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In collaboration with Wolfram Research, Inc., developers of Mathematica, this marriage of technology and textbook for the calculus classroom takes another leap forward as the calculus textbook itself becomes an electronic tool. This CD-ROM version of both Calculus, Single Variable, Second Edition by Hughes-Hallett, Gleason, et. al., and Multivariable Calculus by McCallum, Hughes-Hallett, Gleason, McCallum, et. al. helps calculus come alive for students. Each copy of Calculus Live runs on a limited kernel of Mathematica which is provided on the CD-ROM.
Macintosh:
System 7.1 or higher
With a Power Macintosh, you will need System 7.1.2 or higher
16 megabytes of RAM minimum
Double-speed CD-ROM drive
VGA color monitor with 256 colors
1. A LIBRARY OF FUNCTIONS 1.1 WHAT'S A FUNCTION? 1.2 LINEAR FUNCTIONS 1.3 EXPONENTIAL FUNCTIONS 1.4 POWER FUNCTIONS 1.5 NOTES ON INVERSE FUNCTIONS 1.6 LOGARITHMS 1.7 THE NUMBER e AND NATURAL LOGARITHMS 1.8 NEW FUNCTIONS FROM OLD 1.9 THE TRIGONOMETRIC FUNCTIONS 1.10 POLYMONIALS AND RATIONAL FUNCTIONS 1.11 INTRODUCTION TO CONTINUITY REVIEW PROBLEMS PROJECTS FOCUS ON THEORY UNDERPINNINGS OF CALCULUS THE BINOMIAL THEOREM COMPLETENESS OF THE REAL NUMBERS 2. KEY CONCEPT: THE DERIVATIVE 2.1 HOW DO WE MEASURE SPEED? 2.2 THE DERIVATIVE AT A POINT 2.3 THE DERIVATIVE FUNCTION 2.4 INTERPRETATIONS OF THE DERIVATIVE 2.5 THE SECOND DERIVATIVE REVIEW PROBLEMS PROJECTS FOCUS ON THEORY LIMITS AND CONTINUITY DIFFERENTIABILITY AND LINEAR APPROXIMATION 3. KEY CONCEPT: THE DEFINITE INTEGRAL 3.1 HOW DO WE MEASURE DISTANCE TRAVELED? 3.2 THE DEFINITE INTEGRAL 3.3 INTERPRETATIONS OF THE DEFINITE INTEGRAL 3.4 THEOREMS ABOUT DEFINITE INTEGRALS REVIEW PROBLEMS PROJECTS FOCUS ON THEORY THE DEFINITE INTEGRAL 4. SHORT-CUTS TO DIFFERENTIATION 4.1 POWERS AND POLYNOMIALS 4.2 THE EXPONENTIAL FUNCTION 4.3 THE PRODUCT AND QUOTIENT RULES 4.4 THE CHAIN RULE 4.5 THE TRIGONOMETRIC FUNCTIONS 4.6 APPLICATIONS OF THE CHAIN RULE 4.7 IMPLICIT FUNCTIONS 4.8 LINEAR APPROXIMATIONS AND LIMITS REVIEW PROBLEMS PROJECTS FOCUS ON PRACTICE DIFFERENTIATION 5. USING THE DERIVATIVE 5.1 USING FIRST AND SECOND DERIVATIVES 5.2 FAMILIES OF CURVES: A QUALITATIVE STUDY 5.3 OPTIMIZATION 5.4 APPLICATIONS TO MARGINALITY 5.5 MORE OPTIMIZATION: INTRODUCTION TO MODELING 5.6 HYPERBOLIC FUNCTIONS REVIEW PROBLEMS PROJECTS FOCUS ON THEORY THEOREMS ABOUT CONTINUOUS AND DIFFERENTIABLE FUNCTIONS 6. CONSTRUCTING ANTIDERIVATIVES 6.1 ANTIDERIVATIVES GRAPHICALLY AND NUMERICALLY 6.2 CONSTRUCTING ANTIDERIVATIVES ANALYTICALLY 6.3 DIFFERENTIAL EQUATIONS 6.4 SECOND FUNDAMENTAL THEOREM OF CALCULUS REVIEW PROBLEMS PROJECTS FOCUS ON MODELING THE EQUATIONS OF MOTION 7. INTEGRATION 7.1 INTEGRATION BY SUBSTITUTION PART I 7.2 INTEGRATION BY SUBSTITUTION: PART II 7.3 INTEGRATION BY PARTS 7.4 TABLES OF INTEGRALS 7.5 APPROXIMATING DEFINITE INTEGRALS 7.6 APPROXIMATION ERRORS AND SIMPSON'S RULE 7.7 IMPROPER INTEGRALS 7.8 MORE IMPROPER INTEGRALS REVIEW PROBLEMS PROJECTS FOCUS ON PRACTICE INTEGRATION 8. USING THE DEFINITE INTEGRAL 8.1 APPLICATIONS TO GEOMETRY 8.2 DENSITY AND CENTER OF MASS 8.3 APPLICATIONS TO PHYSICS 8.4 APPLICATIONS TO ECONOMICS REVIEW PROBLEMS PROJECTS FOCUS ON MODELING DISTRIBUTION FUNCTIONS PROBABILITY AND MORE ON DISTRIBUTIONS 9. APPROXIMATIONS AND SERIES 9.1 TAYLOR POLYNOMIALS AND SERIES 9.2 CONVERGENCE OF SERIES 9.3 FINDING AND USING TAYLOR SERIES 9.4 GEOMETRIC SERIES 9.5 FOURIER SERIES REVIEW PROBLEMS PROJECTS FOCUS ON THEORY CONVERGENCE THEOREMS THE ERROR IN TAYLOR APPROXIMATIONS 10. DIFFERENTIAL EQUATIONS 10.1 WHAT IS A DIFFERENTIAL EQUATION? 