18.014
Calculus with Theory
Fall 2010
18.014, Calculus with Theory, covers the same material as 18.01 (Single Variable Calculus), but at a deeper and more rigorous level. It emphasizes careful reasoning and understanding of proofs. The course assumes knowledge of elementary calculus.
Readings
- Apostol, Tom M. Calculus, Volume 1: One-Variable Calculus, with An Introduction to Linear Algebra . Waltham, Mass: Blaisdell, 1967. ISBN: 9780471000051.
- SES #: 0 · TOPICS: Proof writing and set theory · TEXTBOOK READINGS: I 2.1-2.4
- SES #: 1 · TOPICS: Axioms for the real numbers · TEXTBOOK READINGS: I 3.1-3.7
- SES #: 4 · TOPICS: Functions, area axioms · TEXTBOOK READINGS: 1.2-1.10
- SES #: 5 · TOPICS: Definition of the integral · TEXTBOOK READINGS: 1.12-1.17
- SES #: 10 · TOPICS: Proofs of limit theorems, continuity · TEXTBOOK READINGS: 3.5-3.7
- SES #: 12 · TOPICS: Intermediate value theorem · TEXTBOOK READINGS: 3.9-3.11
- SES #: 15 · TOPICS: Definition of the derivative · TEXTBOOK READINGS: 4.3-4.4, 4.7-4.8
- SES #: 17 · TOPICS: Mean value theorem, curve sketching · TEXTBOOK READINGS: 4.13-4.18
- SES #: 22 · TOPICS: Inverse trig; trig substitution · TEXTBOOK READINGS: 6.21
- SES #: 25 · TOPICS: Taylor’s formula · TEXTBOOK READINGS: 7.1-7.2
- SES #: 28 · TOPICS: Sequences and series; geometric series · TEXTBOOK READINGS: 10.1-10.6, 10.8 (first page only)
- SES #: 29 · TOPICS: Absolute convergence, integral test · TEXTBOOK READINGS: 10.11, 10.13, 10.18
- SES #: 32 · TOPICS: Alternating series; improper integrals · TEXTBOOK READINGS: 10.17, 10.23
- SES #: 33 · TOPICS: Sequences of functions, convergence · TEXTBOOK READINGS: 11.1-11.2
Sources
- Course catalogue ↗Historical OpenCourseWare
- MIT OCW syllabus ↗
- MIT OCW readings ↗
- Historical MIT OpenCourseWare offering. Named reading entries and schedule topics are automatically extracted from the linked source pages.