18.014 Calculus with Theory I, Fall 2002

Munkres, James; Lachowska, Anna

Author(s)

Munkres, James; Lachowska, Anna

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Alternative title

Calculus with Theory I

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Abstract

18.014, Calculus with Theory, covers the same material as 18.01 (Calculus), but at a deeper and more rigorous level. It emphasizes careful reasoning and understanding of proofs. The course assumes knowledge of elementary calculus. Topics: 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. Dr. Lachowska wishes to acknowledge Andrew Brooke-Taylor, Natasha Bershadsky, and Alex Retakh for their help with this course web site.

Date issued

2002-12

URI

http://hdl.handle.net/1721.1/74131

Department

Massachusetts Institute of Technology. Department of Mathematics

Other identifiers

18.014-Fall2002

local: 18.014

local: IMSCP-MD5-becc0d3b144d63402822dc4cafaa40fa

Keywords

axioms for the real numbers, the Riemann integral, limits, theorems on continuous functions, derivatives of functions of one variablethe fundamental theorems of calculus, Taylor's theorem, infinite series, power series, rigorous treatment of the elementary functions, Calculus

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