MATH M413
Instructor: Dr. Chris Lang
Text: Kenneth A. Ross, Elementary Analysis: The Theory of Calculus, Springer-Verlag, 1980.
Course objectives: Topics to be covered include mathematical induction, the axioms of the real number system, sequences, series, functions, continuity of functions, and the intermediate value theorem. Students will solve problems relevant to these topics and students will write proofs of such things as the convergence of sequences and of familiar theorems of calculus.
Homework assignments: 1, 2, 3, 4, 5, 6, 7 [Solutions], 8, 9, 10, 11 [Solutions].
Lecture notes: Section 1, 2, 3, 4, 5, 7, 8, 9, 10, 11, 13, 14, 15, 16, 17, 18, 19 [revised].
Solutions to tests: test 1, test 2,
test 3, final exam
MATH M414
Instructor: Dr. Chris Lang
Text: Kenneth A. Ross, Elementary Analysis: The Theory of Calculus, Springer-Verlag, 1980.
Course objectives: Topics to be covered include limits of functions, power series, uniform convergence, derivatives, Taylor's theorem, and the Riemann integral. Students will solve problems and will write proofs of theorems relevant to these topics.
Homework assignments: 1, 2, 3, 4, 5, 6, 7, 8.
Lecture notes: Sections 20, 21, 23, 24, 25, 26, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37