Calculus Early Transcendentals

Book Cover
Diagnostic Tests
	A: Diagnostic Test: Algebra
	B: Diagnostic Test: Analytic Geometry
	C: Diagnostic Test: Functions
	D: Diagnostic Test: Trigonometry
Chapter 1- Functions and Models
	1.1: Four Ways to Represent a Function
	1.2: Mathematical Models: A Catalog of Essential Functions
	1.3: New Functions from Old Functions
	1.4: Exponential Functions
	1.5: Inverse Functions and Logarithms
	Review
	Principles of Problem Solving
Chapter 2- Limits and Derivatives
	2.1: The Tangent and Velocity Problems
	2.2: The Limit of a Function
	2.3: Calculating Limits Using the Limit Laws
	2.4: The Precise Definition of a Limit
	2.5: Continuity
	2.6: Limits at Infinity; Horizontal Asymptotes
	2.7: Derivatives and Rates of Change
	2.8: The Derivative as a Function
	Review
	Problems Plus
Chapter 3- Differentiation Rules
	3.1: Derivatives of Polynomials and Exponential Functions
	3.2: The Product and Quotient Rules
	3.3: Derivatives of Trigonometric Functions
	3.4: The Chain Rule
	3.5: Implicit Differentiation
	3.6: Derivatives of Logarithmic Functions
	3.7: Rates of Change in the Natural and Social Sciences
	3.8: Exponential Growth and Decay
	3.9: Related Rates
	3.10: Linear Approximations and Differentials
	3.11: Hyperbolic Functions
	Review
	Problems Plus
Chapter 4- Applications of Differentiation
	4.1: Maximum and Minimum Values
	4.2: The Mean Value Theorem
	4.3: How Derivatives Affect the Shape of a Graph
	4.4: Indeterminate Forms and L'Hospital's Rule
	4.5: Summary of Curve Sketching
	4.6: Graphing with Calculus and Calculators
	4.7: Optimization Problems
	4.8: Newton's Method
	4.9: Antiderivatives
	Review
	Problems Plus
Chapter 5- Integrals
	5.1: Areas and Distances
	5.2: The Definite Integral
	5.3: The Fundamental Theorem of Calculus
	5.4: Indefinite Integrals and the Net Change Theorem
	5.5: The Substitution Rule
	Review
	Problems Plus
Chapter 6- Applications of Integration
	6.1: Areas between Curves
	6.2: Volumes
	6.3: Volumes by Cylindrical Shells
	6.4: Work
	6.5: Average Value of a Function
	Review
	Problems Plus
Chapter 7- Techniques of Integration
	7.1: Integration by Parts
	7.2: Trigonometric Integrals
	7.3: Trigonometric Substitution
	7.4: Integration of Rational Functions by Partial Fractions
	7.5: Strategy for Integration
	7.6: Integration Using Tables and Computer Algebra Systems
	7.7: Approximate Integration
	7.8: Improper Integrals
	Review
	Problems Plus
Chapter 8- Further Applications of Integration
	8.1: Arc Length
	8.2: Area of a Surface of Revolution
	8.3: Applications to Physics and Engineering
	8.4: Applications to Economics and Biology
	8.5: Probability
	Review
	Problems Plus
Chapter 9- Differential Equations
	9.1: Modeling with Differential Equations
	9.2: Direction Fields and Euler's Method
	9.3: Separable Equations
	9.4: Models for Population Growth
	9.5: Linear Equations
	9.6: Predator-Prey Systems
	Review
	Problems Plus
Chapter 10- Parametric Equations and Polar Coordinates
	10.1: Curves Defined by Parametric Equations
	10.2: Calculus with Parametric Curves
	10.3: Polar Coordinates
	10.4: Areas and Lengths in Polar Coordinates
	10.5: Conic Sections
	10.6: Conic Sections in Polar Coordinates
	Review
	Problems Plus
Chapter 11- Infinite sequences and Series
	11.1: Sequences
	11.2: Series
	11.3: The Integral Test and Estimates of Sums
	11.4: The Comparison Tests
	11.5: Alternating Series
	11.6: Absolute Convergence and the Ratio and Root Tests
	11.7: Strategy for Testing Series
	11.8: Power Series
	11.9: Representations of Functions as Power Series
	11.10: Taylor and Maclaurin Series
	11.11: Applications of Taylor Polynomials
	Review
	Problems Plus
Chapter 12- Vectors and the Geometry of Space
	12.1: Three-Dimensional Coordinate Systems
	12.2: Vectors
	12.3: The Dot Product
	12.4: The Cross Product
	12.5: Equations of Lines and Planes
	12.6: Cylinders and Quadric Surfaces
	Review
	Problems Plus
Chapter 13- Vector Functions
	13.1: Vector Functions and Space Curves
	13.2: Derivatives and Integrals of Vector Functions
	13.3: Arc Length and Curvature
	13.4: Motion in Space: Velocity and Acceleration
	Review
	Problems Plus
Chapter 14- Partial Derivatives
	14.1: Functions of Several Variables
	14.2: Limits and Continuity
	14.3: Partial Derivatives
	14.4: Tangent Planes and Linear Approximations
	14.5: The Chain Rule
	14.6: Directional Derivatives and the Gradient Vector
	14.7: Maximum and Minimum Values
	14.8: Lagrange Multipliers
	Review
	Problems Plus
Chapter 15- Multiple Integrals
	15.1: Double Integrals over Rectangles
	15.2: Double Integrals over General Regions
	15.3: Double Integrals in Polar Coordinates
	15.4: Applications of Double Integrals
	15.5: Surface Area
	15.6: Triple Integrals
	15.7: Triple Integrals in Cylindrical Coordinates
	15.8: Triple Integrals in Spherical Coordinates
	15.9: Change of Variables in Multiple Integrals
	Review
	Problems Plus
Chapter 16- Vector Calculus
	16.1: Vector Fields
	16.2: Line Integrals
	16.3: The Fundamental Theorem for Line Integrals
	16.4: Green's Theorem
	16.5: Curl and Divergence
	16.6: Parametric Surfaces and Their Areas
	16.7: Surface Integrals
	16.8: Stokes' Theorem
	16.9: The Divergence Theorem
	Review
	Problems Plus
Chapter 17- Second-Order Differential Equations
	17.1: Second-Order Linear Equations
	17.2: Nonhomogeneous Linear Equations
	17.3: Applications of Second-Order Differential Equations
	17.4: Series Solutions
	Review
Appendixes
	A: Numbers, Inequalities, and Absolute Values
	B: Coordinate Geometry and Lines
	C: Graphs of Second-Degree Equations
	D: Trigonometry
	E: Sigma Notation
	G: The Logarithm Defined as an Integral
	H: Complex Numbers