Math 5C, Lecture 2, Course Page
(2-3:15 TuTh, North Hall 1006)

Grades: Final exam scores and course grades are posted here.

Office hours during finals week:

• Prof Tuba: 3-5 M (6/9) and 3:30-5 Tu (6/10).
• Darin: 1-3 M (6/9).
• Zhen: 10-12 F (6/6) and 10-12 M (6/9).
  

Office hours:

• Prof Tuba: 3:30-5 Tu and 11-12:30 Th in South Hall 6701. 
• Darin: 1-2 M in SH 6431T and 12-2 Th in SH 1607.
• Zhen: 11-12 M in SH 6431T and 12-2 Th in SH 1607.
  

Syllabus: Check the syllabus for office hours, locations, and general advice on how to do well in the course. Or here is a pdf version to print.

Lecture notes: Here is a link to the lecture notes by Doug Moore. Here are some corrections:

• p. 6 exercise 1.1.1.(b) and (c) and 1.1.2.(c): the lower limit for these sums should be 1 not 0.
• p. 32: In the last two matrix equations (the ones starting with A (b₁ b₂  .  b_n) = ... and AB = ...) the matrices on the right hand side should be switched. That is B should come first followed by the diagonal matrix.
• p. 33: In the matrix equation at the top of the page, the first B should not have an exponent of -1, and the second B should in fact be B^-1. Or the left hand side should be BAB^-1 and the right hand side only the diagonal matrix without the B^-1 and B.
• p. 46: In the Example, dx/dt = A (a symmetric matrix), should be dx/dt = Ax.
• p. 69: In exercise 3.1.1, the function f(t)=cos²(t) is periodic of period Pi, not 2Pi.
• p. 74: about the middle of the page, the first function should be 1/sqrt(2), not 1/sqrt(2L).
• p. 101: second line of third formula from the bottom of the page should be
  + [(-2cPi/L) a₂ sin(2ctPi/L) +  (2cPi/L) b₂ cos(2ctPi/L)] sin(2xPi/L) +  ... .
• p. 107 in exercises 4.6.1, 2, and 3, remove the condition that theta is in [0, 2Pi].

Defective lecture notes: The bookstore alerted us that some of the reader they had were defective in that some pages were out of order and others were missing entirely. If you bought one of these, you may return it to the bookstore, preferably with your receipt for a replacement.

Web-based calculus exercises: A good web-based resource for sharpening your calculus skills is the COW library.

Annoying errors: Here is a link to that article about the most common errors in undergraduate mathematics, which I asked you to read in the first lecture. Many of these same mistakes greatly depress me and put me in an ungenerous mood when it comes to giving partial credit. It's a good idea to reread this before exams. You may understand and remember more each time you read it.

Bessel's equation lecture notes: Here are the slides from the lecture on Bessel's equation.

Conic sections: here is a Java applet that will let you play with conic sections.

Homework hints:

• The conic section in exercise 2.2.2.(c) is the one in part (b) translated to a different point. Compare this with 2.2.1.(b) and (c).
• The conic section in exercise 2.2.3.(b) does not fit formula (2.3). It is still a conic section you saw in lecture, but not an ellipse or a hyperbola. Find the orthogonal transformation matrix B, then substitute x=By into the equation of the conic. What kind of curve does the resulting equation describe?

Practice exams:  Prof Crandall prepared a long list of practice problems for his class. Working through both his and my practice finals would be excellent preparation for the final exam.

Practice exams in pdf	Practice exams in postcript
Practice midterm	Practice midterm
Practice final	Practice final
Prof Crandall's practice final

Midterm solutions: Here are sample solutions to the white version of the midterm. Other colors are similar:

Pdf version

Postscript version

Inverting matrices:

• Here are some additional notes mostly concerned with showing you how to track down and correct a mistake you might have made while finding the inverse of a matrix.
• Here are some matrices for you to practice on.
• Here are some lecture notes from Prof. Hobson's "Just the Math" project at the University of Coventry. These notes discuss finding the inverse of a matrix using Cramer's rule (expansion by minors or cofactors, the method I showed you in class which resembles finding the determinant) and has some examples and some more exercises.
  

Additional notes: Prof. Crandall has prepared some additional notes on solving the heat equation and the wave equation by finding eigenvalues and eigenfunctions of linear differential operators. You may download them here.