Textbook

Published in 1991 by Wellesley-Cambridge Press, the book is a useful resource for educators and self-learners alike. It is well organized, covers single variable and multivariable calculus in depth, and is rich with applications. There is also an online Instructor's Manual and a student Study Guide.

The complete textbook is also available as a single file. ( PDF - 38.5MB)

 

Highlights of Calculus           
MIT Professor Gilbert Strang has created a series of videos to show ways in which calculus is important in our lives. The videos, which include real-life examples to illustrate the concepts, are ideal for high school students, college students, and anyone interested in learning the basics of calculus.           
Watch the videos

Textbook Components

  • Table of Contents ( PDF)
  • Answers to Odd-Numbered Problems ( PDF - 2.4MB)
  • Equations ( PDF)

ChapterS FILES
1: Introduction to Calculus, pp. 1-43   
1.1 Velocity and Distance, pp. 1-7             
1.2 Calculus Without Limits, pp. 8-15             
1.3 The Velocity at an Instant, pp. 16-21             
1.4 Circular Motion, pp. 22-28             
1.5 A Review of Trigonometry, pp. 29-33             
1.6 A Thousand Points of Light, pp. 34-35             
1.7 Computing in Calculus, pp. 36-43
Chapter 1 - complete ( PDF - 2.2MB)           
Chapter 1 - sections:           
1.1 - 1.4 ( PDF - 1.6MB)             
1.5 - 1.7 ( PDF - 1.4MB)
2: Derivatives, pp. 44-90   
2.1 The Derivative of a Function, pp. 44-49             
2.2 Powers and Polynomials, pp. 50-57             
2.3 The Slope and the Tangent Line, pp. 58-63             
2.4 Derivative of the Sine and Cosine, pp. 64-70             
2.5 The Product and Quotient and Power Rules, pp. 71-77             
2.6 Limits, pp. 78-84             
2.7 Continuous Functions, pp. 85-90
Chapter 2 - complete ( PDF - 3.8MB)          
Chapter 2 - sections:          
2.1 - 2.4 ( PDF - 2.3MB)             
2.5 - 2.7 ( PDF - 1.7MB)
3: Applications of the Derivative, pp. 91-153   
3.1 Linear Approximation, pp. 91-95             
3.2 Maximum and Minimum Problems, pp. 96-104             
3.3 Second Derivatives: Minimum vs. Maximum, pp. 105-111             
3.4 Graphs, pp. 112-120             
3.5 Ellipses, Parabolas, and Hyperbolas, pp. 121-129             
3.6 Iterations x[n+1] = F(x[n]), pp. 130-136             
3.7 Newton’s Method and Chaos, pp. 137-145             
3.8 The Mean Value Theorem and l’Hôpital’s Rule, pp. 146-153
Chapter 3 - complete ( PDF - 3.3MB)          
Chapter 3 - sections:         
3.1 - 3.4 ( PDF - 1.5MB)             
3.5 - 3.8 ( PDF - 2.0MB)
4: The Chain Rule, pp. 154-176   
4.1 Derivatives by the Charin Rule, pp. 154-159             
4.2 Implicit Differentiation and Related Rates, pp. 160-163             
4.3 Inverse Functions and Their Derivatives, pp. 164-170             
4.4 Inverses of Trigonometric Functions, pp. 171-176
Chapter 4 - complete ( PDF - 1.1MB)           
Chapter 4 - sections:          
4.1 - 4.2 ( PDF)             
4.3 - 4.4 ( PDF)
5: Integrals, pp. 177-227   
5.1 The Idea of an Integral, pp. 177-181             
5.2 Antiderivatives, pp. 182-186             
5.3 Summation vs. Integration, pp. 187-194             
5.4 Indefinite Integrals and Substitutions, pp. 195-200             
5.5 The Definite Integral, pp. 201-205             
5.6 Properties of the Integral and the Average Value, pp. 206-212             
5.7 The Fundamental Theorem and Its Consequences, pp. 213-219             
5.8 Numerical Integration, pp. 220-227
Chapter 5 - complete ( PDF - 3.3MB)           
Chapter 5 - sections:          
5.1 - 5.4 ( PDF - 1.1MB)             
5.5 - 5.8 ( PDF - 2.3MB)
6: Exponentials and Logarithms, pp. 228-282   
6.1 An Overview, pp. 228-235             
6.2 The Exponential e^x, pp. 236-241             
6.3 Growth and Decay in Science and Economics, pp. 242-251             
6.4 Logarithms, pp. 252-258             
6.5 Separable Equations Including the Logistic Equation, pp. 259-266             
6.6 Powers Instead of Exponentials, pp. 267-276             
6.7 Hyperbolic Functions, pp. 277-282
Chapter 6 - complete ( PDF - 3.1MB)           
Chapter 6 - sections:          
6.1 - 6.4 ( PDF - 2.1MB)             
6.5 - 6.7 ( PDF - 1.2MB)
7: Techniques of Integration, pp. 283-310   
7.1 Integration by Parts, pp. 283-287             
7.2 Trigonometric Integrals, pp. 288-293             
