|
Chapter 6: Applications of Integration
|
Section |
Topic |
6.1 |
Areas Between Curves
6.1.18 Areas Between Curves
6.1.38 Areas Between Curves
6.1.42 Areas Between Curves
|
6.2 |
Volumes
6.2.8 Volumes
6.2.12 Volumes
6.2.17 Volumes
6.2.34 Volumes
6.2.48 Volumes
6.2.56 Volumes
|
6.3 |
Volumes by Cylindrical Shells
6.3.12 Volumes by Cylindrical Shells
6.3.18 Volumes by Cylindrical Shells
6.3.20 Volumes by Cylindrical Shells
6.3.39 Volumes by Cylindrical Shells
|
6.4 |
Work
6.4.10 Work
6.4.14 Work
6.4.18 Work
6.4.24 Work
6.4.26 Work
6.4.34 Work
|
6.5 |
Average Value of a Function
6.5.8 Average Value of a Function
6.5.16 Average Value of a Function
6.5.18 Average Value of a Function
|
|
| |
Chapter 7: Techniques of Integration |
Section |
Topic |
7.1 |
Integration by Parts
7.1.22 Integration by Parts
7.1.40 Integration by Parts
7.1.63 Integration by Parts
|
7.2 |
Trigonometric Integrals
7.2.22 Trigonometric Integrals
7.2.38 Trigonometric Integrals
7.2.66 Trigonometric Integrals
|
7.3 |
Trigonometric Substitution
7.3.8 Trigonometric Substitution
7.3.20 Trigonometric Substitution
7.3.26 Trigonometric Substitution
7.3.30 Trigonometric Substitution
7.3.42 Trigonometric Substitution
|
7.4 |
Integration of Rational Functions by Partial Fractions
7.4.8 Integration of Rational Functions by Partial Fractions
7.4.12 Integration of Rational Functions by Partial Fractions
7.4.20 Integration of Rational Functions by Partial Fractions
7.4.28 Integration of Rational Functions by Partial Fractions
7.4.48 Integration of Rational Functions by Partial Fractions
7.4.67 Integration of Rational Functions by Partial Fractions
7.4.70 Integration of Rational Functions by Partial Fractions
|
7.5 |
Strategy for Integration |
7.6 |
Integration Using Tables and Computer Algebra Systems
7.6.20 Integration Using Tables and Computer Algebra Systems
7.6.26
Integration Using Tables and Computer Algebra Systems
7.6.44
Integration Using Tables and Computer Algebra Systems
7.6.46
Integration Using Tables and Computer Algebra Systems
|
7.7 |
Approximate Integration
7.7.14 Approximate Integration
7.7.24
Approximate Integration
7.7.36
Approximate Integration
7.7.40
Approximate Integration
|
7.8 |
Improper Integrals
7.8.16 Improper Integrals
7.8.30
Improper Integrals
7.8.48
Improper Integrals
7.8.70
Improper Integrals
|
|
| |
Chapter 8: Further Applications of Integration |
Section |
Topic |
8.1 |
Arc Length
8.1.6 Arc Length
8.1.14 Arc Length
8.1.28 Arc Length
8.1.36 Arc Length
|
8.2 |
Area of a Surface of Revolution
8.2.4 Area of a Surface of Revolution
8.2.10 Area of a Surface of Revolution
8.2.18 Area of a Surface of Revolution
8.2.26 Area of a Surface of Revolution
|
8.3 |
Applications to Physics and Engineering
8.3.4 Applications to Physics and Engineering
8.3.10 Applications to Physics and Engineering
8.3.28 Applications to Physics and Engineering
8.3.47 Applications to Physics and Engineering
|
8.4 |
Applications to Economics and Biology
8.4.2 Applications to Economics and Biology
8.4.8 Applications to Economics and Biology
8.4.15,16 Applications to Economics and Biology
8.4.20 Applications to Economics and Biology
|
8.5 |
Probability
8.5.4 Probability
8.5.12 Probability
8.5.16 Probability
|
|
| |
Chapter 9: Differential Equations |
Section |
Topic |
9.1 |
Modeling with Differential Equations
9.1.6 Modeling with Differential Equations
9.1.10 Modeling with Differential Equations
|
9.2 |
Direction Fields and Euler’s Method
9.2.2 Direction Fields and Euler's Method
9.2.14 Direction Fields and Euler's Method
9.2.24 Direction Fields and Euler's Method
|
9.3 |
Separable Equations
9.3.8 Separable Equations
9.3.16 Separable Equations
9.3.28 Separable Equations
9.3.30 Separable Equations
