Kuttler K. Calculus of One and Many Variables

Brigham Young University, 2019. — 735 p.Real Valued Functions of One Variable
Fundamental Concepts.
Functions.
Sequences and Compactness.
Continuous Functions and Limits of Functions.
The Derivative.
The Integral.
Methods for Finding Anti-derivatives.
A Few Standard Applications.
Improper Integrals and Stirling's Formula.
Infinite Series.
Power Series.
Polar Coordinates.
Algebra and Geometry of Rp.
Vector Products.
Sequences, Compactness, and Continuity.
Space Curves.
Some Physical Applications.
Functions of Many Variables
Linear Functions.
Eigenvalues and Eigenvectors.
Functions of Many Variables.
The Derivative of a Function of Many Variables.
Optimization.
Line Integrals.
The Riemannn Integral on Rp.
The Integral in Other Coordinates.
The Integral on Two Dimensional Surfaces in R3.
Calculus of Vector Fields.
Stokes and Green's Theorems.
Curvilinear Coordinates.
Measures and Integrals.
The Lebesgue Measure and Integral in Rp.
App. A The Mathematical Theory of Determinants.
App B Implicit Function Theorem.Last revision: 15.10.2019