## Math 307- 202, Applied Linear Algebra, Spring 2018

• Instructor:
• Kalle Karu
• Office: 213 Math bldg.
• email: karu@math.ubc.ca.
• Office hours: Mon 1-2, Thu 9:30-10:30.
• Final exam on Saturday, April 14, 8:30AM in SRC C.
• Bring your student Id to the exam, these will be checked.
• The exam covers Chapters 1-4 of the textbook. The following sections will not be included:
• I.2.3-I.2.4 The history of splines. I.2.6 A different approach to splines.
• II.2.3 Elementary matrices.
• III.1.5 Football rankings. III.5.2 Fast Fourier Transform. III.5.3 Audio signals.
• IV.2.6 Effective resistance revisited. IV.5 The tight binding model. IV.6.4-6.5 Metropolis algorithm. IV.8 PCA.
• An article on Google PageRank.
• Old exams with solutions: 2011 Final exam, 2013 Final exam, 2013 Final exam #2.
• More past exams on the Math department web page.
• Some solutions to past exams on Math Exam Resources page.
• Exam on Thursday, Feb 15, in class.
• The exam covers the following topics:
• Theory:
• How to solve linear equations; determine if a solution exists; write the solution in parametric form.
• Norm, condition number.
• Vector spaces, subspaces; linear independence, span, basis, dimension.
• Find basis for the nullspace and range of a matrix.
• Dot product, orthogonal complements, nullspace and range of the transpose.
• Applications
• Lagrange interpolation.
• Splines.
• Differential equations.
• Chemical equations.
• Networks. The incidence matrix D of a graph, the four subspaces associated to it. (No resistor networks.)
• Matlab commands
• How to enter matrices, diagonal matrices, block matrices.
• Compute norms, condition number.
• Do Gaussian elimination, find inverses.
• Old exams with solutions:

• Quiz #2 information.
• There will be no homework due the week Jan 29-Feb 2. We will have a quiz on Thursday, Feb 1.
• The quiz will cover material about interpolation and differential equations. Below are some sample problems.
• Interpolation.
• Check the solution to problem 4 in 1.2 that was in Homework #2.
• Problem 4 in 2016 Midterm WT1.
• Problem 4 in 2015 Midterm. Notice that the extra two conditions at the endpoints involve first derivatives instead of the second derivatives.
• Differential equations.
• Read about the equation discussed in the textbook. This is different from the one done in class.
• Do problems in Homework #3 posted below.
• Problem 3 in 2016 Midterm WT2. Note that one boundary condition here uses the first derivative.
• Problem 3 in 2015 Midterm. Again, the boundary condition involves the first derivative.
• Problem 1(d) in 2016 Midterm WT1  and problem 2 in 2014 Midterm discuss a reverse problem: given a matrix, what is the corresponding differential equation it solves.
• Homeworks:
 Homework #1. Due Tuesday, Jan. 16 Problems 1a, 2, 5, 7, 13, 14 in problems_1.1.pdf Solutions to problems 1-15 in 1.1. Homework #2 Due Thursday, Jan. 25 16, 18 in problems_1.1.pdf 1, 2, 3, 4 in problems_1.2.pdf Solutions to all problems in 1.1. Solutions to problems 1-8 in 1.2. Homework #3 For practice only, not collected 1, 2, 3, 4, 5, 6 in in problems_1.3.pdf Solutions to problems in 1.3. Homework #4 Due Tuesday, Feb. 13 1, 3, 4, 5, 6, 7 in problems_2.1.pdf 1 in problems_2.2.pdf Solutions to problems in 2.1. Homework #5 Due Tuesday, March 13 1, 2, 3, 4 in problems_2.3.pdf 4, 5, 7, 9 in problems_3.1.pdf Solutions to problems in 2.3. Solutions to problems in 3.1. Homework #6 For practice only, not collected 1, 2ab, 3 in problems_3.2.pdf 1, 3, 8, 9 in problems_3.3.pdf 1, 2, 3, 4, 5 in problems_4.1.pdf 1, 2 in problems_4.2.pdf Solutions to problems_in_3.2 Solutions to problems_in_3.3 Solutions to problems_in_4.1 Solutions to problems in_4.2 Homework #7 Due Thursday, April 5 1 in problems_3.4.pdf (First find the complex coefficients, then convert complex exponentials into sin and cos to get the real Fourier series.) 1 in problems_4.3.pdf 2, 3, 5 in problems_4.6.pdf Solutions to problems_in_3.4 Solutions to problems_in_4.3 Solutions to problems_in_4.6
• .m files: plotspline2.m, splinemat2.m, plotcubic2.m, hmkgraph.m
• Calendar:
 Jan 4 lecture, octave Jan 9 lecture, octave Jan 11 lecture, octave Jan 16 lecture, octave Jan 18 lecture, octave Jan 23   lecture, Quiz #1 Jan 25 lecture Jan 30 lecture Feb 1  lecture,  Quiz #2 Feb 6 lecture Feb 8 lecture Feb 13 lecture Feb 15 Midterm Feb 27 lecture Mar 1 lecture, octave Mar 6 lecture Mar 8 lecture, octave Mar 13 lecture Mar 15 lecture, Quiz#3 Mar 20 lecture Mar 22 lecture, octave Mar 27 lecture Mar 29 lecture, Quiz#4 Apr 3 lecture Apr 5 lecture

• Overview:
• The lecture notes for this course contain a range of interesting applications of linear algebra, such as cubic splines, Fast Fourier Transform, Markov chains, Google page rank and others. We will cover a selection of these topics. For each topic we will discuss the required background theory and do actual computations.
• Course learning goals.
• Drop in math help at the Math Learning Centre.
• Grade breakdown for the course:
• Homework 10%
• Quizzes 10%
• Midterm exam 30%
• Final exam 50%
• Textbook:
• We will be using online lecture notes specifically written for this course:
•  We will cover a selection of topics from the notes.

• Homework:
• Weekly homework will be posted on this web site. Homeworks are collected in class.
• Late homework will not be accepted, but the lowest score will be dropped from the final mark.

• Matlab/Octave:
• We will use the mathematical software package Matlab to do computations. Alternatively, an open source Matlab clone, GNU Octave, can be used instead.
• UBC has a site license for Matlab. UBC students have access to Matlab at no cost. Detailed instructions can be found here.