Calculus

The text guides students through the core concepts of calculus and helps them understand how those concepts apply to their lives and the world around them.

Calculus Mathematics

Author: Gilbert Strang & Edwin Herman
Publisher: MIT & University of Wisconsin-Stevens Point
Source: LibreTexts
License: CC BY-NC-SA
Language: EN
Category: Basic Sciences

Read online Download PDF (open licence)

Contents· 275 sections

01: Functions and Graphs
1.00: Prelude to Functions and Graphs
1.01: Review of Functions
1.1E: Exercises for Section 1.1
1.02: Basic Classes of Functions
1.2E: Exercises for Section 1.2
1.03: Trigonometric Functions
1.3E: Exercises for Section 1.3
1.04: Inverse Functions
1.4E: Exercises for Section 1.4
1.05: Exponential and Logarithmic Functions
1.5E: Exercises for Section 1.5
1.06: Chapter 1 Review Exercises
02: Limits
2.00: Prelude to Limits
2.01: A Preview of Calculus
2.1E: Exercises for Section 2.1
2.02: The Limit of a Function
2.2E: Exercises for Section 2.2
2.03: The Limit Laws
2.3E: Exercises for Section 2.3
2.04: Continuity
2.4E: Exercises for Section 2.4
2.05: The Precise Definition of a Limit
2.5E: Exercises for Section 2.5
2.06: Chapter 2 Review Exercises
03: Derivatives
3.00: Prelude to Derivatives
3.01: Defining the Derivative
3.1E: Exercises for Section 3.1
3.02: The Derivative as a Function
3.2E: Exercises for Section 3.2
3.03: Differentiation Rules
3.3E: Exercises for Section 3.3
3.04: Derivatives as Rates of Change
3.4E: Exercises for Section 3.4
3.05: Derivatives of Trigonometric Functions
3.5E: Exercises for Section 3.5
3.06: The Chain Rule
3.6E: Exercises for Section 3.6
3.07: Derivatives of Inverse Functions
3.7E: Exercises for Section 3.7
3.08: Implicit Differentiation
3.8E: Exercises for Section 3.8
3.09: Derivatives of Exponential and Logarithmic Functions
3.9E: Exercises for Section 3.9
3.R: Chapter 3 Review Exercises
04: Applications of Derivatives
4.00: Prelude to Applications of Derivatives
4.01: Related Rates
4.1E: Exercises for Section 4.1
4.02: Linear Approximations and Differentials
4.2E: Exercises for Section 4.2
4.03: Maxima and Minima
4.3E: Exercises for Section 4.3
4.04: The Mean Value Theorem
4.4E: Exercises for Section 4.4
4.05: Derivatives and the Shape of a Graph
4.5E: Exercises for Section 4.5
4.06: Limits at Infinity and Asymptotes
4.6E: Exercises for Section 4.6
4.07: Applied Optimization Problems
4.7E: Exercises for Section 4.7
4.08: LHopitals Rule
4.8E: Exercises for Section 4.8
4.09: Newtons Method
4.9E: Exercises for Section 4.9
4.10: Antiderivatives
4.10E: Exercises for Section 4.10
4.R: Chapter 4 Review Exercises
05: Integration
5.00: Prelude to Integration
5.01: Approximating Areas
5.1E: Exercises for Section 5.1
5.02: The Definite Integral
5.2E: Exercises for Section 5.2
5.03: The Fundamental Theorem of Calculus
5.3E: Exercises for Section 5.3
5.04: Integration Formulas and the Net Change Theorem
5.4E: Exercises for Section 5.4
5.05: Substitution
5.5E: Exercises for Section 5.5
5.06: Integrals Involving Exponential and Logarithmic Functions
5.6E: Exercises for Section 5.6
5.07: Integrals Resulting in Inverse Trigonometric Functions
5.7: Integrals Resulting in Inverse Trigonometric Functions
5.7E: Exercises for Section 5.7
5.R: Chapter 5 Review Exercises
06: Applications of Integration
6.00: Prelude to Applications of Integration
6.01: Areas between Curves
6.1E: Exercises for Section 6.1
6.02: Determining Volumes by Slicing
6.2E: Exercises for Section 6.2
6.03: Volumes of Revolution - Cylindrical Shells
6.3E: Exercises for Section 6.3
6.04: Arc Length of a Curve and Surface Area
6.4E: Exercises for Section 6.4
6.05: Physical Applications of Integration
6.5E: Exercises for Section 6.5
6.06: Moments and Centers of Mass
6.6E: Exercises for Section 6.6
6.07: Integrals Exponential Functions and Logarithms
6.7E: Exercises for Section 6.7
6.08: Exponential Growth and Decay
6.8E: Exercises for Section 6.8
6.09: Calculus of the Hyperbolic Functions
6.9E: Exercises for Section 6.9
6.R: Chapter 6 Review Exercises
07: Techniques of Integration
7.00: Prelude to Techniques of Integration
7.01: Integration by Parts
7.1E: Exercises for Section 7.1
7.02: Trigonometric Integrals
7.2E: Exercises for Section 7.2
7.03: Trigonometric Substitution
7.3E: Exercises for Section 7.3
7.04: Partial Fractions
7.4E: Exercises for Section 7.4
7.05: Other Strategies for Integration
7.5E: Exercises for Section 7.5
7.06: Numerical Integration
7.6E: Exercises for Section 7.6
7.07: Improper Integrals
7.7E: Exercises for Section 7.7
7.R: Chapter 7 Review Exercises
08: Introduction to Differential Equations
8.00: Prelude to Differential Equations
8.01: Basics of Differential Equations
8.1E: Exercises for Section 8.1
8.02: Direction Fields and Numerical Methods
8.2E: Exercises for Section 8.2
8.03: Separable Equations
8.3E: Exercises for Section 8.3
