Rafail Abramov's Math 310 Page

Fall 2017



Welcome to Math 310 - Applied Linear Algebra

The course will be meeting at 10 am MWF in 130 Science and Engineering South (Call no. 22632)

Course description/course objectives: Upon successful completion of this course, students should be able to solve systems of linear equations using row reduction (Gaussian elimination) and, when applicable, other methods, carry out matrix operations, including calculating inverses and determinants. Students should demonstrate understanding of the concepts of linear independence, vector spaces, orthogonality and linear transformations. Students should be able to calculate eigenvalues and eigenvectors and solve related problems, use inner products and construct orthogonal/orthonormal bases using the Gram-Schmidt process. A number of applications to dynamical systems, and applications in science and engineering will be covered.

Prerequisites: Grade C or better in Math 181.

Course drop policy: See the university policy

Textbook: Lay, Lay & McDonald, Linear Algebra and its Applications, Addison—Wesley 5th edition.

Quizzes and homework: The homework assignments are on the course webpage. The homework will not be collected. Instead, a quiz will be given once a week based on the homework problems. There will be no make-up quizzes, but the two lowest quiz scores will be dropped at the end of the class.

Calculators: The use of any electronic devices with computing capabilities is prohibited during exams and quizzes

Exams: There will be two midterm exams and a final exam at the end of the class:

Final score:

Grade cutoffs:

Disability policy: The University of Illinois at Chicago is committed to maintaining a barrier-free environment so that students with disabilities can fully access programs, courses, services, and activities at UIC. Students with disabilities who require accommodations for access to and/or participation in this course must be registered with the Disability Resource Center (DRC). You may contact DRC at 312-413-2183 (voice) or 312-413-0123 (TTY).

Academic integrity: Cheating=F

Course Handout

Syllabus:

Date of class Topic Homework Notes
*** Week 1 ***
Mon Aug 28 1.1 Systems of linear equations 1, 5, 7, 9, 11, 13, 15, 17, 19*, 21*
Wed Aug 30 1.2 Row reduction and echelon form 1, 3, 5, 7, 11, 14, 15, 17*, 19*
Fri Sep 1 1.3 Vector equations 1, 3, 5, 9, 11, 13, 15, 19, 29*, *31
*** Week 2 ***
Mon Sep 4 Labor day No class
Wed Sep 6 1.4 The Matrix Equation Ax=b 1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 25 Quiz 1
Fri Sep 8 1.5 Solution Sets of Linear Systems 1, 3, 5, 7, 9, 11, 13, 15
*** Week 3 ***
Mon Sep 11 1.7 Linear Independence 1, 3, 5, 7, 9, 11, 15, 17, 19, 23, 25, 31*, 41*, 43*
Wed Sep 13 1.8 Introduction to Linear Transformations 1, 3, 5, 9, 11, 13, 15, 17, 19, 23*, 35* Quiz 2
Fri Sep 15 1.9 The Matrix of a Linear Transformation 1, 3, 5, 7, 9, 13, 15, 17, 19, 21, 23, 25, 27, 29
*** Week 4 ***
Mon Sep 18 2.1 Matrix Operations 1, 3, 5, 7, 11
Wed Sep 20 2.2 The Inverse of a Matrix 1, 3, 5, 7, 29, 31, 33, 39* Quiz 3
Fri Sep 22 2.3 Characterization of Invertible Matrices 1, 3, 5, 7, 11
*** Week 5 ***
Mon Sep 25 2.5 Matrix Factorization 3, 5, 7, 9
Wed Sep 27 3.1 Introduction to Determinants 1, 3, 5, 9, 11, 13, 37* Quiz 4
Fri Sep 29 3.2 Properties of Determinants 1, 3, 5, 7, 9, 11, 13, 21, 23, 25, 29, 37, 15*, 17*
*** Week 6 ***
Mon Oct 2 Review for Exam 1
Wed Oct 4 Exam 1 (covers 1.1 -- 1.9, 2.1 -- 2.3, and 2.5)
Fri Oct 6 3.3 Cramer's Rule, Volume and Linear Transformations 1, 3, 5, 7, 9, 11, 13, 15, 19, 21, 23, 25, 27, 29
*** Week 7 ***
Mon Oct 9 4.1 Vector Spaces and Subspaces 1, 3, 5, 7, 9, 11, 13, 15, 17
Wed Oct 11 4.2 Null Spaces, Column Spaces, and Linear Transformations 1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 31, 33, 37 Quiz 5
Fri Oct 13 4.3 Linearly Independent Sets; Bases 1, 3, 5, 7, 9, 13
*** Week 8 ***
Mon Oct 16 4.3 Linearly Independent Sets; Bases (cont.) 15, 19, 21, 25
Wed Oct 18 4.4 Coordinate Systems 1, 3, 5, 7, 9, 11, 13, 17, 27, 29, 31 Quiz 6
Fri Oct 20 4.5 The Dimension of a Vector Space 1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23
*** Week 9 ***
Mon Oct 23 4.6 Rank 1, 3, 5, 7, 9, 17, 27, 31
Wed Oct 25 4.7 Change of Basis 1, 3, 5, 7, 9, 13 Quiz 7
Fri Oct 27 5.1 Eigenvectors and Eigenvalues 1, 3, 5, 7, 9, 11, 13, 15, 17, 19*
*** Week 10 ***
Mon Oct 30 5.2 The Characteristic Equation 1, 3, 5, 7, 9, 11, 13, 15, 17
Wed Nov 1 Review for Exam 2
Fri Nov 3 Exam 2 (covers 1.1 -- 1.9, 2.1 -- 2.3, 2.5, 3.1 -- 3.3, 4.1 -- 4.7)
*** Week 11 ***
Mon Nov 6 5.3 Diagonalization 1, 3, 5, 7, 9, 11, 19
Wed Nov 8 5.4 Eigenvectors and Linear Transformations 1, 3, 5, 7, 9, 11, 13, 15, 17 Quiz 8
Fri Nov 10 5.5 Complex Eigenvalues 1, 3, 5, 7, 9, 11
*** Week 12 ***
Mon Nov 13 4.9 Applications to Markov Chains 1, 2, 5, 6, 7, 8, 11, 12
Wed Nov 15 5.7 Applications to Differential Equations 1, 2, 3, 4, 5, 6, 7, 8 Quiz 9
Fri Nov 17 6.1 Inner Product, Length and Orthogonality 1, 3, 5, 7, 9, 11, 13, 15, 17, 23
*** Week 13 ***
Mon Nov 20 6.2 Orthogonal Sets 1, 3, 5, 7, 9, 11, 13, 15, 17, 21
Wed Nov 22 6.3 Orthogonal Projections 1, 3, 5, 7, 9, 11, 13, 15 Quiz 10
Fri Nov 24 Thanksgiving holiday No class
*** Week 14 ***
Mon Nov 27 6.4 The Gram-Schmidt Process 1, 3, 5, 7, 9, 11, 13, 15
Mon Nov 29 6.5 Least-Squares Problems 1a, 3a, 5, 9, 11 Quiz 11
Fri Dec 1 6.6 Applications to Linear Models 1, 3
*** Week 15 ***
Mon Dec 4 6.7 Inner Product Spaces 21, 23, 25
Wed Dec 6 7.1 Diagonalization of Symmetric Matrices TBA Quiz 12
Fri Dec 8 Review for the final exam
*** Week 16 *** Final exam

Sample exams
First midterm: Olga Lukina's past exams: Spring 14, Fall 16, Spring 17