Wong Yan Loi. Multivariable Calculus - Lecture Notes

Self-publishing. — Singapore: National University of Singapore, 2013. — 109 p.A course on Multivariable Calculus. Topics covered include: Vector Functions; Functions of several variables; Limits and Continuity; Partial Derivatives; Maximum and Minimum Values; Lagrange Multipliers; Multiple Integrals; Surface Area; Triple Integrals; Change of Variables in Multiple Integrals; Vector Fields; etc.Notations
Vectors in R3
Cylinders and Quadric Surfaces
Cylindrical and Spherical Coordinates
Vector Functions
Functions of several variables
Limits and Continuity
Partial Derivatives
Maximum and Minimum Values
Lagrange Multipliers
Multiple Integrals
Surface Area
Triple Integrals
Change of Variables in Multiple Integrals
Vector Fields
Line Integrals
Line Integrals of Vector Fields
The Fundamental Theorem for Line Integrals
Independence of Path
Green’s Theorem
The Curl and Divergence of a Vector Field
Parametric Surfaces and their Areas
Oriented Surfaces
Surface Integrals of Vector Fields
Stokes’ Theorem
The Divergence Theorem
Further ExercisesBibliography