Master Math: Calculus (Master Math Series)

Introduction

Chapter 1. Functions

1.1. Functions: types, properties and definitions 1.2. Exponents and logarithms 1.3. Trigonometric functions 1.4. Circular motion 1.5. Relationship between trigonometric and exponential functions 1.6. Hyperbolic functions 1.7. Polynomial functions 1.8. Functions of more than one variable and contour diagrams 1.9. Coordinate systems 1.10. Complex numbers 1.11. Parabolas, circles, ellipses and hyperbolas

Chapter 2. The Derivative

2.1. The limit 2.2. Continuity 2.3. Differentiability 2.4. The definition of the derivative and rate of change 2.5. D (delta) notation and the definition of the derivative 2.6. Slope of a tangent line and the definition of the derivative 2.7. Velocity, distance, slope, area and the definition of the derivative 2.8. Evaluating derivatives of constants and linear functions 2.9. Evaluating derivatives using the derivative formula 2.10. The derivatives of a variable, a constant with a variable, a constant with a function and a variable raised to a power 2.11. Examples of differentiating using the derivative formula 2.12. Derivatives of powers of functions 2.13. Derivatives of ax, ex and ln x 2.14. Applications of exponential equation 2.15. Differentiating sums, differences and polynomials 2.16. Taking second derivatives 2.17. Derivatives of products: the product rule 2.18. Derivatives of quotients: the quotient rule 2.19. The chain rule for differentiating complicated functions9 2.20. Rate problem examples 2.21. Differentiating trigonometric functions 2.22. Inverse functions and inverse trigonometric functions and their derivatives8 2.23. Differentiating hyperbolic functions 2.24. Differentiating multivariable functions 2.25. Differentiation of implicit vs. explicit functions 2.26. Selected rules of differentiation 2.27. Minimum, maximum and the first and second derivatives 2.28. Notes on local linearity, approximating slope of curve and numerical methods

Chapter 3. The Integral

3.1. Introduction 3.2. Sums and sigma notation 3.3. The antiderivative or indefinite integral and the integral formula 3.4. The definite integral and the Fundamental Theorem of Calculus 3.5. Improper integrals 3.6. The integral and the area under a curve 3.7. Estimating integrals using sums and associated error 3.8. The integral and the average value 3.9. Area below the X-axis, even and odd functions and their integrals 3.10. Integrating a function and a constant, the sum of functions, a polynomial, and properties of integrals 3.11. Multiple integrals 3.12. Examples of common integrals 3.13. Integrals describing length 3.14. Integrals describing area 3.15. Integrals describing volume 3.16. Changing coordinates and variables 3.17. Applications of the integral 3.18. Evaluating integrals using integration by parts 3.19. Evaluating integrals using substitution 3.20. Evaluating integrals using partial fractions 3.21. Evaluating integrals using tables

Chapter 4. Series and Approximations

4.1. Sequences, progressions and series 4.2. Infinite series and tests for convergence 4.3. Expanding functions into series, the power series, Taylor series, Maclaurin series, and the binomial expansion

Chapter 5. Vectors, Matrices, Curves, Surfaces and Motion

5.1. Introduction to vectors 5.2. Introduction to matrices 5.3. Multiplication of vectors and matrices 5.4. Dot or scalar products 5.5. Vector or cross product 5.6. Summary of determinants 5.7. Matrices and linear algebra 5.8. The position vector, parametric equations, curves and surfaces 5.9. Motion, velocity and acceleration

Chapter 6. Partial Derivatives

6.1. Partial derivatives: representation and evaluation 6.2. The chain rule 6.3. Representation on a graph 6.4. Local linearity, linear approximations, quadratic approximations and differentials 6.5. Directional derivative and gradient 6.6. Minima, maxima and optimization

Chapter 7. Vector Calculus

7.1. Summary of scalars, vectors, the directional derivative and the gradient 7.2. Vector fields and field lines 7.3. Line integrals and conservative vector fields 7.4. Green's Theorem: tangent and normal (flux) forms 7.5. Surface integrals and flux 7.6. Divergence 7.7. Curl 7.8. Stokes' Theorem

Chapter 8. Introduction to Differential Equations

8.1. First-order differential equations 8.2. Second-order linear differential equations 8.3. Higher-order linear differential equations 8.4. Series solutions to differential equations 8.5. Systems of differential equations 8.6. Laplace transform method 8.7. Numerical methods for solving differential equations 8.8. Partial differential equations

Index


Talk the talk   January 23, 2000
15 out of 18 found this review helpful

This is a good book for calculus refrence, but not for explanations. If you already know calculus, this is a good book to use to brush up with. Just don't expect to use this book to understand calc.