CCSF Calculus

by Kendra Lockman

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Publisher: City College of San Francisco
Subjects: Mathematics
Licence: CC BY-NC-SA 4.0, as LibreTexts states it. Non-commercial use only.
Who can read: Tweens profiles and older, judged from its title and subjects

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Front Matter
TitlePage
InfoPage
Table of Contents
Licensing
1: Critical Concepts for Calculus
1.1: Functions
1.1E: Exercises
1.2: Basic Classes of Functions and Their Graphs
1.2E: Exercises
1.3: Inverse Functions
1.3E: Exercises
1.4: Exponential and Logarithmic Functions
1.4E: Exercises
1.5: Trigonometry
1.5E: Exercises
1.6: Hyperbolic Functions
1.6E: Exercises
1.7: Chapter 1 Review Exercises
2: Learning Limits
2.1: Tangent Lines and Velocity
2.1E: Exercises
2.2: The Limit of a Function - A Numerical and Graphical Investigation
2.2E: Exercises
2.3: The Limit Laws - Limits at Finite Numbers
2.3E: Exercises
2.4: The Limit Laws - Limits at Infinity
2.4E: Exercises
2.5: The Precise Definition of a Finite Limit at a Finite Number
2.5E: Exercises
2.6: The Precise Definitions of Infinite Limits and Limits at Infinity
2.6E: Exercises
2.7: Continuity
2.7E: Exercises
2.8: Defining the Derivative
2.8E: Exercises
2.9: The Derivative as a Function
2.9E: Exercises
2.10: Chapter 2 Review Exercises
3: Discovering Derivatives
3.1: Derivatives of Polynomial Functions
3.1E: Exercises
3.2: Differentiation Techniques - The Product and Quotient Rules
3.2E: Exercises
3.3: Derivatives of Trigonometric Functions
3.3E: Exercises
3.4: Differentiation Techniques - The Chain Rule
3.4E: Exercises
3.5: Derivatives of Exponential and Hyperbolic Functions
3.5E: Exercises
3.6: Implicit Differentiation and the Derivatives of the Inverse Trigonometric and Hyperbolic Functions
3.6.1: Resources and Key Concepts
3.6.2: Homework
3.7: Derivatives of Logarithms and Logarithmic Differentiation
3.7.1: Resources and Key Concepts
3.7.2: Homework
3.8: Related Rates
3.8E: Exercises
3.9: Linear Approximations and Differentials
3.9E: Exercises
3.10: Chapter 3 Review Exercises
4: Appropriate Applications
4.1: Graphing Using Calculus - Maxima and Minima
4.1E: Exercises
4.2: A Theoretical Interlude - The Mean Value Theorem
4.2E: Exercises
4.3: Graphing Using Calculus - Shaping the Curve
4.3E: Exercises
4.4: An Interlude for Limits - L’Hospital’s Rule and Indeterminate Forms
4.4E: Exercises
4.5: Graphing Using Calculus - Putting it Altogether
4.5E: Exercises
4.6: Optimization
4.6E: Exercises
4.7: Newton’s Method
4.7E: Exercises
4.8: Chapter 4 Review Exercises
5: Investigating Integrals
5.1: Antiderivatives and Indefinite Integrals
5.1E: Exercises
5.2: Approximating Areas
5.2E: Exercises
5.3: The Definite Integral
5.3E: Exercises
5.4: The Fundamental Theorem of Calculus
5.4E: Exercises
5.5: The Net Change Theorem, Distances, and Symmetry
5.5E: Exercises
5.6: Integration by Substitution
5.6E: Exercises
5.7: Chapter 5 Review Exercises
6: Applications of Integration
6.1: Volumes of Revolution - The Disk and Washer Methods
6.1E: Exercises
6.2: Volumes of Revolution - Cylindrical Shells
6.2E: Exercises
6.3: Arc Length of a Curve and Surface Area
6.3E: Exercises
6.4: Work
6.4E: Exercises
6.5: Hydrostatic Force and Pressure
6.5E: Exercises
6.6: Moments and Centers of Mass
6.6E: Exercises
6.7: The Mean Value Theorem for Integrals
6.7E: Exercises
6.8: Chapter 1 Review Exercises
6.9: Areas Between Curves
6.9E: Exercises
6.10: Determining Volumes by Slicing
6.10E: Exercises
7: Techniques of Integration
7.1: Expanding the Substitution Method
7.1E: Exercises
7.2: Expanding the Substitution Method - Trigonometric Substitution
7.2E: Exercises
7.3: Integration by Parts
7.3E: Exercises
7.4: Chapter 2 Review Exercises
7.5: Partial Fractions
7.5E: Exercises
7.6: Numerical Integration
7.6E: Exercises
8: Sequences and Series
8.1: Improper Integrals
8.1.1: Exercises
8.2: Sequences
8.2E: Exercises
8.3: Infinite Series
8.3E: Exercises
8.4: The Divergence and Integral Tests
8.4E: Exercises
8.5: The Comparison Tests
8.5E: Exercises
8.6: The Alternating Series Test
8.6E: Exercises
8.7: The Ratio and Root Tests
8.7E: Exercises
8.8: Chapter 3 Review Exercises
9: Power Series
9.1: Power Series and Functions
9.1E: Exercises
9.2: Properties of Power Series
9.2E: Exercises
9.3: Taylor and Maclaurin Series
9.3E: Exercises
