Calculus Using Mathematica

Table of Contents to NoteBooks DiskettePrefaceAcknowledgments Chapter 1. Introduction 1.1. A Mathematica Introduction with aMathcaIntro.ma 1.2. Mathematica on a NeXT 1.3. Mathematica on a Macintosh 1.4. Mathematica on DOS Windows (IBM) 1.5. Free AdvicePart 1 Differentiation in One Variable Chapter 2. Using Calculus to Model Epidemics 2.1. The First Model 2.2. Shortening the Time Steps 2.3. The Continuous Variable Model 2.4. Calculus and the S-I-R Differential Equations 2.5. The Big Picture 2.6. Projects Chapter 3. Numerics, Symbolics and Graphics in Science 3.1. Functions from Formulas 3.2. Types of Explicit Functions 3.3. Logs and Exponentials 3.4. Chaining Variables or Composition of Functions 3.5. Graphics and Formulas 3.6. Graphs without Formulas 3.7. Parameters 3.8. Background on Functional Identities Chapter 4. Linearity vs. Local Linearity 4.1. Linear Approximation of Oxbows 4.2. The Algebra of Microscopes 4.3. Mathematica Increments and Microscopes 4.4. Functions with Kinks and Jumps 4.5. The Cool Canary - Another Kind of Linearity Chapter 5. Direct Computation of Increments 5.1. How Small is Small Enough? 5.2. Derivatives as Limits 5.3. Small, Medium and Large Numbers 5.4. Rigorous Technical Summary 5.5. Increment Computations 5.6. Derivatives of Sine and Cosine 5.7. Continuity and the Derivative 5.8. Instantaneous Rates of Change 5.9. Projects Chapter 6. Symbolic Differentiation 6.1. Rules for Special Functions 6.2. The Superposition Rule 6.3. Symbolic Differentiation with Mathematica 6.4. The Product Rule 6.5. The Expanding House 6.6. The Chain Rule 6.7. Derivatives of Other Exponentials by the Chain Rule 6.8. Derivative of The Natural Logarithm 6.9. Combined Symbolic Rules 6.10. Test Your Differentiation Skills Chapter 7. Basic Applications of Differentiation 7.1. Differentiation with Parameters and Other Variables 7.2. Linked Variables and Related Rates 7.3. Review - Inside the Microscope 7.4. Review - Numerical Increments 7.5. Differentials and The (x,y)-Equation of the Tangent Line Chapter 8. The Natural Logarithm and Exponential 8.1. The Official Definition of the Natural Exponential 8.2. Properties Follow from The Official Definition 8.3. e As a "Natural" Base for Exponentials and Logs 8.4. Growth of Log and Exp Compared with Powers 8.5. Mathematica Limits 8.6. Projects Chapter 9. Graphs and the Derivative 9.1. Planck's Radiation Law 9.2. Graphing and The First Derivative 9.3. The Theorems of Bolzano and Darboux 9.4. Graphing and the Second Derivative 9.5. Another Kind of Graphing from the Slope 9.6. Projects Chapter 10. Velocity, Acceleration and Calculus 10.1. Velocity and the First Derivative 10.2. Acceleration and the Second Derivative 10.3. Galileo's Law of Gravity 10.4. Projects Chapter 11. Maxima and Minima in One Variable 11.1. Critical Points 11.2. Max - min with Endpoints 11.3. Max - min without Endpoints 11.4. Supply and Demand in Economics 11.5. Geometric Max-min Problems 11.6. Max-min with Parameters 11.7. Max-min in S-I-R Epidemics 11.8. Projects Chapter 12. Discrete Dynamical Systems 12.1. Two Models for Price Adjustment by Supply and Demand 12.2. Function Iteration, Equilibria and Cobwebs/indexequilibrium, Discrete 12.3. The Linear System 12.4. Nonlinear Models 12.5.