathematica Is Able To Do So Much More Besides Numerics: This Text Shows How To Tackle Real Mathematical Problems From Basic Analysis. The Reader Learns How Mathematica Represents Domains, Qualifiers And Limits To Implement Actual Proofs - A Requirement To Unlock The Huge Potential Of Mathematica For A Variety Of Applications. The book will deal with functions of many variables: differentiation and integration, extrema with a number of digressions to related subjects such as differential equations and differential geometry of curves and surfaces. The background needed for understanding the examples and how to compute in Mathematica will also be discussed. The book deals with functions of many variables: differentiation and integration, extrema with a number of digressions to related subjects such as curves, surfaces and Morse theory. The background needed for understanding the examples and how to compute in Mathematica® will also be discussed. Contents Preface 1. Number systems 2. Recursive sequences, discrete dynamical systems and their limits 3. Series 4. Limits of functions and continuity 5. Differentiation 6. Sequences and series of functions 7. Integration Bibliography Index