# Patricia Bauman

## Math 442 Spring 2018Professor: Patricia BaumanOffice: Math 718 Phone: 494-1945 Email: baumanp@purdue.edu
Office Hours: Monday at 1:30-2:30 pm, Wednesday at 2:00-3:00 pm, or by appointment.
Course Lectures:MWF 10:30-11:20 in REC 309. Textbook: The Elements of Real Analysis, Second Edition, by Robert G.
Bartle, John Wiley and Sons, 1975.
Syllabus: Most of Chapters VI-VIII in the text, and additional topics.
Prerequisite: MATH 44000H and some knowledge of linear algebra (pertaining to matrix multiplication, determinants and inverses of matrices).
Homework will be collected weekly in class on Wednesdays (with some
exceptions). No late homeworks will be accepted; however, the lowest homework
score will be dropped. The assignments are posted below.
Exams: There will be two midterm exams (in class) and a final exam.
Exam 1 is on Friday, Feb. 23, in class. Course Grade: Your course grade will be computed by the scheme:Final Score = 25% Homework + 20% Exam 1 + 20% Exam 2 + 35% Final Exam. Topics Covered: Mon, Jan. 8: Riemann Integrability of functions of bounded variation on [a,b], Fundamental Theorem of Calculus. Wed, Jan. 10: Sec. 34. Absolute and conditional convergence of Series in R^p, Cauchy Criterion, nonnegative series, examples. Fri, Jan. 12: Harmonic series, rearrangement theorem. Mon, Jan. 15 No class- Martin Luther King Day Wed, Jan. 17: Sec. 35. Comparison test, limit comparison test for series. Root tests for absolute convergence of series in R^p. Fri, Jan. 19: Ratio tests and Raabe's tests for absolute convergence of series in R^p. Integral test. Mon, Jan. 22: Sec. 36. Abel's lemma, Dirichlet's test. Wed, Jan. 24: Abel's test, application of Dirichlet's test, other examples. Fri, Jan. 26: Sec. 18. The limit superior and limit inferior. Definition, examples, and equivalent statements. Mon, Jan. 29: Proof of equivalent statements to the definition of the limit superior and lim inferior. Wed, Jan. 31: Further results on lim sup and lim inf. Sec. 39. Differentiation of functions from domains in R^p into R^q. Fri, Feb. 2: Directional derivatives for functions from domains in R^p to R^q. Computation of Derivatives for differentiable functions from domains in R^p to R. Mon, Feb. 5: Computation of derivatives for differentiable functions from domains in R^p to R^q. Wed, Feb. 7: Sufficient conditions for a function with domain in R^p and range in R^q to be differentiable. Fri, Feb. 9: Differentiability of the product of a scalar-valued differentiable function and a vector valued differentiable function with domain in R^p. Mon, Feb. 12: The chain rule for differentiability of the composition of a differentiable function f defined on a neighborhood of a point c in R^p with range in R^q and a differentible function defined on a neighborhood of f(c) in R^q with range in R^r. Wed, Feb. 14: Mean Value Theorems for functions with domain in R^p and range in R or R^q. Homework Assignments: 1.) Due Wed, Jan. 17: 34H,34K,34N. 2.) Due Wed, Jan. 31: 35D(d,e,f),35I,35J, 36A,36B. 3.) Due Wed, Feb. 7: 35E, 39D,39F. 4.) Due Wed, Feb. 14: 39A,39B,29H,39I,39J(a). 5.) Due Wed, Feb. 21: 40A,40B,40L,40U. Home || Courses || Preprints || Publications |