9.3.48 Separable Equations
9.3.54 Separable Equations
|
9.4 |
Models for Population Growth
9.4.10 Models for Population Growth
9.4.16 Models for Population Growth
9.4.22 Models for Population Growth
|
9.5 |
Linear Equations
9.5.10 Linear Equations
9.5.18 Linear Equations
9.5.34 Linear Equations
|
9.6 |
Predator-Prey Systems
9.6.4 Predator-Prey Systems
9.6.6 Predator-Prey Systems
9.6.10 Predator-Prey Systems
|
|
| |
Chapter 10: Parametric Equations and Polar Coordinates |
Section |
Topic |
10.1 |
Curves Defined by Parametric Equations
10.1.8 Curves Defined by Parametric Equations
10.1.18 Curves Defined by Parametric Equations
10.1.40 Curves Defined by Parametric Equations
|
10.2 |
Calculus with Parametric Curves
10.2.6 Calculus with Parametric Curves
10.2.14 Calculus with Parametric Curves
10.2.24 Calculus with Parametric Curves
10.2.34 Calculus with Parametric Curves
10.2.44 Calculus with Parametric Curves
10.2.58 Calculus with Parametric Curves
|
10.3 |
Polar Coordinates
10.3.14 Polar Coordinates
10.3.16 Polar Coordinates
10.3.26 Polar Coordinates
10.3.40 Polar Coordinates
10.3.64 Polar Coordinates
10.3.70 Polar Coordinates
|
10.4 |
Areas and Lengths in Polar Coordinates
10.4.6 Areas and Lengths in Polar Coordinates
10.4.16 Areas and Lengths in Polar Coordinates
10.4.26 Areas and Lengths in Polar Coordinates
10.4.40 Areas and Lengths in Polar Coordinates
|
10.5 |
Conic Sections |
10.6 |
Conic Sections in Polar Coordinates |
|
| |
Chapter 11: Infinite Sequences and Series |
Section |
Topic |
11.1 |
Sequences
11.1.20 Sequences
11.1.22 Sequences
11.1.30 Sequences
11.1.36 Sequences
11.1.58 Sequences
11.1.62 Sequences
11.1.74 Sequences
11.1.90 Sequences
|
11.2 |
Series
11.2.4 Series
11.2.8 Series
11.2.12 Series
11.2.18 Series
11.2.26 Series
11.2.30 Series
11.2.38 Series
11.2.46 Series
11.2.58 Series
11.2.72 Series
|
11.3 |
The Integral Test and Estimates of Sums
11.3.8 The Integral Test and Estimates of Sums
11.3.14 The Integral Test and Estimates of Sums
11.3.20 The Integral Test and Estimates of Sums
|
11.4 |
The Comparison Tests
11.4.6 The Comparison Tests
11.4.20 The Comparison Tests
11.4.30 The Comparison Tests
11.5.34 The Comparison Tests
|
11.5 |
Alternating Series
11.5.6 Alternating Series
11.5.12 Alternating Series
11.5.22 Alternating Series
11.5.26 Alternating Series
11.5.30 Alternating Series
|
11.6 |
Absolute Convergence and the Ratio and Root Tests
11.6.4 Absolute Convergence and the Ratio and Root Tests
11.6.10 Absolute Convergence and the Ratio and Root Tests
11.6.22 Absolute Convergence and the Ratio and Root Tests
11.6.28 Absolute Convergence and the Ratio and Root Tests
11.6.36 Absolute Convergence and the Ratio and Root Tests
11.6.46,48 Absolute Convergence and the Ratio and Root Tests
|
11.7 |
Strategy for Testing Series |
11.8 |
Power Series
11.8.6 Power Series
11.8.8 Power Series
11.8.16 Power Series
11.8.24 Power Series
11.8.36 Power Series
|
11.9 |
Representation of Functions as Power Series
11.9.4 Representation of Functions as Power Series
11.9.10 Representation of Functions as Power Series
11.9.18 Representation of Functions as Power Series
11.9.26 Representation of Functions as Power Series
|
11.10 |
Taylor and
Maclaurin Series
11.10.10 Taylor and Maclaurin Series
11.10.16 Taylor and Maclaurin Series
11.10.24 Taylor and Maclaurin Series
11.10.32 Taylor and Maclaurin Series
11.10.40 Taylor and Maclaurin Series
11.10.60 Taylor and Maclaurin Series
11.10.78 Taylor and Maclaurin Series |
11.11 |
Applications of Taylor Polynomials
11.11.08 Applications of Taylor Polynomials
11.11.18 Applications of Taylor Polynomials
11.11.28 Applications of Taylor Polynomials
11.11.38 Applications of Taylor Polynomials |