9.4: The Binomial Theorem and Applications of Taylor Series
9.4E: Exercises
9.5: Chapter 4 Review Exercises
10: Parametric Equations and Polar Coordinates
10.1: Chapter 5 Review Exercises
10.2: Parametric Equations
10.2E: Exercises
10.3: Calculus of Parametric Curves
10.3E: Exercises
10.4: Polar Coordinates
10.4E: Exercises
10.5: Area and Arc Length in Polar Coordinates
10.5E: Exercises
10.6: Conic Sections
10.6E: Exercises
11: Introduction to Differential Equations
11.1: Chapter 6 Review Exercises
11.2: Basics of Differential Equations
11.2E: Exercises for Section 8.1
11.3: Direction Fields and Numerical Methods
11.3E: Exercises for Section 8.2
11.4: Separable Equations
11.4E: Exercises for Section 8.3
11.5: The Logistic Equation
11.5E: Exercises for Section 8.4
11.6: First-order Linear Equations
11.6E: Exercises for Section 8.5
12: Vectors in Space
12.1: Prelude to Vectors in Space
12.2: Vectors in the Plane
12.2E: Exercises for Section 12.1
12.3: Vectors in Three Dimensions
12.3E: Exercises for Section 12.2
12.4: The Dot Product
12.4E: Exercises for Section 12.3
12.5: The Cross Product
12.5E: Exercises for Section 12.4
12.6: Equations of Lines and Planes in Space
12.6E: Exercises for Section 12.5
12.7: Quadric Surfaces
12.7E: Exercises for Section 12.6
12.8: Cylindrical and Spherical Coordinates
12.8E: Exercises for Section 12.7
12.R: Chapter 12 Review Exercises
13: Vector-Valued Functions
13.1: Prelude to Vector-Valued Functions
13.2: Vector-Valued Functions and Space Curves
13.2E: Exercises for Section 13.1
13.3: Calculus of Vector-Valued Functions
13.3E: Exercises for Section 13.2
13.4: Arc Length and Curvature
13.4E: Exercises for Section 13.3
13.5: Motion in Space
13.5E: Exercises for Section 13.4
13.R: Chapter 13 Review Exercises
14: Differentiation of Functions of Several Variables
14.1: Prelude to Differentiation of Functions of Several Variables
14.2: Functions of Several Variables
14.2E: Exercises for Section 14.1
14.3: Limits and Continuity
14.3E: Exercises for Section 14.2
14.4: Partial Derivatives
14.4E: Exercises for Section 14.3
14.5: Tangent Planes and Linear Approximations
14.5E: Exercises for Section 14.4
14.6: The Chain Rule for Multivariable Functions
14.6E: Exercises for Section 14.5
14.7: Directional Derivatives and the Gradient
14.7E: Exercises for Section 14.6
14.8: Maxima/Minima Problems
14.8E: Exercises for Section 14.7
14.9: Lagrange Multipliers
14.9E: Exercises for Section 14.8
14.R: Chapter 14 Review Exercises
15: Multiple Integration
15.1: Prelude to Multiple Integration
15.2: Double Integrals over Rectangular Regions
15.2E: Exercises for Section 15.1
15.3: Double Integrals over General Regions
15.3E: Exercises for Section 15.2
15.4: Double Integrals in Polar Coordinates
15.4E: Exercises for Section 15.3
15.5: Triple Integrals
15.5E: Exercises for Section 15.4
15.6: Triple Integrals in Cylindrical and Spherical Coordinates
15.6E: Exercises for Section 15.5
15.7: Calculating Centers of Mass and Moments of Inertia
15.7E: Exercises for Section 15.6
15.8: Change of Variables in Multiple Integrals
15.8E: Exercises for Section 15.7
15.R: Chapter 15 Review Exercises
16: Vector Calculus
16.1: Prelude to Vector Calculus
16.2: Vector Fields
16.2E: Exercises for Section 16.1
16.3: Line Integrals
16.3E: Exercises for Section 16.2
16.4: Conservative Vector Fields
16.4E: Exercises for Section 16.3
16.5: Green’s Theorem
16.5E: Exercises for Section 16.4
16.6: Divergence and Curl
16.6E: Exercises for Section 16.5
16.7: Surface Integrals
16.7E: Exercises for Section 16.6
16.8: Stokes’ Theorem
16.8E: Exercises for Section 16.7
16.9: The Divergence Theorem
16.9E: Exercises for Section 16.8
16.R: Chapter 16 Review Exercises
17: Second-Order Differential Equations
17.1: Prelude to Second-Order Differential Equations
17.2: Second-Order Linear Equations
17.2E: Exercises for Section 17.1
17.3: Nonhomogeneous Linear Equations
17.3E: Exercises for Section 17.2
17.4: Applications of Second-Order Differential Equations
17.4E: Exercises for Section 17.3
17.5: Series Solutions of Differential Equations
17.5E: Exercises for Section 17.4
17.R: Chapter 17 Review Exercises
18: Appendices
18.1: Table of Derivatives
18.2: Table of Integrals
18.3: Other Strategies for Integration
18.3.1: Exercises
Back Matter
Index
Glossary
Detailed Licensing
Detailed Licensing

CCSF Calculus

Contents