Calculus using "Mathematica"

Calculus Using Mathematica is intended for college students taking a course in calculus. It teaches the basic skills of differentiation and integration and how to use Mathematica, a scientific software language, to perform very elaborate symbolic and numerical computations. This is a set composed of the core text, science and math projects, and computing software for symbolic manipulation and graphics generation. Topics covered in the core text include an introduction on how to get started with the program, the ideas of independent and dependent variables and parameters in the context of some down-to-earth applications, formulation of the main approximation of differential calculus, and discrete dynamical systems. The fundamental theory of integration, analytical vector geometry, and two dimensional linear dynamical systems are elaborated as well. This publication is intended for beginning college students. Content: Front Matter, Page iii Copyright, Page iv Contents of Mathematica NoteBooks for Calculus Using Mathematica, Pages xv-xxii Preface, Pages xxiii-xxiv Acknowledgments, Page xxv CHAPTER 1 - Introduction, Pages 1-11 CHAPTER 2 - Using Calculus to Model Epidemics, Pages 15-29 CHAPTER 3 - Numerics, Symbolics and Graphics in Science, Pages 31-48 CHAPTER 4 - Linearity vs. Local Linearity, Pages 49-60 CHAPTER 5 - Direct Computation of Increments, Pages 61-84 CHAPTER 6 - Symbolic Differentiation, Pages 85-103 CHAPTER 7 - Basic Applications of Differentiation, Pages 105-122 CHAPTER 8 - The Natural Logarithm and Exponential, Pages 123-135 CHAPTER 9 - Graphs and the Derivative, Pages 137-159 CHAPTER 10 - Velocity, Acceleration and Calculus, Pages 161-168 CHAPTER 11 - Maxima and Minima in One Variable, Pages 169-199 CHAPTER 12 - Discrete Dynamical Systems, Pages 201-220 CHAPTER 13 - Basic Integration, Pages 223-248 CHAPTER 14 - Symbolic Integration, Pages 249-268 CHAPTER 15 - Applications of Integration, Pages 269-282 CHAPTER 16 - Basic Vector Geometry, Pages 285-319 CHAPTER 17 - Analytical Vector Geometry, Pages 321-341 CHAPTER 18 - Linear Functions and Graphs in Several Variables, Pages 343-358 CHAPTER 19 - Differentiation of Functions of Several Variables, Pages 361-387 CHAPTER 20 - Maxima and Minima in Several Variables, Pages 389-410 CHAPTER 21 - Continuous Dynamical Systems, Pages 413-446 CHAPTER 22 - Autonomous Linear Dynamical Systems, Pages 447-467 CHAPTER 23 - Equilibria of Continuous Dynamical Systems, Pages 469-489 CHAPTER 24 - Geometric Series, Pages 493-506 CHAPTER 25 - Power Series, Pages 507-522 CHAPTER 26 - The Edge of Convergence, Pages 523-530 Index, Pages 531-532 This package features "Mathematica NoteBooks" on diskette for symbolic manipulation and graphics generation, and includes a separate "Mathematical Background and Scientific Projects" volume which provides interdisciplinary applications. A casebound textbook is also included.