Syllabus

Course Meeting Times

Lectures: 3 sessions / week, 1 hour / session

Recitations: 2 sessions / week, 1 hour / session

Textbook

Apostol, Tom M. Calculus, Volume 1: One-Variable Calculus, with An Introduction to Linear Algebra. Waltham, Mass: Blaisdell, 1967. ISBN: 9780471000051.

(Vol. 2 will be needed for those who wish to continue on to 18.024 Multivariable calculus with theory.)

Additional course notes by James Raymond Munkres, Professor of Mathematics, Emeritus, are also provided.

Prerequisites

We will assume a working knowledge of Calculus I (18.01 Single Variable Calculus), but no familiarity with proofs or proof writing.

Description

We will cover the same material as 18.01 but with an emphasis on proofs and conceptual understanding rather than computation. Topics include:

• Axioms for the real numbers;
• The Riemann integral;
• Limits, theorems on continuous functions;
• Derivatives of functions of one variable;
• The fundamental theorems of calculus;
• Taylor's theorem;
• Infinite series, power series, rigorous treatment of the elementary functions.

Recitation Assignments

At the beginning of each unit, students will receive a schedule that includes problems to complete in advance of the next recitation. Students should be prepared to present their proofs in clear detail. This will give them the opportunity to very deliberately improve their proof writing skills.

Problem Sets

Problem sets are assigned weekly, and due the following week. At the end of the course, the lowest two pset scores for each student will be replaced by his or her average score on all of the psets.

Exams

There will be three in-class, one hour exams, and one three-hour comprehensive final exam.

Grading

Calendar