Math 335 syllabus
Advanced Calculus II
Course description: This is the second of a two course sequence designed to provide students with the
theoretical context of concepts encountered in MA 125 through MA 227. Topics covered
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, Implicit Function Theorem.
Prerequisites: MA 334 Minimum Grade of C.
Suggested Texts: Introduction to Real Analysis Stoll 2 ed. Addison Wesley;
Introduction to Analysis (5th ed.) by Edward D. Gaughan, American Mathematical Society, 2009.
Learning outcomes: Upon the successful completion of the course a student will:
Increase their ability to read and write mathematics, understand difficult proofs, comprehend new definitions and conjecture and prove their consequences.
Know the definition of the Riemann integral.
Know to show integrability of certain classes of functions.
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.