Ernest Schimmerling

21-259 Calculus in three dimensions

Course information (PDF)

Link to webpage of TA Shaun Allison's webpage (TA Hanif Cheung uses the same homework exercises listed there)

January 19 (scan of handwritten notes with small differences compared to what was presented in lecture)

January 22 (scan of handwritten notes with small differences compared to what was presented in lecture)

January 24 (scan of handwritten notes with small differences compared to what was presented in lecture)

January 26 (scan of handwritten notes with small differences compared to what was presented in lecture)

January 29 (scan of handwritten notes with small differences compared to what was presented in lecture)

January 31 (scan of handwritten notes with small differences compared to what was presented in lecture)

February 2 (scan of handwritten notes with small differences compared to what was presented in lecture)

February 5 (scan of handwritten notes with small differences compared to what was presented in lecture;
last page of these notes to be covered next time)


February 7 (A TYPO IN THESE NOTES WAS CORRECTED IN THE FEB 14 NOTES)

February 9 (scan of handwritten notes with small differences compared to what was presented in lecture)

Midterm 1 distribution and grade cutoffs (February 12)

February 14 (scan of handwritten notes with small differences compared to what was presented in lecture)

Midterm 1 solutions (February 14)

February 16 (scan of handwritten notes with small differences compared to what was presented in lecture)

February 19 (scan of handwritten notes with small differences compared to what was presented in lecture) [Part 1] [Part 2]

February 21 (scan of handwritten notes with small differences compared to what was presented in lecture) [Part 1] [Part 2]

February 23 (scan of handwritten notes with small differences compared to what was presented in lecture) [Compare with Stewart 13.3]

Remark on references for matrix algebra: Unfortunately, students wishing to learn more about matrix algebra than was covered in lecture won't find it in Stewart. An alternative textbook for 21-259 that has this material is "Vector Calculus" by Marsden and Tromba, which is in the CMU library and the Pitt library. There are many other good sources, for example, any textbook used for 21-240, 21-241 or 21-242; these are found in the library and the student store.

February 26 (scan of handwritten notes with small differences compared to what was presented in lecture) [Compare with Stewart 13.3]

February 28 and the beginning of March 2 (scan of handwritten notes with small differences compared to what was presented in lecture) [Compare with Stewart 13.3]

Study problems for Midterm 2 (warning: some of these problems are too messy for an exam, they would have to be tweaked)

March 5, Midterm 2 Solutions [ Problem 1, Part 1 ] [ All the rest ]

Midterm 2 distribution and grade cutoffs (March 7)

March 7 (scan of handwritten notes with small differences compared to what was presented in lecture) [Compare with Stewart 14.3]

REVISED (refresh your browser):
March 19 and 21 (scan of handwritten notes w/ differences compared to what was presented in lecture) [Compare with Stewart 14.4]

March 23 (scan of handwritten notes with small differences compared to what was presented in lecture) [Compare with Stewart 14.6]

March 26 (scan of handwritten notes with small differences compared to what was presented in lecture) [Compare with Stewart 14.5 and 14.6]

March 28 (scan of handwritten notes with small differences compared to what was presented in lecture) [Compare with Stewart 14.5, 14.6 and 14.7]
[These notes contain a sketch of a proof that was not covered in lecture.]

March 30 (scan of handwritten notes with small differences compared to what was presented in lecture) [Compare with Stewart 14.7]

April 2 (scan of handwritten notes with small differences compared to what was presented in lecture) [Part 1] [Compare with Stewart 14.7]
Part 2 was the start of Lagrange Multipliers; see the next installment of notes.

April 4 (scan of handwritten notes with small differences compared to what was presented in lecture) [Compare with Stewart 14.8]

April 6 (scan of handwritten notes with small differences compared to what was presented in lecture) [Compare with Stewart 14.8]

April 9 (scan of handwritten notes with small differences compared to what was presented in lecture) [Compare with Stewart 15.1]

April 11 (scan of handwritten notes with small differences compared to what was presented in lecture) [Compare with Stewart 15.1 and 15.2]

Practice problems for Midterm Exam 3 [Part 1] [Part 2] [Part 3]

Two more examples of calculating double integrals that were given in lecture on Friday, April 13

Midterm 3 solutions (April 16)

Midterm 3 distribution and grade cutoffs (April 16)

April 18 (scan of handwritten notes with small differences compared to what was presented in lecture) [Compare with Stewart 15.9] [I didn't get through all the material in these notes yet.]

April 23 (scan of handwritten notes with small differences compared to what was presented in lecture) [Compare with Stewart 15.3 and 15.9]

April 25 (scan of handwritten notes with differences compared to what was presented in lecture) [Compare with Stewart 15.3 and 15.9]