Spring 2009
Math 20-580-01: Introduction to Linear Algebra and Differential Equations
Course Information
Instructor: Zhiliang Xu,
zxu2@nd.edu
Office phone number: 1-3423
Office Hours (subject to change): M 6:30pm-7:30pm, W 4:30pm- 5:30pm, Hayes-Healy 226, and by appointment
Textbook: Linear algebra and its applications (3rd ed) by David Lay.
Elementary Differential Equations and Boundary Value Problems (9th ed) by William Boyce and Richard DiPrima.
Class Time: MWF 8:30am-9:20am, in Hayes Healy Center 129
Other course information is available here Math20580
Week 1:
Jan 14: Section 1.1 System of linear equations.
Homework: Sec. 1.1.
Jan 16: Section 1.2 Row reduction & echelon forms
Homework: Sec. 1.2.
Week 2:
Homework Due on 01/23: 1.1, 1.2, 1.3, 1.4.
Jan 19: Section 1.3 Vector equations.
Homework: Sec. 1.3.
Jan 21: Section 1.4 Matrix equations; Section 1.5 Soln sets of linear systems
Homework: Sec. 1.4; Sec. 1.5.
Jan 23: Section 1.7 Linear Independence
Homework: Sec. 1.7.
Week 3:
Homework Due on 01/30: 1.5, 1.7, 1.8, 1.9.
Jan 26: Section 1.8 Linear transformation; Section 1.9 Matrix of linear transformation
Homework: Sec. 1.8.
Jan 28: Section 1.9 Matrix of linear transformation; Section 2.1 Matrix operations
Homework: Sec. 1.9.
Jan 30: Section 2.1 Matrix operations
Homework: Sec. 2.1.
Week 4:
Homework Due on 02/6: 2.1, 2.2, 2.3.
Group 1: 6:30pm; Group 2: 7:10pm.
Feb 2: Section 2.2 Inverse of a matrix
Homework: Sec. 2.2.
Feb 4: Section 2.3 Invertible matrix thm; 2.8 Subspaces in R^n
Homework: Sec. 2.3.
Feb 6: 2.8 Subspaces in R^n; 2.9 Dim. and Rank
Homework: Sec. 2.8; Sec. 2.9
Week 5:
Exam on 02/12: 213 DeBartolo Hall; 8:00am - 9:15 am
Homework Due on 02/13: 2.8, 2.9, 3.1.
Feb 9: 3.1 Intr. to Determinants
Homework: Sec. 3.1
Feb 11: 3.2 Properties of Determinants; Exam Review
Homework: Sec. 3.2
Extended Office Hr: 4:30pm - 7:00pm
Feb 13: 3.2 Properties of Determinants; 3.3 Cramer's rule
Homework: Sec. 3.2
Week 6:
Homework Due on 02/20: 3.2, 3.3
Feb 16: 3.3 Cramer's rule
Homework: Sec. 3.3
Feb 18: 4.1 Spaces & Subspaces
Homework: Sec. 4.1
Feb 20: 4.2 NulA, ColA & Linear transformation
Homework: Sec. 4.2
Week 7:
Homework Due on 02/27: 4.1 --- 4.4
Feb 23: 4.3 Linear indep. & Bases; 4.4 Coord. systems
Homework: Sec. 4.3
Feb 25: 4.4 Coord. systems; 4.5 Dimensions
Homework: Sec. 4.4
Feb 27: 4.6 - 4.7
Homework: Sec. 4.5, 4,6, 4.7.
Week 8:
Homework Due on 02/27: 4.5 --- 5.1
Group 1: 6:30pm; Group 2: 7:10pm.
Mar 02: 4.7 Change of basis; 5.1 Eigenvalues and eigenvectors
Homework: Sec. 4.7; Sec. 5.1
Mar 04: 5.1 Eigenvalues and eigenvectors; 5.2 Char. eqn.
Homework: Sec. 5.1
Week 9:
Spring Break;
Week 10:
Exam on 03/17: 8:00am --- 9:15am, DBRT 213
Review on 03/16: 7:00pm --- 8:00pm, DBRT 141
Office Hour on 03/16: 5:00pm --- 7:00pm
Homework Due on 03/20: 5.2 --- 5.3
Mar 16: Exam review & 5.3 Diaganolization.
Homework: Sec. 5.3
Mar 18: 5.3 Diaganolization.
Homework: Sec. 5.3
Mar 20: 5.4 Eigenvalues and linear transformation.
Homework: Sec. 5.4
Week 11:
Homework Due on 03/27: 5.4 --- 6.1
Mar 23: 5.5 Complex eigenvalues.
Homework: Sec. 5.5
Mar 25: 6.1 Inner product & orthogonality; 6.2 Orth. sets
Homework: Sec. 6.1
Mar 27: 6.2 Orth. sets; 6.3 Orth. proj.
Homework: Sec. 6.2
Week 12:
Homework Due on 04/03: 6.2 --- 6.4
Mar 30: 6.3 Orth. proj.
Homework: Sec. 6.3
Apr 01: 6.4 Gram-Schmidt process; 6.5 least square problems
Homework: Sec. 6.4
Apr 03: 6.5 least square problems; Chapter 1 (DE)
Homework: Sec. 6.5; Sec1.2 - 1.3
Week 13:
Review on 04/06: group 1 at 6:30pm; group 2 at 7:10pm
Apr 06: 2.1 (DE) Method of integrating factor
Homework: Sec. 2.1
Apr 08: 2.2 (DE) Separable eqns
Homework: Sec. 2.2
Week 14:
Review on 04/15: 7:00pm - 8:00pm DBRT 141
Exam on 04/16: 8:00am - 9:15am DBRT 213
Apr 15: Exam review
Apr 17: 2.3 Math. modeling
Homework: Sec. 2.3
Week 15:
Homework Due on 04/24: 2.3 --- 2.5
Apr 20: 2.5 Autonomous eqns
Homework: Sec. 2.5
Apr 22: 3.1 2nd order linear eqns with const. coefficients; 3.2 Solutions of linear homogeneous eqns
Homework: Sec. 3.1; Sec. 3.2: 9, 11, 14.
Apr 24: 3.3 Complex roots; 3.4 Repeated Roots
Homework: Sec. 3.3; Sec. 3.4.
Week 16:
Apr 27: 3.5 Undetermined coefficients
Homework: Sec. 3.5.
Apr 29: Review
Final exam: 05/06, 1:45-3:45pm, HH 129
Exam review: 05/05, 7-8pm, DBRT 142
There are still office hours next week or by appointment.