Math 335 syllabus
Advanced Calculus II
This second of a two-course sequence provides students with the theoretical context of concepts encountered in MA 125 through MA 227. Topics include integration of functions of one variable, pointwise and uniform convergence, integration and differentiation of series, differentiable mappings of several variables, chain rule, product rule and gradients, Mean Value Theorem, Taylor's Theorem, Inverse Function Theorem, and Implicit Function Theorem.
Prerequisites: “C” or better in MA 334.
Text: Introduction to Real Analysis Stoll 2 ed. Addison Wesley
Increased sophistication in students’ ability to read and write mathematics, understand difficult proofs, comprehend new definitions and conjecture and prove their consequences. They will: know the definition of the Riemann integral, be able to show integrability of certain classes of functions, be able state and apply the Fundamental Theorem of Calculus, Integral Mean Value Theorem, Change of Variables Theorem, and Taylor’s Theorem. Know and be able to prove and use basic tests for convergence of series. Know the basic theory of power series and Taylor series and methods of determining intervals of convergence. Understand uniform convergence of sequences and series of functions, and its consequences. Additional topics, such as functions of several variables, may be added as time permits.
Last updated February 12, 2014