Jan 3 (Thu):

introduction and review of solving linear equation: write system of equations in matrix notation; Gauss elimination; basics of solving system; a few M/O examples ...
key differences in octave and matlab: see here for example

Jan 8 (Tue):
Login info given to students. Norms of vector and matrices, + examples. An interesting link is here where you can learn application of linear algebra for fun. Notice: I’d like to move my office hours to every Thursday 3:30pm-5:00pm from next week on.

Jan 10 (Thu):
More examples on calculate matrix norms, condition number and relative error. Some information about Rotation matrix can be found here (take a look at the 2D examples; the idea for reflection matrix would be similar; the matrix used in class is just one example).
Read notes 1.1.7. (1.1.8 for summary of M/O commands)
Homework hw1 due Jan 17 Solution1hw1_solution (for TA information, see main page of this course).

Jan 15 (Tue):
Lagrangian interpolation + examples in M/O; here is another way to view Lagrange interpolation polynomial, which I didn’t have time to cover in class. You can think about why that is equivalent to the p(x) we learned in class (hint: what is the solution of a_i s formally?).

Jan 17 (Thu)
Cubic spline interpolation and its linear equations (construction procedure).
Homework hw2 due Jan 24 Solution 2 (please see problems 1,3,4,5,7 in the attached file): solutions1.2
m-file you may use for the homework:, plotspline,splinemat

Jan 22 (Tue)
Extra example for Cubic spline interpolation; Finite difference approximation; solving boundary value problem (BVP) via system linear equations.

Jan 24 (Thu)
More examples on finite difference approximation + M/O example.
Homework: problems 1, 2, 3, 4, 5 of hw3 due Jan 31 solution3 solutions1.3
Class examples: fdexample1, fdexample2 (a typo in 2nd example in class has been corrected.); m-file you may use for homework heat (this is basically our 1st example).

Jan 29 (Tue)
Move to Chapter 3: definition of projection, orthogonal projection matrices, least squares ...
Section on least squares from wolfram mathworld.

Jan 31 (Thu)

Least squares, polynomial fit + examples
Homework: problems 1, 2, 3, 4, 5, 8 of problems3.1 due Feb 7; solution solutions3.1

Feb 5 (Tue)
Dr. Sarah will cover a class for me since I have to travel to US for a conference. Orthonormal basis, orthogonal matrices and unitary matrices

Feb 7 (Thu)
Quick review on complex numbers and orthogonal and unitary matrices; introduced Fourier series.
Homework: problem 2 of problems3.2, problem 1(skip the Parseval’s formula part),3,4 of problems3.4due Feb 14 (note: try to calculate c_n’s in problem; a_n and b_n’s are for bonus. Although I didn’t introduce the real form of Fourier series, you can still try to derive them. Idea: split e^{ix} into cos(x) and sin(x).)

Feb 12 (Tue)
Real form of Fourier series and Parsaval’s fomula; start Chap 4 with eigenvalue problem.

Feb 14 (Thu)

More on eigenvalue problem; briefly included (sub)space, linear independence, basis ...
Homework: calculate a_n, b_n’s in problem 1,3,4 in previous problem set (see problems_3.4 in Feb 7) and answer the question about Parseval’s formula in question 1 there; problem 1, 2 (a,c,e) of problems2.1 problem 1 (in part c, we mentioned algebraic multiplicity in class, please find the definition of geometric multiplicity in lecturenotes so that you can do that question), 3, 5 ofproblems4.1 due Feb 28
solutions solutions3.4 solutions3.2 (other solutions will be released in a later time solutions4.1)

Feb 18-22 break

Feb 26 (Tue)
Spaces, subspaces, basis, dimension, four fundamental subspaces ...

Feb 28 (Thu)
Computing basis for four fundamental subspaces, R(A), N(A), R(A^T), N(A^T)
No homework.

Mar 5 (Tue)
Chemical system and reaction matrix. FYI: sample exams from previous years (notice they may have different topics) can be found in the following here (search old tests and exams e.g.).

Mar 7 Midterm test (MCLD 228 one hour basically) No cell phone, no calculators, ... as usual exams.
* Solutions to midterm exam will be released at a later time. You are expected to work on those on your own first.
Homework: problem 3,4,5,6,7 of problem set 2.1 (see the one in Feb 14) due Mar 14
solutions2.1

Mar 12 (Tue)
Resistor network

Mart 14 (Thu)
Hermitian matrices and real sysmmetric matrices
Homework problem 1, 2 of problems2.3 and problem 1,2 ofproblems4.2; problem 3 and 4 in problem set 4.2 are for bonus (you probably need to do a little bit more reading on that section). Due Mar 21
solutions2.3 solutions4.2

Mar 19 (Tue)
Power method
Here the midterm problems are attached, please redo prob 2 and 3 if your score for that question less than or equal to 6 (due Mar 28), no extra credit. The solutions will be released in a later time.
Midterm307202_2013 solutions (as reference, the way to solve the problem may not be unique) to the midterm solns

Mar 21 (Thu)
Recursion relations
Homework problem 3 of set 4.2 and all problems in problems4.3 due Mar 28 solutions4.3

Mar 26 (Tue)
Markov Chain