Mathematics

# MATH 5101: Analysis 1: Functions of One Variable

Lecture - 4 credits

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- Offers a rigorous, proof-based introduction to mathematical analysis and its applications.
- Topics include metric spaces, convergence, compactness, and connectedness; continuous and uniformly continuous functions; derivatives, the mean value theorem, and Taylor series; Riemann integration and the fundamental theorem of calculus; interchanging limit operations; sequences of functions and uniform convergence; ArzelĂ -Ascoli and Stone-Weierstrass theorems; inverse and implicit function theorems; successive approximations and existence/uniqueness for ordinary differential equations; linear operators on finite-dimensional vector spaces and applications to systems of ordinary differential equations.
- Provides a series of computer projects that further develop the connections between theory and applications.
- Requires permission of instructor and head advisor for undergraduate students.

Offers a rigorous, proof-based introduction to mathematical analysis and its applications.

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