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1.1 Review of Functions
1.2 Basic Classes of Functions
1.3 Trigonometric Functions
1.4 Inverse Functions
1.5 Exponential and Logarithmic Functions
2.1 Preview of Calculus
2.2 The Limit of a Function
2.3 The Limit Laws
2.4 Trigonometric Limits
2.5 Continuity
2.6 The Precise Definition of a Limit
3.1 Defining the Derivative
3.2 Differentiation Rules
3.3 Derivatives as Rates of Change
3.4 Derivatives of Trigonometric Functions
3.5 The Chain Rule
3.6 Implicit Differentiation
3.7 Derivatives of Exponential and Logarithmic Functions
3.8 Related Rates
4.1 Linear Approximations and Differentials
4.2 Maxima and Minima
4.3 The Mean Value Theorem
4.4 Derivatives and Graphing
4.5 Limits at Infinity and Asymptotes
4.6 Applied Optimization Problems
4.7 L'Hôpital's Rule
4.8 Newton's Method
4.9 Antiderivatives
5.1 Approximating Areas
5.2 The Definite Integral
5.3 The Fundamental Theorem of Calculus
5.4 Indefinite Integrals
5.5 The Substitution Method
6.1 Areas Between Curves
6.2 Volumes of Revolution: Slicing
6.3 Volumes of Revolution: Cyllindrical Shells
6.4 Length of a Curve
6.5 Force, Work, and Energy
6.6 Integrals, Exponential Functions, and Logarithms
6.7 Exponential Growth and Decay
6.8 Hyperbolic and Inverse Trigonometric Functions
6.9 Applications to Biology, Business/Economics, and Probability
7.1 Integration by Parts
7.2 Trigonometric Integrals
7.3 Trigonometric Substitution
7.4 Partial Fractions
7.5 Other Strategis for Integration
7.6 Numerical Integration
7.7 Improper Integrals
8.1 Sequences
8.2 Infinite Series
8.3 The Integral and Convergence Tests
8.4 Comparison Tests
8.5 Alternating Series
9.1 Power Series
9.2 Representing Functions as Power Series
9.3 Taylor and Maclaurin Series
9.4 Applications of Taylor Series
10.1 Basics of Differential Equations
10.2 Direction Fields and Numerical Methods
10.3 Separable Equations
10.4 The Logistic Equation
10.5 First-Order Linear Equations
11.1 Parametric Equations
11.2 Calculus of Parametric Curves
11.3 Polar Coordinates
11.4 Area and Arc Length in Polar Coordinates
11.5 Conic Sections
12.1 Vectors in the Plane
12.2 Vectors in Three Dimensions
12.3 The Dot Product
12.4 The Cross Product
12.5 Equations of Lines and Planes
12.6 Quadratic Surfaces
12.7 Cylindrical and Sperical Coordinates
13.1 Vector-Valued Functions
13.2 Calculus of Vector-Valued Functions
13.3 Arc Length and Curvature
13.4 Motion in Space
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
14.7 Maxima/Minima Problems
14.8 Lagrange Multipliers
15.1 Double Integrals over Rectangular Regions
15.2 Double Integrals over General Regions
15.3 Double Integrals in Polar Coordinates
15.4 Triple Integrals
15.5 Triple Integrals in Cylindrical and Spherical Coordinates
15.6 Calculating Centers of Mass and Moments of Inertia
15.7 Change of Variables in Multiple Integrals
16.1 Vector Fields
16.2 Line Integrals
16.3 Conservative Vector Fields
16.4 Green’s Theorem
16.5 Curl and Divergence
16.6 Surface Integrals
16.7 Stokes’ Theorem
16.8 The Divergence Theorem
1.1 Four Ways to Represent a Function
1.2 Mathematical Models
1.3 New Functions from Old Functions
1.5 Exponential Functions
1.6 Inverse Functions and Logarithms
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
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
4.1 Maximum and Minimum Values
4.2 The Mean Value Theorem
4.3 How Derivatives Affect the Shape of a Graph
4.4 Inderterminate Forms and l'Hôpital'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
