MATH 223 Syllabus, Spring 2017

COURSE SYLLABUS FORM American University of Beirut Faculty of Arts and Sciences Department of Mathematics Course Number and Title: Math 223; Advanced Calculus 1. Course Learning Outcomes: Basic knowledge of the following topics: • Metric spaces. • Normed vector spaces. • Derivatives of functions of several variables. • Chain rule for functions of several variables. • Mean-value theorems for functions of several variables. • Taylor’s theorem for functions of several variables. • Implicit and Inverse function theorems. • Differential forms. • Stoke’s theorem. • Notions from Differential Geometry. 2. Resources Available to Students: Textbook: Principles of Mathematical Analysis; W. Rudin; 3rd Edition; McGraw-Hill. 3. Grading Criteria: Two quizzes each allocated 20 points, a final examination allocated 40 points, and weekly homework assignments allocated 20 points. 4. Schedule: • One Week: Metric spaces. • One week: Normed vector spaces. • One Week: Derivatives of functions of several variables. • One Week: Chain rule for functions of several variables. • One Week: Mean-value theorems for functions of several variables. • One Week: Taylor’s theorem for functions of several variables. • Two Weeks: Implicit and Inverse function theorems. • Three Weeks: Differential forms. • Two Weeks: Divergence and Stoke’s theorem. • Two weeks: Notions from Differential Geometry 5. Course Policy (if any): Two quizzes, a final examination, and weekly homework assignment.