# Kittttttan*s Web

## Calculus

This is HTML of Calculus, Gilbert Strang.
You can read PDFs at MIT OpenCourseWare.

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

### Contents

1. Introduction to Calculus
2. Derivatives
3. Applications of the Derivative
4. The Chain Rule
5. Integrals
6. Exponentials and Logarithms
1. An Overview
2. The Exponential ex
3. Growth and Decay in Science and Economics
4. Logarithms
5. Separable Equations Including the Logistic Equation
7. Hyperbolic Functions
7. Techniques of Integration
1. Integration by Parts
2. Trigonometric Integrals
3. Trigonometric Substitutions
4. Partial Fractions
5. Improper Integrals
8. Applications of the Integral
1. Areas and Volumes by Slices
2. Length of a Plane Curve
3. Area of a Surface of Revolution
4. Probability and Calculus
5. Masses and Moments
6. Force, Work, and Energy
9. Polar Coordinates and Complex Numbers
1. Polar Coordinates
2. Polar Equations and Graphs
3. Slope, Length, and Area for Polar Curves
4. Complex Numbers
10. Infinite Series
1. The Geometric Series
2. Convergence Tests: Positive Series
3. Convergence Tests: All Series
4. The Taylor Series for ex, sin x, and cos x
5. Power Series
11. Vectors and Matrices
1. Vectors and Dot Products
2. Planes and Projections
3. Cross Products and Determinants
4. Matrices and Linear Equations
5. Linear Algebra in Three Dimensions
12. Motion along a Curve
1. The Position Vector
2. Plane Motion: Projectiles and Cycloids
3. Tangent Vector and Normal Vector
4. Polar Coordinates and Planetary Motion
13. Partial Derivatives
1. Surfaces and Level Curves
2. Partial Derivatives
3. Tangent Planes and Linear Approximations
5. The Chain Rule
6. Maxima, Minima, and Saddle Points
7. Constraints and Lagrange Multipliers
14. Multiple Integrals
1. Double Integrals
2. Changing to Better Coordinates
3. Triple Integrals
4. Cylindrical and Spherical Coordinates
15. Vector Calculus
1. Vector Fields
2. Line Integrals
3. Green's Theorem
4. Surface Integrals
5. The Divergence Theorem
6. Stokes' Theorem and the Curl of F
16. Mathematics after Calculus
1. Linear Algebra
2. Differential Equations
3. Discrete Mathematics