Page 1 2017-2018 Math 4545 Mathematics 4545 Analysis Overview Autumn 4 credits Catalog Description: Topics in calculus and analysis. Prerequisites: Either C- or better in 2153, 2162.xx, 2173, 2182H, or 4182H; or credit for 254, 263.xx, 263.01H, 264H, or equivalent; -and-C- or better in Math 2568, 5520H, or equivalent. Exclusions: Entry to this course is restricted to graduate students in Statistics or Biostatistics who have permission from the Departments of Statistics or Biostatistics. Text: Introduction to Real Analysis, by William F. Trench, Edition1.03, published by Library of Congress Cataloging-in-Publication Data, ISBN: 0-13-045786-8 Topics List: 1.Limits and continuity of functions. 2.Derivative, mean value theorem, optimization. 3.Sequences and series, uniform convergence, power series, Taylor's theorem. 4.Riemann integral, substitution, bounded variation, limit properties, Rieman-Stieltjes integral. 5.Multivariable functions, directional derivatives, chain rule, Taylor's theorem. 6.Inverse and implicit function theorems, Lagrange multipliers, multiple integrals, Jacobians, differentiation under the integral sign.