This course will develop the theory of calculus in one and several variables. Key topics are the familiar ones from previous calculus courses, namely the theory of limits, continuity, differentiation, integration and series. The underlying topological notions of open sets, closed sets, compactness and connectedness that are essential to proofs form the first part of the course.
Grading will be based on the following combination of student work: homework (100 points), hour exams (2 -- 200 points total), course journal (50 points) and final exam (150 points).
Students who have need of a particular grade for the course are expected to act accordingly. I will work with you so that you may earn your grade fairly. I will not inflate grades at the end of the course.
Tentative schedule of topics from text by week (7 total):
1. Preliminaries -- Buck 1.1-1.5 ; Topological Concepts, Sequences-- Buck 1.5-1.7
2. More Topology -- Compactness -- Buck 1.7-1.8; Continuity -- Buck 2.1-2.3
3. Uniform Continuity, Theorems for Continuous Functions, Limits -- Buck 2.4-2.7; Finish Continuity, Exam 1 (on Chapters 1, 2).
Note break for June 22-26
4. Derivatives -- Buck 3.1--3.3; Chain Rule, Taylor's Theorem -- Buck 3.4--3.5
5. Extremum problems, start integration -- Buck 3.6, 4.1-4.2; More integration -- Buck 4.2-4.4
6. Improper integrals and infinite series -- Buck 4.5, 5.1-5.2; Exam 2 (Chapters 3, 4 and 5.2), Power series -- Buck 6.1, 6.3
7. Series and Sequences of Functions; Uniform convergence; Improper integrals with parameters-- Buck 6.2, 6.4; More on uniform convergence vs. pointwise convergence; review for final.
Final exam -- Tuesday, July 28.
A separate list of suggested problems will be handed out.