Material
covered to date:
Mon March 26 Sec. 1.1
Tue March 27 Sec 1.2
Wed March 28 Sec 1.4
Thu March 29 Sec 1.3
Fri March 30 Sec 1.5
Mon April 2 Sec 1.6
Tue April 3 Sec 1.7
Wed April 4 Sec 1.8
Thu April 5 Sec 2.2 plots of xy/(x^2+y^2)
click
Fri April 6 Parts of Sec 2.3 and 2.10: the chain rule;
directional derivatives vs differentiability
Mon April 9, 2.3 and 2.10, cont.
Tue April 10 2.4
Wed April 11 2.5 and 2.6 up to higher order chain rule;
the function in Ex 2 p. 78 and its partial derivatives, Maple 15
plots
Thu April 12 2.6 and 2.7 up to the multivariate Taylor formula
Fri April 13 2.7 up to uniqueness of the Taylor polynomial
Examples and further exercises.
Mon April 16 2.8 (except for the 2 by 2 case, left for tomorrow) I found
the Wikipedia entry on eigenvectors
pretty good.
Some standard types of critical points in 2d.
Tue April 17 2.8 and most of 2.9. Here is a Self-contained elementary intro to eigenvalue problems.
Wed April 18 2.9, 2.10 and review
Thu April 19 2.9, 2.10 and review
Fri April 20 review and 3.1
Practice problems for Midterm1 .
Mon April 23 Midterm
Tue April 24 3.1 and 3.2 3d surfaces related to examples in book .
Wed April 25 3.2 and 3.3 Row rank=column rank, proof for 3X2 matrices .
Thu April 26 3.4 Plots of transformations in the plane.
Fri April 27 3.5
Mon April 30 4.2 (part)
Tue May 1 4.2 (part)
Wed May 2 4.2
Thu May 3 4.3, part of 4.5 Proof of equality of a double int with an iterated one, continuous case.
Fri May 3 Part of 4.4
Mon May 7 4.4 (linear changes of coords)
A quick course in the algebra of matrices
Mon May 7 4.4 (linear changes of coords)
Tue May 8 4.4, 4.5
Wed May 9 4.7
Thu May 10 4.8 Notes on Lebesgue measure and integration
Fri May 11 5.1 Notes on rectifiable curves
Mon May 14 5.2
Tue May 15 5.3
Why surface area cannot be straightforwardly approximated by polygonal tilings
Wed May 16 5.4
Thu: Midterm 2
Practice problems for Midterm 2 (Syllabus: Sec. 3.1-3.5, 4.1-4.5.)
Fri May 18 5.5
Mon May 21 5.6
Tue May 22 5.7
Wed May 23 5.8 and review of series
Thu May 24 Series: review of results. Class notes
Fri May 25 A short intro to Complex Analysis based on advanced calculus
Tue May 29 Introduction to Fourier series. Supplementary reading about Fourier coefficients
Wed May 30 8.1; part of 8.2
Thu May 31 selection of results from 8.2-8.5
Practice problems for the final (Syllabus: Folland Sec. 3.1-3.5, 4.1-4.8, 5.1-5.5, 5.7,5.8 Bonus problems: 8.1-8.3)
Occasional quizzes will be based on problems very similar
to the homework ones.
Grading policy
For the final score I
will use the formula
s=0.35 · homework +0.15 · midterm1+0.15 · midterm2+0.35 · final
and the final grade is:
A if s∈[90,100], A- if s∈[82,90), B+ if s∈[74,82), B if
s∈[66,74), B- if s∈[58,66), C+ if s∈[50,58), C if s∈[42,50), C- if
s∈[34,42), D+ if s∈[26,34), D if s∈[18,26), D- if s∈[10,18), E if
s∈[0,10).