Course Information

For lecture information, including instructor and TA contact information, please see the Canvas site for this course.

Course Description: First course in an introductory two-quarter sequence on analysis. Topics include the real number system, numerical sequences and series, infinite limits, limits of functions, continuity, differentiation.

Course Textbook: Advanced Calculus by Patrick Fitzpatrick. Published by the American Mathematical Society. (Second Edition.)

Description from the AMS Website: "...intended as a text for courses that furnish the backbone of the student's undergraduate education in mathematical analysis. The goal is to rigorously present the fundamental concepts within the context of illuminating examples and stimulating exercises. This book is self-contained and starts with the creation of basic tools using the completeness axiom. The continuity, differentiability, integrability, and power series representation properties of functions of a single variable are established. The next few chapters describe the topological and metric properties of Euclidean space. These are the basis of a rigorous treatment of differential calculus (including the Implicit Function Theorem and Lagrange Multipliers) for mappings between Euclidean spaces and integration for functions of several real variables."

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