Calculus

Gilbert Strang

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

Textbook Components

Table of Contents (PDF)
Answers to Odd-Numbered Problems (PDF)
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)