M600 Advanced Calculus (3 cr.)

This course provides a formal exploration of elementary topology of both R and Rⁿ, differentiability and Riemann integrability of functions in R and Rⁿ, infinite series of real numbers, sequences of functions, and uniform convergence.

Upon completion of the course, students are expected to be able to do the following:

1. Define convergence, continuity, differentiability, and Riemann integrability in R and Rⁿ, and uniform convergence of sequences, series, and functions. (1.c)
2. Determine and prove convergence or divergence of sequences in R and Rⁿ, series in R, and sequences and series of functions. (2.d)
3. Evaluate derivatives and Riemann integrals in R and Rⁿ. (4.a)
4. Prove theorems about differentiability and Riemann integrability in R and Rⁿ. (2.c)