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1. Functions and Graphs

2. Limits

3. Derivatives

4. Applications of Derivatives

5. Integration

6. Applications of Integration

7. Techniques of Integration

8. Sequences and Series

9. Power Series

10. Intro. to Differential Eq.

11. Parametric Eq. and Polar Coords.

12. Vectors in Space

13. Vector-Valued Functions

14. Differentiation of Functions of Several Variables

15. Multiple Integration

16. Vector Calculus

1. Intro. to Calculus

2. Derivatives

3. Applications of Derivatives

4. The Chain Rule

5. Integrals

6. Exponentials and Logarithms

7. Techniques of Integration

8. Applications of the Integral

9. Polar Coords. and Complex numbers

10. Infinite Series

11. Vectors and Matricies

12. Motion Along a curve

13. Partial Derivatives

14. Multiple Integrals

15. Vector Calculus

16. Math After Calculus

1. Functions and Models

2. Limits and Derivatives

3. Differentiation Rules

4. Applications of Differentiation

5. Integrals

6. Application of Integration

7. Techniques of Integration

8. Further Applications of Integration

9. Differential Equations

10. Parametric Equations

11. Infinite Sequences of Integration

12. Vectors and the Geometry of Space

13. Vector Functions

14. Partial Derivatives

15. Multiple Integrals

16. Vector Caclulus

17. Second-Order Differentiation

1. Precalculus Review

2. Limits

3. Differentiation

4. Applications of the Derivative

5. The Integral

6. Applications of the Integral

7. The Exponential Function

8. Techniques of Inetgration

9. Further Applications of the Integral and Taylor Polynomials

10. Introduction to Differential Equations

11. Infinite Series

12. Parametric Equations, Polar Coordinates, and Conic Sections

13. Vector Geometry

14. Calculus of Vector-Values Functions

15. Differentiation in Several Variables

16. Multiple Integration

17. Line Surface Integrals

18. Fundamental Theorems of Vector Analysis

1. Functions

2. Limits

3. Derivatives

4. Applications of Derivatives

5. Integration

6. Applications of Integration

7. Integration Techniques

8. Sequences and Infinite Series

9. Power Series

10. Parametric and Polar Curves

11. Vectors and Vector-Values Functions

12. Functions of Several Variables

13. Multiple Integration

14. Vector Calculus

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