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
6.1 Areas between Curves
6.2 Volumes
6.3 Volumes by Cylindrical Shells
6.4 Work
6.5 Average Value of a Function
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
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
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
10.1 Curves Defined by Parametric Equations
10.2 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
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
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
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
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
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
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
16.10 Summary
17.1 Second-order Linear Equations
17.2 Nonhomogeneous Linear Equations
17.3 Applications of Second-Order Differential Equations
17.4 Series Solutions
1.1 Velocity and Distance
1.2 Calculus Without Limits
1.3 The Velocity at an Instant
1.4 Circular Motion
1.5 A Review of Trigonometry
1.6 A Thousand Points of Light
1.7 Computing in Calculus
2.1 The Derivative of a Function
2.2 Powers and Polynomials
2.3 The Slope and the Tangent Line
2.4 Derivative of the Sine and Cosine
2.5 The Product and Quotient and Power Rules
2.6 Limits
2.7 Continuous Functions
3.1 Linear Approximation
3.2 Maximum and Minimum Problems
3.3 Second Derivatives: Minimum vs. Maximum
3.4 Graphs
3.5 Ellipses, Parabolas, and Hyperbolas
3.6 Iterations
3.7 Newton's Method and Chaos
3.8 The Mean Value Theorem and l'Hôpital's Rule
4.1 Derivatives by the Chain Rule
4.2 Implicit Differentiation and Related Rates
4.3 Inverse Functions and Their Derivatives
4.4 Inverses of Trigonometric Functions
5.1 The Idea of the Integral
5.2 Antiderivatives
5.3 Summation vs. Integration
5.4 Indefinite Integrals and Substitutions
5.5 The Definite Integral
5.6 Properties of the Integral and the Average Value
5.7 The Fundamental Theorem and Its Consequences
5.8 Numerical Integration
6.1 An Overview
6.2 The Exponential e^x
6.3 Growth and Decay in Science and Economics
6.4 Logarithms
6.5 Separable Equations Including the Logistic Equation
6.6 Powers Instead of Exponentials
6.7 Hyperbolic Functions
7.1 Integration by Parts
7.2 Trigonometric Integrals
7.3 Trigonometric Substitutions
7.4 Partial Fractions
7.5 Improper Integrals
8.1 Areas and Volumes by Slices
8.2 Length of a Plane Curve
8.3 Area of a Surface of Revolution
8.4 Probability and Calculus
8.5 Masses and Moments
8.6 Force, Work, and Energy
9.1 Polar Coordinates
9.2 Polar Equations and Graphs
9.3 Slope, Length, and Area for Polar Curves
9.4 Complex Numbers
10.1 The Geometric Series
10.2 Convergence Tests: Positive Series
10.3 Convergence Tests: All Series
10.4 The Taylor Series for e^x, sin(x), and cos(x)
10.5 Power Series
11.1 Vectors and Dot Products
11.2 Planes and Projections
11.3 Cross Products and Determinants
11.4 Matrices and Linear Equations
11.5 Linear Algebra in Three Dimensions
12.1 The Position Vector
12.2 Plane Motion: Projectiles and Cycloids
12.3 Tangent Vector and Normal Vector
12.4 Polar Coordinates and Planetary Motion
13.1 Surfaces and Level Curves
13.2 Partial Derivatives
13.3 Tangent Planes and Linear Approximations
13.4 Directional Derivatives and Gradients
13.5 The Chain Rule
13.6 Maxima, Minima, and Saddle Points
13.7 Constraints and Lagrange Multipliers
14.1 Double Integrals
14.2 Changing to Better Coordinates
14.3 Triple Integrals
