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SyllabusCourse Title: Real Analysis, Math 63
Lectures: 120 Kemeny Hall, MWF 11:1512:20
Instructor: Erik van Erp
Office: Kemeny, room 308
Office hours: Mon 34, Tue 34, Thu 24
Phone: 6036469837
Email: erik dot van dot erp at dartmouth dot edu
Course description
"Real Analysis" is the theoretical version of singlevariable 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", "function", "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 vectorvalued 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:
There are two exams: one midterm and a final.
The midterm exam has an inclass and a takehome component,
the final exam is a takehome exam only.
The inclass component tests knowledge of definitions and theorems.
The takehome part requires that you solve problems.
Midterm exam, Tuesday February 8, 1212:50pm, 103 Reed. Final exam: due Tuesday March 15, 12noon.
Homework
Homework will be assigned weekly.
Completed homework must be submitted on Wednesdays at the beginning of class.
Tuesday's xhours are scheduled as problem sessions the day before homework is due.
Grades
Midterm Exam: 1/3
Final Exam: 1/3
Homework: 1/3
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.
