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Calculus by Gilbert Strang

OCW is pleased to make this textbook available online.  Published in 1991 and still in print from 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.

Strang Calculus Textbook Cover Art
Cover of Calculus, by Professor Gilbert Strang. (Image courtesy of Gilbert Strang.)


Calculus Textbook Components

Table of Contents (PDF)

Index (PDF)

Answers to Odd-Numbered Problems (PDF)

Supplementary Tables and 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 - 4.1 MB)

Chapter 1 - sections:

1.1 - 1.4 (PDF - 2.8 MB)
1.5 - 1.7 (PDF - 1.6 MB)

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 - 4.3 MB)

Chapter 2 - sections:

2.1 - 2.4 (PDF - 2.6 MB)
2.5 - 2.7 (PDF - 2.0 MB)
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'Hopital's Rule, pp. 146-153
Chapter 3 - complete (PDF - 5.9 MB)

Chapter 3 - sections:

3.1 - 3.4 (PDF - 3.2 MB)
3.5 - 3.8 (PDF - 3.3 MB)
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 - 2.0 MB)

Chapter 4 - sections:

4.1 - 4.2 (PDF - 1.0 MB)
4.3 - 4.4 (PDF - 1.2 MB)
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 - 4.8 MB)

Chapter 5 - sections:

5.1 - 5.4 (PDF - 2.2 MB)
5.5 - 5.8 (PDF - 2.8 MB)
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 - 4.9 MB)

Chapter 6 - sections:

6.1 - 6.4 (PDF - 3.0 MB)
6.5 - 6.7 (PDF - 2.2 MB)
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 - 2.6 MB)

Chapter 7 - sections:

7.1 - 7.3 (PDF - 1.7 MB)
7.4 - 7.5 (PDF - 1.0 MB)
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 - 3.4 MB)

Chapter 8 - sections:

8.1 - 8.3 (PDF - 1.7 MB)
8.4 - 8.6 (PDF - 2.0 MB)
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 - 1.7 MB)

Chapter 9 - sections:

9.1 - 9.2 (PDF)
9.3 - 9.4 (PDF - 1.0 MB)
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 - 2.9 MB)

Chapter 10 - sections:

10.1 - 10.3 (PDF - 1.9 MB)
10.4 - 10.5 (PDF - 1.2 MB)
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 - 4.0 MB)

Chapter 11 - sections:

11.1 - 11.3 (PDF - 2.5 MB)
11.4 - 11.5 (PDF - 1.7 MB)
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 - 2.2 MB)

Chapter 12 - sections:

12.1 - 12.2 (PDF - 1.2 MB)
12.3 - 12.4 (PDF - 1.1 MB)
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 - 4.9 MB)

Chapter 13 - sections:

13.1 - 13.4 (PDF - 2.7 MB)
13.5 - 13.7 (PDF - 2.5 MB)
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 - 2.5 MB)

Chapter 14 - sections:

14.1 - 14.2 (PDF - 1.4 MB)
14.3 - 14.4 (PDF - 1.3 MB)
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 - 4.3 MB)

Chapter 15 - sections:

15.1 - 15.3 (PDF - 2.1 MB)
15.4 - 15.6 (PDF - 2.3 MB)
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 - 1.8 MB)

Chapter 16 - sections:

16.1 - 16.2 (PDF - 1.5 MB)
16.3 (PDF)

 


 
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