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