CCSF Calculus

Mathematics

Author: Kendra Lockman
Publisher: City College of San Francisco
Source: LibreTexts
License: CC BY-NC-SA
Language: EN
Category: Basic Sciences

Read online Download PDF (open licence)

Contents· 267 sections

01: Critical Concepts for Calculus
1.01: Functions
1.1E: Exercises
1.02: Basic Classes of Functions and Their Graphs
1.2E: Exercises
1.03: Inverse Functions
1.3E: Exercises
1.04: Exponential and Logarithmic Functions
1.4E: Exercises
1.05: Trigonometry
1.5E: Exercises
1.06: Hyperbolic Functions
1.6E: Exercises
1.07: Chapter 1 Review Exercises
02: Learning Limits
2.01: Tangent Lines and Velocity
2.1E: Exercises
2.02: The Limit of a Function - A Numerical and Graphical Investigation
2.2E: Exercises
2.03: The Limit Laws - Limits at Finite Numbers
2.3E: Exercises
2.04: The Limit Laws - Limits at Infinity
2.4E: Exercises
2.05: The Precise Definition of a Finite Limit at a Finite Number
2.5E: Exercises
2.06: The Precise Definitions of Infinite Limits and Limits at Infinity
2.6E: Exercises
2.07: Continuity
2.7E: Exercises
2.08: Defining the Derivative
2.8E: Exercises
2.09: The Derivative as a Function
2.9E: Exercises
2.10: Chapter 2 Review Exercises
03: Discovering Derivatives
3.01: Derivatives of Polynomial Functions
3.1E: Exercises
3.02: Differentiation Techniques - The Product and Quotient Rules
3.2E: Exercises
3.03: Derivatives of Trigonometric Functions
3.3E: Exercises
3.04: Differentiation Techniques - The Chain Rule
3.4E: Exercises
3.05: Derivatives of Exponential and Hyperbolic Functions
3.5E: Exercises
3.06: Implicit Differentiation and the Derivatives of the Inverse Trigonometric and Hyperbolic Functions
3.6.01: Resources and Key Concepts
3.6.02: Homework
3.07: Derivatives of Logarithms and Logarithmic Differentiation
3.7.01: Resources and Key Concepts
3.7.02: Homework
3.08: Related Rates
3.8E: Exercises
3.09: Linear Approximations and Differentials
3.9E: Exercises
3.10: Chapter 3 Review Exercises
04: Appropriate Applications
4.01: Graphing Using Calculus - Maxima and Minima
4.1E: Exercises
4.02: A Theoretical Interlude - The Mean Value Theorem
4.2E: Exercises
4.03: Graphing Using Calculus - Shaping the Curve
4.3E: Exercises
4.04: An Interlude for Limits - LHospitals Rule and Indeterminate Forms
4.4E: Exercises
4.05: Graphing Using Calculus - Putting it Altogether
4.5E: Exercises
4.06: Optimization
4.6E: Exercises
4.07: Newtons Method
4.7E: Exercises
4.08: Chapter 4 Review Exercises
05: Investigating Integrals
5.01: Antiderivatives and Indefinite Integrals
5.1E: Exercises
5.02: Approximating Areas
5.2E: Exercises
5.03: The Definite Integral
5.3E: Exercises
5.04: The Fundamental Theorem of Calculus
5.4E: Exercises
5.05: The Net Change Theorem Distances and Symmetry
5.5E: Exercises
5.06: Integration by Substitution
5.6E: Exercises
5.07: Chapter 5 Review Exercises
06: Applications of Integration
6.01: Volumes of Revolution - The Disk and Washer Methods
6.1E: Exercises
6.02: Volumes of Revolution - Cylindrical Shells
6.2E: Exercises
6.03: Arc Length of a Curve and Surface Area
6.3E: Exercises
6.04: Work
6.4E: Exercises
6.05: Hydrostatic Force and Pressure
6.5E: Exercises
6.06: Moments and Centers of Mass
6.6E: Exercises
6.07: The Mean Value Theorem for Integrals
6.7E: Exercises
6.08: Chapter 1 Review Exercises
6.09: Areas Between Curves
6.9E: Exercises
6.10: Determining Volumes by Slicing
6.10E: Exercises
07: Techniques of Integration
7.01: Expanding the Substitution Method
7.1E: Exercises
7.02: Expanding the Substitution Method - Trigonometric Substitution
7.2E: Exercises
7.03: Integration by Parts
7.3E: Exercises
7.04: Chapter 2 Review Exercises
7.05: Partial Fractions
7.5E: Exercises
7.06: Numerical Integration
7.6E: Exercises
08: Sequences and Series
8.01: Improper Integrals
8.1.01: Exercises
8.02: Sequences
8.2E: Exercises
8.03: Infinite Series
8.3E: Exercises
8.04: The Divergence and Integral Tests
8.4E: Exercises
8.05: The Comparison Tests
8.5E: Exercises
8.06: The Alternating Series Test
8.6E: Exercises
8.07: The Ratio and Root Tests
8.7E: Exercises
8.08: Chapter 3 Review Exercises
09: Power Series
9.01: Power Series and Functions
9.1E: Exercises
9.02: Properties of Power Series
9.2E: Exercises
9.03: Taylor and Maclaurin Series
9.3E: Exercises
9.04: The Binomial Theorem and Applications of Taylor Series