8.04: The Logistic Equation
8.4E: Exercises for Section 8.4
8.05: First-order Linear Equations
8.5E: Exercises for Section 8.5
8.R: Chapter 8 Review Exercises
09: Sequences and Series
9.00: Prelude to Sequence and Series
9.01: Sequences
9.1E: Exercises for Section 9.1
9.02: Infinite Series
9.2E: Exercises for Section 9.2
9.03: The Divergence and Integral Tests
9.3E: Exercises for Section 9.3
9.04: Comparison Tests
9.4E: Exercises for Section 9.4
9.05: Alternating Series
9.5E: Exercises for Section 9.5
9.06: Ratio and Root Tests
9.6E: Exercises for Section 9.6
9.R: Chapter 9 Review Exercises
10: Power Series
10.00: Prelude to Power Series
10.01: Power Series and Functions
10.1E: Exercises for Section 10.1
10.02: Properties of Power Series
10.2E: Exercises for Section 10.2
10.03: Taylor and Maclaurin Series
10.3E: Exercises for Section 10.3
10.04: Working with Taylor Series
10.4E: Exercises for Section 10.4
10.R: Chapter 10 Review Exercises
11: Parametric Equations and Polar Coordinates
11.00: Prelude to Parametric Equations and Polar Coordinates
11.01: Parametric Equations
11.1E: Exercises for Section 11.1
11.02: Calculus of Parametric Curves
11.2E: Exercises for Section 11.2
11.03: Polar Coordinates
11.3E: Exercises for Section 11.3
11.04: Area and Arc Length in Polar Coordinates
11.4E: Exercises for Section 11.4
11.05: Conic Sections
11.5E: Exercises for Section 11.5
11.R: Chapter 11 Review Exercises
12: Vectors in Space
12.00: Prelude to Vectors in Space
12.01: Vectors in the Plane
12.1E: Exercises for Section 12.1
12.02: Vectors in Three Dimensions
12.2E: Exercises for Section 12.2
12.03: The Dot Product
12.3E: Exercises for Section 12.3
12.04: The Cross Product
12.4E: Exercises for Section 12.4
12.05: Equations of Lines and Planes in Space
12.5E: Exercises for Section 12.5
12.06: Quadric Surfaces
12.6E: Exercises for Section 12.6
12.07: Cylindrical and Spherical Coordinates
12.7E: Exercises for Section 12.7
12.R: Chapter 12 Review Exercises
13: Vector-Valued Functions
13.00: Prelude to Vector-Valued Functions
13.01: Vector-Valued Functions and Space Curves
13.1E: Exercises for Section 13.1
13.02: Calculus of Vector-Valued Functions
13.2E: Exercises for Section 13.2
13.03: Arc Length and Curvature
13.3E: Exercises for Section 13.3
13.04: Motion in Space
13.4E: Exercises for Section 13.4
13.R: Chapter 13 Review Exercises
14: Differentiation of Functions of Several Variables
14.00: Prelude to Differentiation of Functions of Several Variables
14.01: Functions of Several Variables
14.1E: Exercises for Section 14.1
14.02: Limits and Continuity
14.2E: Exercises for Section 14.2
14.03: Partial Derivatives
14.3E: Exercises for Section 14.3
14.04: Tangent Planes and Linear Approximations
14.4E: Exercises for Section 14.4
14.05: The Chain Rule for Multivariable Functions
14.5E: Exercises for Section 14.5
14.06: Directional Derivatives and the Gradient
14.6E: Exercises for Section 14.6
14.07: Maxima Minima Problems
14.7E: Exercises for Section 14.7
14.08: Lagrange Multipliers
14.8E: Exercises for Section 14.8
14.R: Chapter 14 Review Exercises
15: Multiple Integration
15.00: Prelude to Multiple Integration
15.01: Double Integrals over Rectangular Regions
15.1E: Exercises for Section 15.1
15.02: Double Integrals over General Regions
15.2E: Exercises for Section 15.2
15.03: Double Integrals in Polar Coordinates
15.3E: Exercises for Section 15.3
15.04: Triple Integrals
15.4E: Exercises for Section 15.4
15.05: Triple Integrals in Cylindrical and Spherical Coordinates
15.5E: Exercises for Section 15.5
15.06: Calculating Centers of Mass and Moments of Inertia
15.6E: Exercises for Section 15.6
15.07: Change of Variables in Multiple Integrals
15.7E: Exercises for Section 15.7
15.R: Chapter 15 Review Exercises
16: Vector Calculus
16.00: Prelude to Vector Calculus
16.01: Vector Fields
16.1E: Exercises for Section 16.1
16.02: Line Integrals
16.2E: Exercises for Section 16.2
16.03: Conservative Vector Fields
16.3E: Exercises for Section 16.3
16.04: Greens Theorem
16.4E: Exercises for Section 16.4
16.05: Divergence and Curl
16.5E: Exercises for Section 16.5
16.06: Surface Integrals
16.6E: Exercises for Section 16.6
16.07: Stokes Theorem
16.7E: Exercises for Section 16.7
16.08: The Divergence Theorem
16.8E: Exercises for Section 16.8
16.R: Chapter 16 Review Exercises
17: Second-Order Differential Equations
17.00: Prelude to Second-Order Differential Equations
17.01: Second-Order Linear Equations
17.1E: Exercises for Section 17.1
17.02: Nonhomogeneous Linear Equations
17.2E: Exercises for Section 17.2
17.03: Applications of Second-Order Differential Equations
17.3E: Exercises for Section 17.3
17.04: Series Solutions of Differential Equations
17.4E: Exercises for Section 17.4
17.R: Chapter 17 Review Exercises
18: Appendices
18.A: Table of Derivatives
18.B: Table of Integrals