Mathematics and Computer Science at Western Carolina University

Revised: November 2006

Derivatives and Integrals; inverses and change of variables. Prerequisite: Math 622. Three semester hours.

To continue the objectives of Math 622.

Marsden. Elementary Classical Analysis. W.H. Freeman and Company, 1974.

Grading procedures and factors influencing course grade are left to the discretion of individual instructors, subject to general university policy.

Attendance policy is left to the discretion of individual instructors, subject to general university policy.

Chapter 6: Differentiable Mappings (12 days)
Definition and conditions for differentiability; derivative rules and theorems; higher order derivatives
Chapter 7: The Inverse and Implicit Function Theorems and related Topics (10 days)
Theorems surrounding and consequences of the Implicit Function Theorem; Ordinary differential equations; LaGrange Multipliers
Chapter 8: Integration (12 days)
Integrable functions, measure theory, the Fundamental Theorem of Calculus, and convergence theorems
Chapter 9: Fubini's Theorem and the Change of Variables Formula (10 days)
General change of variables; polar, spherical, and cylindrical coordinates; Lebesque Integral
Times include review and testing.