9.4E: Exercises
9.05: Chapter 4 Review Exercises
10: Parametric Equations and Polar Coordinates
10.01: Chapter 5 Review Exercises
10.02: Parametric Equations
10.2E: Exercises
10.03: Calculus of Parametric Curves
10.3E: Exercises
10.04: Polar Coordinates
10.4E: Exercises
10.05: Area and Arc Length in Polar Coordinates
10.5E: Exercises
10.06: Conic Sections
10.6E: Exercises
11: Introduction to Differential Equations
11.01: Chapter 6 Review Exercises
11.02: Basics of Differential Equations
11.2E: Exercises for Section 8.1
11.03: Direction Fields and Numerical Methods
11.3E: Exercises for Section 8.2
11.04: Separable Equations
11.4E: Exercises for Section 8.3
11.05: The Logistic Equation
11.5E: Exercises for Section 8.4
11.06: First-order Linear Equations
11.6E: Exercises for Section 8.5
12: Vectors in Space
12.01: Prelude to Vectors in Space
12.02: Vectors in the Plane
12.2E: Exercises for Section 12.1
12.03: Vectors in Three Dimensions
12.3E: Exercises for Section 12.2
12.04: The Dot Product
12.4E: Exercises for Section 12.3
12.05: The Cross Product
12.5E: Exercises for Section 12.4
12.06: Equations of Lines and Planes in Space
12.6E: Exercises for Section 12.5
12.07: Quadric Surfaces
12.7E: Exercises for Section 12.6
12.08: Cylindrical and Spherical Coordinates
12.8E: Exercises for Section 12.7
12.R: Chapter 12 Review Exercises
13: Vector-Valued Functions
13.01: Prelude to Vector-Valued Functions
13.02: Vector-Valued Functions and Space Curves
13.2E: Exercises for Section 13.1
13.03: Calculus of Vector-Valued Functions
13.3E: Exercises for Section 13.2
13.04: Arc Length and Curvature
13.4E: Exercises for Section 13.3
13.05: Motion in Space
13.5E: Exercises for Section 13.4
13.R: Chapter 13 Review Exercises
14: Differentiation of Functions of Several Variables
14.01: Prelude to Differentiation of Functions of Several Variables
14.02: Functions of Several Variables
14.2E: Exercises for Section 14.1
14.03: Limits and Continuity
14.3E: Exercises for Section 14.2
14.04: Partial Derivatives
14.4E: Exercises for Section 14.3
14.05: Tangent Planes and Linear Approximations
14.5E: Exercises for Section 14.4
14.06: The Chain Rule for Multivariable Functions
14.6E: Exercises for Section 14.5
14.07: Directional Derivatives and the Gradient
14.7E: Exercises for Section 14.6
14.08: Maxima Minima Problems
14.8E: Exercises for Section 14.7
14.09: Lagrange Multipliers
14.9E: Exercises for Section 14.8
14.R: Chapter 14 Review Exercises
15: Multiple Integration
15.01: Prelude to Multiple Integration
15.02: Double Integrals over Rectangular Regions
15.2E: Exercises for Section 15.1
15.03: Double Integrals over General Regions
15.3E: Exercises for Section 15.2
15.04: Double Integrals in Polar Coordinates
15.4E: Exercises for Section 15.3
15.05: Triple Integrals
15.5E: Exercises for Section 15.4
15.06: Triple Integrals in Cylindrical and Spherical Coordinates
15.6E: Exercises for Section 15.5
15.07: Calculating Centers of Mass and Moments of Inertia
15.7E: Exercises for Section 15.6
15.08: Change of Variables in Multiple Integrals
15.8E: Exercises for Section 15.7
15.R: Chapter 15 Review Exercises
16: Vector Calculus
16.01: Prelude to Vector Calculus
16.02: Vector Fields
16.2E: Exercises for Section 16.1
16.03: Line Integrals
16.3E: Exercises for Section 16.2
16.04: Conservative Vector Fields
16.4E: Exercises for Section 16.3
16.05: Greens Theorem
16.5E: Exercises for Section 16.4
16.06: Divergence and Curl
16.6E: Exercises for Section 16.5
16.07: Surface Integrals
16.7E: Exercises for Section 16.6
16.08: Stokes Theorem
16.8E: Exercises for Section 16.7
16.09: The Divergence Theorem
16.9E: Exercises for Section 16.8
16.R: Chapter 16 Review Exercises
17: Second-Order Differential Equations
17.01: Prelude to Second-Order Differential Equations
17.02: Second-Order Linear Equations
17.2E: Exercises for Section 17.1
17.03: Nonhomogeneous Linear Equations
17.3E: Exercises for Section 17.2
17.04: Applications of Second-Order Differential Equations
17.4E: Exercises for Section 17.3
17.05: Series Solutions of Differential Equations
17.5E: Exercises for Section 17.4
17.R: Chapter 17 Review Exercises
18: Appendices
18.01: Table of Derivatives
18.02: Table of Integrals
18.03: Other Strategies for Integration
18.3.01: Exercises