# Calculus: Early Transcendental Functions

### Chapter 0: Preliminaries

#### 0.1, "The Real Numbers and the Cartesian Plane"

#### 0.2, "Lines and Functions"

#### 0.3, "Graphing Calculators and Computer Algebra Systems"

#### 0.4, "Trigonometric Functions"

#### 0.5, "Transformations of Functions"

### Chapter 1: Limits and Continuity

#### 1.1, "A Brief Preview of Calculus: Tangent Lines and the Length of a Curve

#### 1.2, "The Concept of Limit"

#### 1.3, "Computation of Limits"

#### 1.4, "Continuity and Its Consequences"

#### 1.5, "Limits Involving Infinity; Asymptotes"

#### 1.6, "Formal Definition of the Limit"

#### 1.7, "Limits and Loss-of-Significance Errors"

### Chapter 2: Differentiation

#### 2.1, "Tangent Lines and Velocity"

#### 2.2, "The Derivative"

#### 2.3, "Computation of Derivatives: The Power Rule"

#### 2.4, "The Product and Quotient Rules"

#### 2.5, "The Chain Rule"

#### 2.6, "Derivatives of Trigonometric Functions"

#### 2.7, "Implicit Differentiation"

#### 2.8, "The Mean Value Theorem"

### Chapter 3: Applications of the Derivative

#### 3.1, "Linear Approximations and Newton's Method""

#### 3.2, "Maximum and Minimum Values"

#### 3.3, "Increasing and Decreasing Functions"

#### 3.4, "Concavity and the Second Derivative Test"

#### 3.5, "Overview of Curve Sketching"

#### 3.6, "Optimization"

#### 3.7, "Related Rates"

#### 3.8, "Rates of Change in Economics and the Sciences"

### Chapter 4: Integration

#### 4.1, "Antiderivatives"

#### 4.2, "Sums and Sigma Notation"

#### 4.3, "Area"

#### 4.4, "The Definite Integral"

#### 4.5, "The Fundamental Theorem of Calculus"

#### 4.6, "Integration by Substitution"

#### 4.7, "Numerical Integration"

### Chapter 5: Applications of the Definite Integral

#### 5.1, "Area Between Curves"

#### 5.2, "Volume: Slicing, Disks and Washers"

#### 5.3, "Volumes by Cylindrical Shells"

#### 5.4, "Arc Length and Surface Area"

#### 5.5, "Projectile Motion"

#### 5.6, "Applications of Integration to Physics and Engineering"

### Chapter 6: Exponentials, Logarithms and Other Transcendental Functions

#### 6.1, "The Natural Logarithm"

#### 6.2, "Inverse Functions"

#### 6.3, "The Exponential Function"

#### 6.4, "The Inverse Trigonometric Functions"

#### 6.5, "The Calculus of the Inverse Trigonometric Functions"

#### 6.6, "The Hyperbolic Functions"

### Chapter 7: Integration Techniques

#### 7.1, "Review of Formulas and Techniques"

#### 7.2, "Integration by Parts"

#### 7.3, "Trigonometric Techniques of Integration"

#### 7.4, "Integration of Rational Functions Using Partial Fractions"

#### 7.5, "Integration Tables and Computer Algebra Systems"

#### 7.6, "Indeterminate Forms and L'Hopital's Rule"

#### 7.7, "Improper Integrals"

#### 7.8, "Probability"

### Chapter 8: First-Order Differential Equations

#### 8.1, "Modeling with Differential Equations"

#### 8.2, "Separable Differential Equations"

#### 8.3, "Direction Fields and Euler's Method"

#### 8.4, "Systems of First-Order Differential Equations"

### Chapter 9: Infinite Series

#### 9.1, "Sequences of Real Numbers"

#### 9.2, "Infinite Series"

#### 9.3, "The Integral and Comparison Tests"

#### 9.4, "Alternating Series"

#### 9.5, "Absolute Convergence and the Ratio Test"

#### 9.6, "Power Series"

#### 9.7, "Taylor Series"

#### 9.8, "Applications of Taylor Series"

#### 9.9, "Fourier Series"

### Chapter 10: Parametric Equations and Polar Coordinates

#### 10.1, "Plane curves and Parametric Equations"

#### 10.2, "Calculus and Parametric Equations"

#### 10.3, "Arc Length and Surface Area in Parametric Equations"

#### 10.4, "Polar Coordinates"

#### 10.5, "Calculus and Polar Coordinates"

#### 10.6, "Conic Sections"

#### 10.7, "Conic Sections in Polar Coordinates"

### Chapter 11: Vectors and the Geometry of Space

#### 11.1, "Vectors in the Plane"

#### 11.2, "Vectors in Space"

#### 11.3, "The Dot Product"

#### 11.4, "The Cross Product"

#### 11.5, "Lines and Planes in Space"

#### 11.6, "Surfaces in Space"

### Chapter 12: Vector-Valued Functions

#### 12.1, "Vector-Valued Functions"

#### 12.2, "The Calculus of Vector-Valued Functions"

#### 12.3, "Motion in Space"

#### 12.4, "Curvature"

#### 12.5, "Tangent and Normal Vectors"

#### 12.6, "Parametric Surfaces"

### Chapter 13: Functions of Several Variables and Partial Differentiation

#### 13.1, "Functions of Several Variables"

#### 13.2, "Limits and Continuity"

#### 13.3, "Partial Derivatives"

#### 13.4, "Tangent Planes and Linear Approximations"

#### 13.5, "The Chain Rule"

#### 13.6, "The Gradient and Directional Derivatives"

#### 13.7, "Extrema of Functions of Several Variables"

#### 13.8, "Constrained Optimization and and Lagrange Multipliers"

### Chapter 14: Multiple Integrals

#### 14.1, "Double Integrals"

#### 14.2, "Area, Volume and Center of Mass"

#### 14.3, "Double Integrals in Polar Coordinates"

#### 14.4, "Surface Area"

#### 14.5, "Triple Integrals"

#### 14.6, "Cylindrical Coordinates"

#### 14.7, "Spherical Coordinates"

#### 14.8, "Change of Variables in Multiple Integrals"

### Chapter 15: Vector Calculus

#### 15.1, "Vector Fields"

#### 15.2, "Line Integrals"

#### 15.3, "Independence of Path and Conservative Vector Fields"

#### 15.4, "Green's Theorem"

#### 15.5, "Curl and Divergence"

#### 15.6, "Surface Integrals"

#### 15.7, "The Divergence Theorem"

#### 15.8, "Stokes' Theorem"

#### 15.9, "Applications of Vector Calculus"

### Chapter 16: Second Order Differential Equations

#### 16.1, Second-Order Equations With Constant Coefficients"

#### 16.2, "Nonhomogeneous Equations: Undetermined Coefficients"

#### 16.3, "Applications of Second-Order Equations"

#### 16.4, "Power Series Solutions of Differential Equations"

#### Appendix A: Proofs of Selected Theorems

#### Appendix B: Answers to Odd-Numbered Exercises