14.4 Cylindrical and Spherical Coordinates
15.1 Vector Fields
15.2 Line Integrals
15.3 Green's Theorem
15.4 Surface Integrals
15.5 The Divergence Theorem
15.6 Stokes' Theorem and the Curl of F
16.1 Linear Algebra
16.2 Differential Equations
16.3 Discrete Mathematics
1.1 Real Numbers, Functions, and Graphs
1.2 Linear and Quadratic Functions
1.3 The Basic Classes of Functions
1.4 Trigonometric Functions
1.5 Inverse Functions
1.6 Exponential and Logarithmic Functions
1.7 Technology: Calculators and Computers
2.1 Limits, Rates of Change, and Tangent Lines
2.2 Limits: A Numerical and Graphical Approach
2.3 Basic Limit Laws
2.4 Limits and Continuity
2.5 Evaluating Limits Algebraically
2.6 Trigonometric Limits
2.7 Limits at Infinity
2.8 Intermediate Value Theorem
2.9 The Formal Definition of a Limit
3.1 Definition of the Derivative
3.2 The Derivative as a Function
3.3 Product and Quotient Rules
3.4 Rates of Change
3.5 Higher Derivatives
3.6 Trigonometric Functions
3.7 The Chain Rule
3.8 Derivatives of Inverse Functions
3.9 Related Rates
4.1 Linear Approximation and Applications
4.2 Extreme Values
4.3 The Mean Value Theorem and Monotonicity
4.4 The Shape of a Graph
4.5 Graph Sketching and Asymptotes
4.6 Applied Optimization
4.7 Newton's Method
4.8 Antiderivatives
5.1 Approximating and Computing Area
5.2 The Definite Integral
5.3 The Fundamental Theorem of Calculus, Part I
5.4 The Fundamental Theorem of Calculus, Part II
5.5 Net Change as the Integral of a Rate
5.6 Substitution Method
6.1 Area Between Two Curves
6.2 Setting Up Integrals: Volume, Density, Average Value
6.3 Volumes of Revolution
6.4 The Method of Cylindrical Shells
6.5 Work and Energy
7.1 Derivative of f(x) = bx and the Number e
7.2 Inverse Functions
7.3 Logarithms and Their Derivatives
7.4 Exponential Growth and Decay
7.5 Compound Interest and Present Value
7.6 Models Involving y? = k ( y – b)
7.7 L’Hôpital’s Rule
7.8 Inverse Trigonometric Functions
7.9 Hyperbolic Functions
8.1 Integration by Parts
8.2 Trigonometric Integral
8.3 Trigonometric Substitution
8.4 Integrals Involving Hyperbolic and Inverse Hyperbolic Functions
8.5 The Method of Partial Fractions
8.6 Improper Integrals
8.7 Probability and Integration
8.8 Numerical Integration
9.1 Arc Length and Surface Area
9.2 Fluid Pressure and Force
9.3 Center of Mass
9.4 Taylor Polynomials
10.1 Solving Differential Equations
10.2 Graphica and Numerical Methods
10.3 The Logistic Equation
10.4 First-Order Linear Equations
11.1 Sequences
11.2 Summing an Infinite Series
1.3 Convergence of Series with Positive Terms
11.4 Absolute and Conditional Convergence
11.5 The Ratio and Root Tests
11.6 Power Series
11.7 Taylor Series
12.1 Parametric Equations
12.2 Arc Length and Speed
12.3 Polar Coordinates
12.4 Area and Arc Length in Polar Coordinates
12.5 Conic Sections
13.1 Vectors in the Plane
13.2 Vectors in Three Dimensions
13.3 Dot Product and the Angle between Two Vectors
13.4 The Cross Product
13.5 Planes in Three-Space
13.6 A Survey of Quadric Surfaces
13.7 Cylindrical and Spherical Coordinates
14.1 Vector-Valued Functions
14.2 Calculus of Vector-Valued Functions
14.3 Arc Length and Speed
14.4 Curvature
14.5 Motion in Three-Space
14.6 Planetary Motion According to Kepler and Newton
15.1 Functions of Two or More Variables
15.2 Limits and Continuity in Several Variables
15.3 Partial Derivatives
15.4 Differentiability and Tangent Planes
15.5 The Gradient and Directional Derivatives
15.6 The Chain Rule
15.7 Optimization in Several Variables
