# Multivariable Calculus

Written by: George Cain and James Herod (GA Tech)

This calculus textbook has been used for several years by the students and faculty at Georgia Tech for a course on multivariable calculus. It was written by George Cain and James Herod, both of whom are professors at Georgia Tech.

1. Euclidean Three Space
1. Introduction
2. Coordinates in Three-Space
3. Some Geometry
4. Some More Geometry–Level Sets
2. Vectors–Algebra and Geometry
1. Vectors
2. Scalar Product
3. Vector Product
3. Vector Functions
1. Relations and Functions
2. Vector Functions
3. Limits and Continuity
4. Derivatives
1. Derivatives
2. Geometry of Space Curves–Curvature
3. Geometry of Space Curves–Torsion
4. Motion
5. More Dimensions
1. The space Rn
2. Functions
6. Linear Functions and Matrices
1. Matrices
2. Matrix Algebra
7. Continuity, Derivatives, and All That
1. Limits and Continuity
2. Derivatives
3. The Chain Rule
8. f:Rn-› R
1. Introduction
2. The Directional Derivative
3. Surface Normals
4. Maxima and Minima
5. Least Squares
6. More Maxima and Minima
7. Even More Maxima and Minima
9. The Taylor Polynomial
1. Introduction
2. The Taylor Polynomial
3. Error
Supplementary material for Taylor polynomial in several variables.
10. Sequences, Series, and All That
1. Introduction
2. Sequences
3. Series
4. More Series
5. Even More Series
6. A Final Remark
11. Taylor Series
1. Power Series
2. Limit of a Power Series
3. Taylor Series
12. Integration
1. Introduction
2. Two Dimensions
13. More Integration
1. Some Applications
2. Polar Coordinates
3. Three Dimensions
14. One Dimension Again
1. Scalar Line Integrals
2. Vector Line Integrals
3. Path Independence
15. Surfaces Revisited
1. Vector Description of Surfaces
2. Integration
16. Integrating Vector Functions
1. Introduction
2. Flux
17. Gauss and Green
1. Gauss’s Theorem
2. Green’s Theorem
3. A Pleasing Application
18. Stokes
1. Stokes’s Theorem
2. Path Independence Revisited
19. Some Physics
1. Fluid Mechanics
2. Electrostatics

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Multivariable Calculus 