Table of Contents -- 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 Δ (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 a[sup(x)], e[sup(x)], and ln x -- 2.14 Applications of Exponential Equations -- 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 Functions -- 2.20 Rate Problem Examples -- 2.21 Differentiating Trigonometric Functions -- 2.22 Inverse Functions and Inverse Trigonometric Functions and Their Derivatives -- 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 the Associated Error -- 3.8 The Integral and the Average Value -- 3.9 Area Below the X-axis, Even and Odd Functions, and The 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 Approximation -- 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 -- A -- B -- C -- D -- E -- F -- G -- H -- I -- J -- L -- M -- N -- O -- P -- Q -- R -- S -- T -- U -- V -- W -- X -- Y -- Z.