# MATH 310: Applied Linear Algebra

### COURSE DESCRIPTION

Matrices, Gaussian elimination, vector spaces, LU-decomposition, orthogonality, Gram-Schmidt process, determinants, inner products, eigenvalue problems, applications to differential equations and Markov processes. Credit is not given in both Mathematics 310 and 320.

### TEXTBOOK

Introduction to Linear Algebra, 4th edition, Gilbert Strang, Wellesley Publishing, ISBN-10: 0980232716, ISBN-13: 978-0980232714

Lots of interesting material (including video lectures on many topics) can be found on the MIT OPEN COURSE LINEAR ALGEBRA WEBSITE.

### SCHEDULE

Week 1 M Introduction
W 1.2, 1.3
F 6.1, 6.2; 2.1, 2.2 ,2.3
Week 2 M 2.6 (2.3-2.5); 6.1, 6.2
W 2.6 (2.3-2.5); 6.1, 6.2
F 2.7 (2.3-2.5); 3.1, 3.2

### EXAMS

There will be two midterm exams (Friday, July 11th and Wednesday, July 30th) and one final exam (Friday, August 8th).

 100 pts. Participation and quizzes 100 pts. Midterm Exam 1 100 pts. Midterm Exam 2 200 pts. Final Exam

85-100 A 75-84 B 65-74 C 55-64 D <55 F

### SUGGESTED HOMEWORK

Study Guide for Little Midterm 2

To begin preparing for Midterm 2 on 7/30:

Problem Set 4

For Monday, 6/23:

Problem Set 3

For Friday, 6/20:

Problem Set 2

For Wednesday, 6/18:

Using the ideas discussed in Monday's class, do the following:

Find a 2 x 2 matrix that represents a reflection across the x-axis.

Find a 2 x 2 matrix that represents a reflection across the y-axis.

Find a 2 x 2 matrix that represents a projection to the the y-axis.

Find a 2 x 2 matrix that represents a projection to the the x-axis.

Work out what the normal vector is to a line of the form ax + by = c, and make up a simple example that helps you remember how this works.

Work out what the normal vector is to a plane of the form ax + by + cz = d, and make up a simple example that helps you remember how this works. (Note an earlier version mistakenly had "line" instead of "plane." My thanks to alert readers.)

Sketch the vector u = <cos A, sin A>, where A is some angle measured in degrees counterclockwise from the x-axis, and also sketch the vector v = <1,0>. Explain in this simple example why the dot product of u and v is equal to the product of the length of u, the length of v, and the cosine of the angle between u and v. What happens to this equality when you stretch u by a factor of 2? (Draw a picture. Compute the dot product of this new u and v. Compute the product of the lengths of this new u and v and the cosine of the angle between them. Does the equality still hold?) Try this again when you stretch v by a factor of 3. What happens to the sides of the equality when you do both: scale u by a factor of 2 and scale v by a factor of 3?

Now consider again the original u and v. Sketch the vectors obtained by rotating both u and v by B degrees counterclockwise (say, B = 90 degrees). Explain in your own words why the equality described above still holds. (For fun: What happens to the equality if you combine rotations and stretches of u and/or v? What about reflections?)

Read through the sections of the text listed above to acquaint yourself with the author's style and the layout. Visit the website listed above ("MIT OPEN COURSE LINEAR ALGEBRA WEBSITE"). Watch some parts (or all) of a few of the lectures there to get a feel for what this course is about, and what the lectures look like. Look at some of the assigned problems (on the MIT site) along with the worked solutions.

Come with questions!

### STUDENTS WITH DISABILITIES

Students with disabilities who require special accommodations for access and participation in this course must be registered with the Office of Disability Services (ODS). Students who need exam accommodations must contact ODS in the first week of the term to arrange a meeting with a Disability Specialist.