18.014: Calculus with theory

Ravi Vakil, Rm. 2-271, vakil@math.mit.edu

Final grades (and quiz 4 grades and miscellaneous comments) are here.


The description in the catalog: Covers the same material as 18.01, but at a deeper and more rigorous level. Emphasizes careful reasonsing and understanding of proofs. 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.

Lectures: Tuesdays and Thursdays 1-2, Friday 2-3, in Rm. 4-370.

My office hours (in 2-271): Thursdays 2-3; I will also be available for at least a half hour after class on Tuesday and Friday, as well as Thursdays 4-5 (and occasionally 3-4 too), but let me know if you're interested in dropping by, so I'll be sure to be in.

Pramod Achar, Tuesdays and Thursdays at 12 (Rm 4-153), pramod@math.mit.edu, office hour Wed. 3-4 in Rm. 2-251 .
Prof. David Ingerman, Tuesdays at Thursdays at 9 (Rm 2-142), ingerman@math.mit.edu, office hours Wed. 10-12 in Rm 2-372 (or by appointment, or you can talk to him after class).

Text: Apostol's Calculus vol. I, plus Notes, which may soon be purchased in 11-004 (the copy center in the basement).

Miscellaneous: Basic information about the course (ps, pdf). Questions most commonly asked about 18.014-18.024 (ps, pdf). (All files here will be in postscript and pdf format; pdf format is probably easiest for you to download.)


  • A tentative syllabus (ps, pdf).
  • Unit 1 (ps, pdf).
  • Unit 2 (ps, pdf).
  • Unit 3 (ps, pdf).
  • Practice quiz 1 (ps, pdf). Quiz 1 (ps, pdf).
  • Unit 4 (ps, pdf).
  • Practice quiz 2 (ps, pdf). Quiz 2 (ps, pdf).
  • Unit 5 (ps, pdf).
  • Unit 6 (ps, pdf).
  • Ian Stewart, a mathematician from the University of Warwick and also a well-known writer about mathematics, will give a special public lecture entitled Minesweeper Math on Wed. Nov. 1, at 6:30 pm in Emerson Hall 105, Harvard Yard. This lecture will describe how understanding the popular computer game Minesweeper can lead to the solution of one of the great mathematical questions of our time, the P versus NP problem. Further information can be found here.
  • Unit 7 (ps, pdf).
  • Practice quiz 3 (ps, pdf). Quiz 3 (ps, pdf).
  • Unit 8 (ps, pdf).
  • On Fri., Dec. 8, I'll explain why you can't trisect an angle with straightedge and compass (or double the cube or square the circle). The handout is here: (ps, pdf).
  • On Tues., Dec. 12, Prof. Munkres will give a special guest lecture on Fourier Series.
  • Practice quiz 4 (ps, pdf). Quiz 4 will take place on Tuesday, Dec. 19, 10-11 am, in Rm 4-159.
    To 18.024.
    Back to my home page.
    Ravi Vakil
    Department of Mathematics Rm. 2-271
    Massachusetts Institute of Technology
    77 Massachusetts Ave.
    Cambridge MA USA 02139
    Phone: 617-253-2683 (but e-mail is better)
    Fax: 617-253-4358
    Email: vakil@math.mit.edu