15.8 Lagrange Multipliers: Optimizing with a Constraint
16.1 Integration in Variables
16.2 Double Integrals over More General Regions
16.3 Triple Integrals
16.4 Integration in Polar, Cylindrical, and Spherical Coordinates
16.5 Applications of Multiple Integrals
16.6 Change of Variables
17.1 Vector Fields
17.2 Line Integrals
17.3 Conservative Vector Fields
17.4 Parametrized Surfaces and Surface Integrals
17.5 Surface Integrals of Vector Fields
18.1 Green's Theorem
18.2 Stokes' Theorem
18.3 Divergence Theorem
1.1 Review of Functions
1.2 Representing Functions
1.3 Inverse, exponential, and logarithmic functions
1.4 Trigonometic functions and their inverses
2.1 The Idea of Limits
2.2 Definition of Limits
2.3 Techniques for Computing Limits
2.4 Infinite Limits
2.5 Limits at Infinity
2.6 Continuity
2.7 Precise Definition of Limits
3.1 Introducing the Derivative
3.2 Working with Derivatives
3.3 Rules of Differentiation
3.4 The Product and Quotient Rules
3.5 Derivatives of Trigonometic Functions
3.6 Derivatives as Rates of Change
3.7 The Chain Rule
3.8 Implicit Differentiation
3.9 Derivatives of Logarithmic and Exponential Functions
3.10 Derivatives of Inverse Trigonometric Functions
3.11 Related Rates
4.1 Maxima and Minima
4.2 What Derivatives Tell Us
4.3 Graphing Functions
4.4 Optimization Problems
4.5 Linear Approximation and Differentials
4.6 Mean Value Theorem
4.7 L'Hospital's Rule
4.8 Newton's Method
4.9 Antiderivatives
5.1 Approximating Areas Under Curves
5.2 Definite Integrals
5.3 Fundamental Theorem of Calculus
5.4 Working with Integrals
5.5 Substitution Rule
6.1 Velocity and Net Change
6.2 Regions Between Curves
6.3 Volume by Slicing
6.4 Volume by Shells
6.5 Length of Curves
6.6 Surface area
6.7 Physical Applications
6.8 Logarithmic and Exponential Functions Revisited
6.9 Exponential Models
6.10 Hyperbolic Functions
7.1 Basic Approaches
7.2 Integration by Parts
7.3 Trigonometric Integrals
7.4 Trigonometric Substitutions
7.5 Partial Fractions
7.6 Other Integration Strategies
7.7 Numerical Integration
7.8 Improper Integrals
7.9 Introduction to Differential Equations
8.1 An Overview
8.2 Sequences
8.3 Infinite Series
8.4 The Divergence and Integral Tests
8.5 The Ratio, Root, and Comparison Tests
8.6 Alternating Series
9.1 Approximating Functions with Polynomials
9.2 Properties of Power Series
9.3 Taylor Series
9.4 Working with Taylor Series
10.1 Parametric Equations
10.2 Polar coordinates
10.3 Calculus in Polar Coordinates
10.4 Conic Sections
11.1 Vectors in the Plane
11.2 Vectors in Three Dimensions
11.3 Dot Products
11.4 Cross Products
11.5 Lines and Curves in Space
11.6 Calculus of Vector-Valued Functions
11.7 Motion in Space
11.8 Length of Curves
11.9 Curvature and Normal Vectors
12.1 Planes and Surfaces
12.2 Graphs and Level Curves
12.3 Limits and Continuity
12.4 Partial Derivatives
12.5 The Chain Rule
12.6 Directional Derivatives and the Gradient
12.7 Tangent Planes and Linear Approximation
12.8 Maximum / Minimum Problems
12.9 Lagrange Multipliers
13.1 Double Integrals over Rectangular Regions
13.2 Double Integrals over General Regions
13.3 Double Integrals in Polar Coordinates
13.4 Triple Integrals
13.5 Triple Integrals in Cylindrical and Spherical Coordinates
13.6 Integrals for Mass Calculations
13.7 Change of Variables in Multiple Integrals
14.1 Vector Fields
14.2 Line Integrals
14.3 Conservative Vector Fields
14.4 Green's Theorem
14.5 Divergence and Curl
14.6 Surface Integrals
14.7 Stokes' Theorem
14.8 Divergence Theorem