10.2 SLOPE FIELDS 10.3 EULER'S METHOD 10.4 SEPARATION OF VARIABLES 10.5 GROWTH AND DECAY 10.6 APPLICATIONS AND MODELING 10.7 MODELS OF POPULATION GROWTH 10.8 SECOND-ORDER DIFFERENTIAL EQUATIONS: OSCILLATIONS 10.9 LINEAR SECOND-ORDER DIFFERENTIAL EQUATIONS REVIEW PROBLEMS PROJECTS 11. FUNCTIONS OF SEVERAL VARIABLES 11.1 FUNCTIONS OF TWO VARIABLES 11.2 A TOUR OF THREE-DIMENSIONAL SPACE 11.3 GRAPHS OF FUNCTIONS OF TWO VARIABLES 11.4 CONTOUR DIAGRAMS 11.5 LINEAR FUNCTIONS 11.6 FUNCTIONS OF MORE THAN TWO VARIABLES REVIEW PROBLEMS PROJECTS FOCUS ON THEORY LIMITS AND CONTINUITY 12. A FUNDAMENTAL TOOL: VECTORS 12.1 DISPLACEMENT VECTORS 12.2 VECTORS IN GENERAL 12.3 THE DOT PRODUCT 12.4 THE CROSS PRODUCT REVIEW PROBLEMS PROJECTS 13. DIFFERENTIATING FUNCTIONS OF MANY VARIABLES 13.1 THE PARTIAL DERIVATIVE 13.2 COMPUTING PARTIAL DERIVATIVES ALGEBRAICALLY 13.3 LOCAL LINEARITY AND THE DIFFERENTIAL 13.4 GRADIENTS AND DIRECTIONAL DERIVATIVES IN THE PLANE 13.5 GRADIENTS AND DIRECTIONAL DERIVATIVES IN SPACE 13.6 THE CHAIN RULE 13.7 SECOND ORDER PARTIAL DERIVATIVES 13.8 TAYLOR APPROXIMATIONS REVIEW PROBLEMS PROJECTS FOCUS ON THEORY DIFFERENTIABILITY 14. OPTIMIZATION: LOCAL AND GLOBAL EXTREMA 14.1 LOCAL EXTREMA 14.2 GLOBAL EXTREMA: UNCONSTRAINED OPTIMIZATION 14.3 CONSTRAINED OPTIMIZATION: LAGRANGE MULTIPLIERS REVIEW PROBLEMS PROJECTS FOCUS ON MODELING THE LAGRANGIAN AND ITS INTERPRETATION 15. INTEGRATING FUNCTIONS OF MANY VARIABLES 15.1 THE DEFINITE INTEGRAL OF A FUNCTION OF TWO VARIABLES 15.2 ITERATED INTEGRALS 15.3 TRIPLE INTEGRALS 15.4 DOUBLE INTEGRALS IN POLAR COORDINATES 15.5 INTEGRALS IN CYLINDRICAL AND SPHERICAL COORDINATES 15.6 APPLICATIONS OF INTEGRATION TO PROBABILITY REVIEW PROBLEMS PROJECTS FOCUS ON THEORY CHANGE OF VARIABLES IN A MULTIPLE INTEGRAL 16. PARAMETERIZED CURVES 16.1 PARAMETERIZED CURVES 16.2 MOTION, VELOCITY, AND ACCELERATION REVIEW PROBLEMS PROJECTS 17. VECTOR FIELDS 17.1 VECTOR FIELDS 17.2 THE FLOW OF A VECTOR FIELD REVIEW PROBLEMS 18. LINE INTEGRALS 18.1 THE IDEA OF A LINE INTEGRAL 18.2 COMPUTING LINE INTEGRALS OVER PARAMETERIZED CURVES 18.3 GRADIENT FIELDS AND PATH-INDEPENDENT FIELDS 18.4 PATH-DEPENDENT VECTOR FIELDS AND GREEN'S THEOREM REVIEW PROBLEMS PROJECTS FOCUS ON THEORY PROOF OF GREEN'S THEOREM 19. FLUX INTEGRALS 19.1 THE IDEA OF A FLUX INTEGRAL 19.2 FLUX INTEGRALS FOR GRAPHS, CYLINDERS, AND SPHERES REVIEW PROBLEMS PROJECTS 20. CALCULUS OF VECTOR FIELDS 20.1 THE DIVERGENCE OF A VECTOR FIELD 20.2 THE DIVERGENCE THEOREM 20.3 THE CURL OF A VECTOR FIELD 20.4 STOKES' THEOREM REVIEW PROBLEMS PROJECTS FOCUS ON THEORY THE THREE FUNDAMENTAL THEOREMS APPENDIX A. POLAR COORDINATES B. COMPLEX NUMBERS C. DETERMINANTS D. PROJECTS ANSWERS TO OFF NUMBER PROBLEMS INDEX