Cargando…
Calculus using Mathematica /
| Clasificación: | Libro Electrónico |
|---|---|
| Autor principal: | |
| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
Boston :
Academic Press,
�1993.
|
| Temas: | |
| Acceso en línea: | Texto completo |
Tabla de Contenidos:
- Front Cover; Calculus Using Mathematica; Copyright Page; Table of Contents; Contents of Mathematica NoteBooks for Calculus Using Mathematica; Preface; Acknowledgments; CHAPTER 1. Introduction; 1.1. A Mathematica Introduction with aMathcalntro.ma; 1.2. Mathematica on a NeXT; 1.3. Mathematica on a Macintosh; 1.4. Mathematica on DOS Windows (IBM); 1.5. Free Advice; Part 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 Picture2.6. 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 Increments5.1. 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 Rule6.8. 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 Definition8.3. 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