# Calculus.pdf

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Tags: Calculus, Derivative, Integral, Textbook, Vector Calculus » 2 Comments » October 8, 2009

Calculus, by Gilbert Strang, published in 1991 and still in print from Wesley-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. **This book is available online free at MIT Open Courseware.**

Contents:

**1: Introduction to Calculus**- 1.1 Velocity and Distance
- 1.2 Calculus Without Limits
- 1.3 The Velocity at an Instant
- 1.4 Circular Motion
- 1.5 A Review of Trigonometry
- 1.6 A Thousand Points of Light
- 1.7 Computing in Calculus

**2: Derivatives**- 2.1 The Derivative of a Function
- 2.2 Powers and Polynomials
- 2.3 The Slope and the Tangent Line
- 2.4 Derivative of the Sine and Cosine
- 2.5 The Product and Quotient and Power Rules
- 2.6 Limits
- 2.7 Continuous Functions

**3: Applications of the Derivative**- 3.1 Linear Approximation
- 3.2 Maximum and Minimum Problems
- 3.3 Second Derivatives: Minimum vs. Maximum
- 3.4 Graphs
- 3.5 Ellipses, Parabolas, and Hyperbolas
- 3.6 Iterations x[n+1] = F(x[n])
- 3.7 Newton’s Method and Chaos
- 3.8 The Mean Value Theorem and l’Hopital’s Rule

**4: The Chain Rule**- 4.1 Derivatives by the Charin Rule
- 4.2 Implicit Differentiation and Related Rates
- 4.3 Inverse Functions and Their Derivatives,pp. 164-170
- 4.4 Inverses of Trigonometric Functions

**5: Integrals**- 5.1 The Idea of an Integral
- 5.2 Antiderivatives
- 5.3 Summation vs. Integration
- 5.4 Indefinite Integrals and Substitutions
- 5.5 The Definite Integral
- 5.6 Properties of the Integral and the Average Value
- 5.7 The Fundamental Theorem and Its Consequences
- 5.8 Numerical Integration

**6: Exponentials and Logarithms**- 6.1 An Overview
- 6.2 The Exponential e^x
- 6.3 Growth and Decay in Science and Economics
- 6.4 Logarithms
- 6.5 Separable Equations Including the Logistic Equation
- 6.6 Powers Instead of Exponentials
- 6.7 Hyperbolic Functions

**7: Techniques of Integration**- 7.1 Integration by Parts
- 7.2 Trigonometric Integrals
- 7.3 Trigonometric Substitutions
- 7.4 Partial Fractions
- 7.5 Improper Integrals

**8: Applications of the Integral**- 8.1 Areas and Volumes by Slices
- 8.2 Length of a Plane Curve
- 8.3 Area of a Surface of Revolution
- 8.4 Probability and Calculus
- 8.5 Masses and Moments
- 8.6 Force, Work, and Energy

**9: Polar Coordinates and Complex Numbers**- 9.1 Polar Coordinates
- 9.2 Polar Equations and Graphs
- 9.3 Slope, Length, and Area for Polar Curves
- 9.4 Complex Numbers

**10: Infinite Series**- 10.1 The Geometric Series
- 10.2 Convergence Tests: Positive Series
- 10.3 Convergence Tests: All Series
- 10.4 The Taylor Series for e^x, sin x, and cos x
- 10.5 Power Series

**11: Vectors and Matrices**- 11.1 Vectors and Dot Products
- 11.2 Planes and Projections
- 11.3 Cross Products and Determinants
- 11.4 Matrices and Linear Equations
- 11.5 Linear Algebra in Three Dimensions

**12: Motion along a Curve**- 12.1 The Position Vector
- 12.2 Plane Motion: Projectiles and Cycloids
- 12.3 Tangent Vector and Normal Vector
- 12.4 Polar Coordinates and Planetary Motion

**13: Partial Derivatives**- 13.1 Surface and Level Curves
- 13.2 Partial Derivatives
- 13.3 Tangent Planes and Linear Approximations
- 13.4 Directional Derivatives and Gradients
- 13.5 The Chain Rule
- 13.6 Maxima, Minima, and Saddle Points
- 13.7 Constraints and Lagrange Multipliers

**14: Multiple Integrals**- 14.1 Double Integrals
- 14.2 Changing to Better Coordinates
- 14.3 Triple Integrals
- 14.4 Cylindrical and Spherical Coordinates

**15: Vector Calculus**- 15.1 Vector Fields
- 15.2 Line Integrals
- 15.3 Green’s Theorem
- 15.4 Surface Integrals
- 15.5 The Divergence Theorem
- 15.6 Stokes’ Theorem and the Curl of F

**16: Mathematics after Calculus**- 16.1 Linear Algebra
- 16.2 Differential Equations
- 16.3 Discrete Mathematics

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### Comments

**2 Responses to “Calculus.pdf”**

Calculus, by Gilbert Strang, published in 1991 and still in print from Wesley-Cambridge Press, the book is a useful resource for educators and self-learners alike

may l have all related maths books with calculus linear algebra computer science all for operations reserch and applied statistics