Math 351: Linear Algebra


Course Information

Professor: Kiril Datchev
Email: kdatchev@purdue.edu
Lectures: Mondays, Wednesdays, and Fridays, 11:30 to 12:20, in PHYS 202.
Office hours: 3-3:30 Tuesdays, 1:30-2 Wednesdays, 1:30-3 Fridays, or by appointment, in MATH 602.

Textbook: Linear Algebra for Students, by James E. McClure.

We will cover the following topics: Systems of linear equations, finite dimensional vector spaces, matrices, determinants, eigenvalues and eigenvectors, with applications to analytical geometry.

Grading is based on
  • Almost weekly homework assignments, worth 20% of the total grade,
  • two in-class midterm exams, one on February 17th and one on March 31st, each worth 20% of the total grade,
  • a final exam, as scheduled here, worth 40% of the total grade.

    • Homework

    Homework is due on paper at the beginning of class on Wednesdays. Here are the assignments:

    Homework 1, due January 22nd, is problems 1.1.3, 1.1.5, 1.1.7, 1.2.1, 1.2.4, and 2.1.3.
    Homework 2, due January 29th, is problems 2.2.1, 2.2.3, 2.5.4, 2.5.5, 2.5.6, 2.7.2, and 2.7.4.
    Homework 3, due February 5th, is problems 2.7.3, 2.7.5, 2.11.2, 3.4.2, 3.6.3, 3.8.2, 3.8.3, and 3.8.4.
    Review problems for Midterm 1.
    Homework 4, due February 26th, is problems 4.11.1, 4.12.3, 5.7.1, 5.7.4, 5.8.1, and 5.9.2.
    Homework 5, due March 5th, is problems 7.7.2, 7.7.3, 8.3.1, 8.3.2, 8.3.3, 8.3.4, and the Exercise from these notes on recursive sequences.
    Homework 6, due March 12th , is problems 8.5.1, 8.5.3, 8.5.4, 8.6.3, 8.6.4, 8.10.2 and Exercises 1, 2, 3, and 4 from these notes on inverses and determinants.
    Review problems for Midterm 2.
    Homework 7, due April 9th, is problems 10.8.1(i) (for this one, let c=2), 11.4.1, 11.4.2, 11.6.1, 11.13.2, 11.13.3, 12.4.1, and 12.5.1.
    Homework 8, due April 16th, is problems 12.6.1, 12.11.1, 12.11.2, 12.11.5, 12.14.1, 13.2.2, 13.3.2, 13.4.2, and 14.3.2.
    Homework 9, due April 25th, is problems 14.7.1, 15.3.2, 17.3.4 (it is not necessary to use matlab; you may use any method) from McClure, and Problems 4.1.6, 4.1.9 (you may omit the parts about sums of errors), 4.2.2c, 4.2.5 from Shifrin and Adams.
    Notes on symmetric matrices.
    Review problems for the final.

    Additional Materials

    Paul's Notes have more examples of solving systems by elimination.

    Here is a matrix multiplication calculator.

    Here is a matrix visualizer.

    These notes show how to blur and sharpen an image using translation.

    Section 1.5.3 of Linear Algebra and Differential Equations by Alexander Givental gives more geometric insight into eigenvalues and eigenvectors in the complex and defective cases.

    Finally, a list of general policies and procedures can be found here.