7.3 Trigonometric Substitutions, pp. 294-299             
7.4 Partial Fractions, pp. 300-304             
7.5 Improper Integrals, pp. 305-310
Chapter 7 - complete ( PDF - 1.7MB)           
Chapter 7 - sections:          
7.1 - 7.3 ( PDF - 1.2MB)             
7.4 - 7.5 ( PDF)
8: Applications of the Integral, pp. 311-347   
8.1 Areas and Volumes by Slices, pp. 311-319             
8.2 Length of a Plane Curve, pp. 320-324             
8.3 Area of a Surface of Revolution, pp. 325-327             
8.4 Probability and Calculus, pp. 328-335             
8.5 Masses and Moments, pp. 336-341             
8.6 Force, Work, and Energy, pp. 342-347
Chapter 8 - complete ( PDF - 2.1MB)          
Chapter 8 - sections:         
8.1 - 8.3 ( PDF - 1.1MB)             
8.4 - 8.6 ( PDF - 1.1MB)
9: Polar Coordinates and Complex Numbers, pp. 348-367   
9.1 Polar Coordinates, pp. 348-350             
9.2 Polar Equations and Graphs, pp. 351-355             
9.3 Slope, Length, and Area for Polar Curves, pp. 356-359             
9.4 Complex Numbers, pp. 360-367
Chapter 9 - complete ( PDF)          
Chapter 9 - sections:         
9.1 - 9.2 ( PDF)             
9.3 - 9.4 ( PDF)
10: Infinite Series, pp. 368-391   
10.1 The Geometric Series, pp. 368-373             
10.2 Convergence Tests: Positive Series, pp. 374-380             
10.3 Convergence Tests: All Series, pp. 325-327             
10.4 The Taylor Series for e^x, sin x, and cos x, pp. 385-390             
10.5 Power Series, pp. 391-397
Chapter 10 - complete ( PDF - 2.0MB)          
Chapter 10 - sections:         
10.1 - 10.3 ( PDF - 1.3MB)             
10.4 - 10.5 ( PDF)
11: Vectors and Matrices, pp. 398-445   
11.1 Vectors and Dot Products, pp. 398-406             
11.2 Planes and Projections, pp. 407-415             
11.3 Cross Products and Determinants, pp. 416-424             
11.4 Matrices and Linear Equations, pp. 425-434             
11.5 Linear Algebra in Three Dimensions, pp. 435-445
Chapter 11 - complete ( PDF - 3.3MB)          
Chapter 11 - sections:         
11.1 - 11.3 ( PDF - 2.2MB)             
11.4 - 11.5 ( PDF - 1.2MB)
12: Motion along a Curve, pp. 446-471   
12.1 The Position Vector, pp. 446-452             
12.2 Plane Motion: Projectiles and Cycloids, pp. 453-458             
12.3 Tangent Vector and Normal Vector, pp. 459-463             
12.4 Polar Coordinates and Planetary Motion, pp. 464-471
Chapter 12 - complete ( PDF - 1.2MB)          
Chapter 12 - sections:         
12.1 - 12.2 ( PDF)             
12.3 - 12.4 ( PDF)
13: Partial Derivatives, pp. 472-520   
13.1 Surface and Level Curves, pp. 472-474             
13.2 Partial Derivatives, pp. 475-479             
13.3 Tangent Planes and Linear Approximations, pp. 480-489             
13.4 Directional Derivatives and Gradients, pp. 490-496             
13.5 The Chain Rule, pp. 497-503             
13.6 Maxima, Minima, and Saddle Points, pp. 504-513             
13.7 Constraints and Lagrange Multipliers, pp. 514-520
Chapter 13 - complete ( PDF - 3.9MB)          
Chapter 13 - sections:         
13.1 - 13.4 ( PDF - 2.3MB)             
13.5 - 13.7 ( PDF - 1.5MB)
14: Multiple Integrals, pp. 521-548   
14.1 Double Integrals, pp. 521-526             
14.2 Changing to Better Coordinates, pp. 527-535             
14.3 Triple Integrals, pp. 536-540             
14.4 Cylindrical and Spherical Coordinates, pp. 541-548
Chapter 14 - complete ( PDF - 1.9MB)          
Chapter 14 - sections:         
14.1 - 14.2 ( PDF - 1.0MB)             
14.3 - 14.4 ( PDF)
15: Vector Calculus, pp. 549-598   
15.1 Vector Fields, pp. 549-554             
15.2 Line Integrals, pp. 555-562             
15.3 Green’s Theorem, pp. 563-572             
15.4 Surface Integrals, pp. 573-581             
15.5 The Divergence Theorem, pp. 582-588             
15.6 Stokes’ Theorem and the Curl of F, pp. 589-598
Chapter 15 - complete ( PDF - 3.1MB)          
Chapter 15 - sections:         
15.1 - 15.3 ( PDF - 1.5MB)             
15.4 - 15.6 ( PDF - 1.6MB)
16: Mathematics after Calculus, pp. 599-615   
16.1 Linear Algebra, pp. 599-602             
16.2 Differential Equations, pp. 603-610             
16.3 Discrete Mathematics, pp. 611-615
Chapter 16 - complete ( PDF)          
Chapter 16 - sections:         
16.1 - 16.2 ( PDF)             
16.3 ( PDF)

Course Info

Learning Resource Types

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