MATH 341 (sec. 030): Linear Algebra I
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Instructor: Yevgeniy Kovchegov
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e-mail:
kovchegy
@math.
oregonstate.edu
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Office: Kidder 368C
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Office Phone No: 7-1379
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Office Hours: MW 1:00 pm - 2:30 pm, or by appointment.
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Homework 30%
Midterm 30%
Final 40%
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Place and time: MWF 11:00 am to 11:50 am, room BEXL 328.
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Textbook: Kenneth Kuttler, Elementary Linear Algebra available as a FREE e-book at http://tinyurl.com/ElemLinAlg
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Goals: Topics will include systems of linear equations, row echelon form, matrix algebra, determinants, Cramer's rule, linear independence, vector spaces, matrix representations of linear transformations, and computational aspects of eigenvalues and eigenvectors.
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Prerequisites: MATH 254 or instructor's approval.
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Syllabus: PDF
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Homework: There will be seven homework assignments. The assignments will be collected at the beginning of class on due date.
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Homework #1 (due Wednesday, October 4): Homework1.pdf
Homework #2 (due Wednesday, October 11): Homework2.pdf
Homework #3 (due Wednesday, October 18): Homework3.pdf
Homework #4 (due Wednesday, October 25): Homework4.pdf
Homework #5 (due Wednesday, November 8): Homework5.pdf
Homework #6 (due Monday, November 20): Homework6.pdf
Homework #7 (due Friday, December 1): Homework7.pdf
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Midterm: There will be one midterm exam given on Friday, November 3, 6:30 pm - 7:50 pm in BEXL 328.
This is an open notes exam. Notes and simple calculators are allowed. The graphic calculators, and other electronic devices that can perform linear algebra and calculus tasks are prohibited.
Practice problems: Sec. 4.4 #15, 17, 22, 24; Sec. 5.3 #5, 34, 41, 44; Sec. 6.4 #1(c), 2-4, 11-15, 19, 26, 32, 33.
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Final Exam: Thursday, December 7, 9:30 am - 11:20 am in BEXL 328.
This is an open notes exam. Notes and simple calculators are allowed. The graphic calculators, and other electronic devices that can perform linear algebra and calculus tasks are prohibited.
Practice problems: 8.7 (p. 147) #15, 16, 17, 29; Sec. 9.3 (p.164) #9, 14, 58; Sec. 12.5 (p.235) #14, 39, 54, 55.
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Schedule:
Wednesday, September 20 Vectors. Vector algebra. Dot products. The Cauchy-Schwarz Inequality. Sections 2.2, 2.3, and 3.1. Lecture 1 slides (PDF)
Friday, September 22 Dot products. The Cauchy-Schwarz Inequality. Sections 3.1 and 3.2, and 4.1. Lecture 2 slides (PDF)
Monday, September 25 Row and column vectors. Parametric lines. Lines and planes. Systems of linear equations. Sections 2.6 and 4.1. Lecture 3 slides (PDF)
Wednesday, September 27 Systems of linear equations. Gaussian elimination. Sections 4.1, 4.2, and 6.1. Lecture 4 slides (PDF)
Friday, September 29 Gaussian elimination. Determinants (via Laplace expansion). 2X2 and 3X3 examples. Sections 4.1, 4.2, and 6.1. Lecture 5 slides (PDF)
Monday, October 2 Gaussian elimination. Pivot and free variables. nXn determinants (via Laplace expansion). Sections 4.2 and 6.1. Lecture 6 slides (PDF)
Wednesday, October 4 Basic matrix operations. Linear systems in matrix form. Matrix multiplication. Identity matrix. The inverse of a square matrix. Sections 5.1 and 6.1. Lecture 7 slides (PDF)
Friday, October 6 Matrix multiplication. Identity matrix. The inverse of a square matrix. Section 5.1. Lecture 8 slides (PDF)
Monday, October 9 The inverse of a square matrix. Transposition of a matrix. nXn determinants (via Laplace expansion). Sections 5.1 and 6.1. Lecture 9 slides (PDF)
Wednesday, October 11 Determinants. Properties of determinants. Section 6.1. Lecture 10 slides (PDF)
Friday, October 13 Determinants. Properties of determinants. Computing determinants. Section 6.1. Lecture 11 slides (PDF)
Monday, October 16 Computing determinants. Determinants via permutations. Cramer's rule. Sections 6.1 and 6.2. Lecture 12 slides (PDF)
Wednesday, October 18 Cramer's rule. Inverse matrix via determinants. Section 6.2. Lecture 13 slides (PDF)
Friday, October 20 Inverse matrix via determinants. Linear dependence and independence. Sections 6.2, 8.2, and 8.5. Lecture 14 slides (PDF)
Monday, October 23 Linear dependence and independence. The row space. The column space. The rank of a matrix. Sections 8.2, 8.3, and 8.5. Lecture 15 slides (PDF)
Wednesday, October 25 Linear dependence and independence. The row space. The column space. The rank of a matrix. Sections 8.2, 8.3, and 8.5. Lecture 16 slides (PDF)
Friday, October 27 The rank of a matrix. Subspaces. Null space (kernel) of a matrix. Sections 8.2, 8.3, and 8.5. Lecture 17 slides (PDF)
Monday, October 30 Subspaces. Null space (kernel) of a matrix. Basis of a subspace. Section 8.5. Lecture 18 slides (PDF)
Friday, November 3 Review. Lecture 19 slides (PDF)
Monday, November 6 Linear transformations. Matrix of a linear transformation. 2D examples. Rotation. Sections 9.1 and 9.2. Lecture 20 slides (PDF)
Wednesday, November 8 Matrix of a linear transformation. Composition of linear transformations. Rotation, reflection, projection, scaling. Sections 9.1 and 9.2. Lecture 21 slides (PDF)
Monday, November 13 Composition of linear transformations. Rotation, reflection, projection, scaling. Sections 9.1 and 9.2. Lecture 22 slides (PDF)
Wednesday, November 15 Scaling. Eigenvalues and Eigenvectors. Sections 9.2 and 12.1. Lecture 23 slides (PDF)
Friday, November 17 Eigenvalues and Eigenvectors. Characteristic equations. Diagonalization. Section 12.1. Lecture 24 slides (PDF)
Monday, November 20 Eigenvalues and Eigenvectors. Characteristic equations. Diagonalization. Section 12.1. Lecture 25 slides (PDF)
Wednesday, November 22 Diagonalization. Eigenspaces. Algebraic and geometric multiplicities. Section 12.1. Lecture 26 slides (PDF)
Monday, November 27 Algebraic and geometric multiplicities. Exponentiation. Systems of linear differential equations. Section 12.1. Lecture 27 slides (PDF)
Wednesday, November 29 Systems of linear differential equations. Complex numbers. Complex eigenvalues. Section 12.1. Lecture 28 slides (PDF)
Friday, December 1 Complex numbers. Complex eigenvalues. Symmetric and Hermitian matrices. Sections 12.1 and 12.2. Lecture 29 slides (PDF)
Wednesday, December 6, 11:00 am - 12:00 pm Review (in BEXL 328).
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