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# Syllabus

Course Title: Real Analysis, Math 63
Lectures: Kemeny 007, MWF 11:15-12:20
Instructor: Erik van Erp
Office: Kemeny, room 308
Office hours: Mon 3-4pm, Tue 2-3pm, Wed 10-11am
Phone: 603-646-9837
E-mail: erik dot van dot erp at dartmouth dot edu

Course description

"Real Analysis" is the theoretical version of single-variable calculus. Calculus courses develop progressively more complicated forms of calculation using mostly elementary functions. Analysis deals with abstract functions, and uses precise definitions of fundamental notions ("real number", "funtion", "continuity", "limit", etc.) to prove key theorems about derivatives, integrals and series, and establish the precise extent to which they apply. Can every function be integrated? Does a Fourier series always converge? The rigorous approach to analysis allows us to answer such tricky questions that remain puzzling without solid logical foundations.
Topics include: the theory of numbers and sets; various convergence issues; abstract metric spaces; the theory of integration; approximation of functions.

Course prerequisites

Linear algebra (Math 22 or 24), or Calculus of vector-valued functions (Math 13) and permission of the instructor

Textbook

Introduction to Analysis
by Maxwell Rosenlicht.

Topics

We will follow the textbook and aim to cover in full or in part the following chapters:
• Notions from set theory
• The real number system
• Metric spaces
• Continuous functions
• Differentiation
• Riemann Integration
• Interchange of limit operations
Exams

There are two exams: one mid-term and a final. The mid-term exam has an in-class and a take-home component, the final exam is a take-home exam only. The in-class component tests knowledge of definitions and theorems. The take-home part requires that you solve problems.

Midterm exam, Tuesday February 9, 12-12:50pm, Kemeny 007.
Final exam: due Saturday March 13, 12noon.

Homework

Homework will be assigned weekly. Completed homework must be submitted on Wednesdays at the beginning of class. Tuesday's x-hours are scheduled as problem sessions the day before homework is due.

Midterm Exam: 30%
Final Exam: 40%
Homework: 30%

Honors code

Collaboration and discussion of general ideas related to homework problems are allowed and encouraged. However you must write down all solutions by yourself in your own words; copying is obviously a violation of the honor code. No collaboration is permitted on exams.

Students with disabilities

Students with disabilities who will be taking this course and may need disability related classroom accommodations are encouraged to make an appointment to see their instructor as soon as possible. Also, they should stop by the Academic Skills Center in Collis Center to register for support services.