Spring 2011

Math 20-580-05: Introduction to Linear Algebra and Differential Equations

Course Information

Instructor: Zhiliang Xu, zxu2@nd.edu

Office phone number: (574)631-3423

Office Hours (subject to change): Zhiliang Xu M 5:00 - 6:00 , W 5:00 - 6:00 or by appointment and drop-in (when available)i

Nicole Kroeger T 3:45 - 4:45, W 4:00 - 5:30

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 and Place: MWF 9:35am-10:25am, E.J. DeBartolo Hall 141

Syllabus is here.

Class schedule is here.

Homework collection: Homework assigned on W, F, M is due on R in tutorials.

About online lecture notes: The online lecture notes are not complete notes for class lectures. You must combine online notes with inclass notes to have a complete picture of topics covered in lectures.

Link to online ODE solver.

Important Dates
First exam Thursday, 02/17 8:00-9:15, Haggar Hall 117

Practice exam 1 is here. Answer key is here.

Review 1 (TA): Tue(02/15), 6:15pm - 7:45pm DBRT 129; Review 2 (Prof. Liu): W(02/16), 7:00pm - 9:00pm HAYE 127
Second exam Tuesday, 03/22 8:00-9:15, Haggar Hall 117

Practice exam 2 is here. The second set of practice exam is here.

Review 1 (TA): M(03/21), 5 - 7pm DBRT 138; Review 2 (Prof. Liu): M(03/21), 7 - 9:00pm DBRT 155.
Third exam Thursday, 04/21 8:00-9:15, Haggar Hall 117

The 1st practice exam is here, (Answer key). The 2nd practice exam is here.

Review 1 (TA): T(04/19), 6:15 - 8:00pm DBRT 140; Review 2 (Prof. Xu): W(04/20), 7 - 9:00pm DBRT 155.
Final exam Friday, 05/13 1:45-3:45, Nieuwland Sci. Hall 123.

The practice exam.

Review 1 (TA): W(05/11), 5: - 7:00pm DBRT 136; Review 2 (Prof. Xu): TBA.

Week 1:

Handout 1 for system of linear equations and echelon form of matrix in Sections 1.1, 1.2.

  • Wednesday (01/19): Section 1.1. HW: Section 1.1: 1, 11, 13, 15, 17, 19, 25, 31.

    Handout 2 for review of vectors in Section 1.3.

  • Wednesday (01/21): Sections 1.2; 1.3. HW: Section 1.2: 1, 3, 7, 9, 11, 12, 13.

    Week 2:

  • Monday (01/24): Section 1.3. HW: Section 1.2: 17, 18, 19. Section 1.3: 1, 5, 9, 11, 17, 18, 27.

    Handout 3 for Theorem 4 in Section 1.4 Matrix Equations

  • Wednesday (01/26): Section 1.4; 1.5 HW: Section 1.4: 1, 3, 11, 17, 19, 37.
  • Friday (01/28): Section 1.5; 1.7 HW: Section 1.5: 7, 11, 15, 19, 23, 35.

    Week 3:

  • Monday (01/31): Section 1.7. HW: Section 1.7: 1, 3, 5, 7, 9, 13, 15, 17, 19, 21.
  • Wednesday (02/02): canceled due to snow closing

    Handout 4 for Sections 1.8, 1.9, 2.1 (some definitions and theorems)

  • Friday (02/04): Sections 1.8, 1.9, 2.1 HW: Section 1.8: 1, 5, 7, 13, 14, 15, 16, 17, 19, 21, 31. Section 1.9: 1. 3, 5, 7, 13, 17, 19, 25, 27.

    Week 4:

    Handout 5 for Sections 2.1, 2.2 (some definitions and theorems)

  • Monday (02/07): Sections 1.9, 2.1, 2.2 HW: Section 2.1: 1, 3, 5, 9, 11, 15, 17, 27.

    Handout 6 for Section 2.3 (More on invertible matrices)

  • Wednesday (02/09): Sections 2.2, 2.3 HW: Section 2.2: 1, 3, 7, 15, 19, 21, 31, 32, 33, 35.

    Handout 7 for Section 2.8, 2.9 (definitions of subspace and coordinates of vectors)

  • Friday (02/11): Sections 2.8 HW: Section 2.3: 1, 5, 7, 13, 15, 17, 21, 23, 33. Section 2.8: 1, 3, 5, 7, 9, 11, 15, 17, 19, 22, 23, 24, 25.

    Week 5:

    Handout 8 for Sections 2.9, 3.1 (Basis Thm. More on invertible matrix thh. Determinant)

  • Monday (02/14): Sections 2.9, 3.1 HW: Section 2.9: 1, 5, 9, 11, 13, 19, 21, 23.
  • Wednesday (02/16): Sections 3.1, review HW: Section 3.1: 1, 5, 9, 13, 19, 21, 23, 27.
  • Friday (02/18): Sections 3.2, 3.3 HW: Section 3.2: 5, 7, 9, 15, 17, 19, 25, 29, 31, 35, 39.

    Week 6:

    Handout 9 for Sections 4.1 (Vector space)

  • Monday (02/21): Sections 3.3, 4.1 HW: Section 3.3: 3, 5, 13, 18, 21, 23, 25, 31

    Handout 10 for Sections 4.3 (Spanning set theorem)

  • Wednesday (02/23): Sections 4.1, 4.2 HW: Section 4.1: 1, 2, 3, 4, 5, 7, 9, 11, 13, 15, 17, 21, 27, 29. Section 4.2: 1, 3, 5, 7, 9, 11, 19, 21, 27, 31, 33.
  • Friday (02/25): Sections 4.3, 4.4 HW: Section 4.3: 1, 3, 5, 9, 11, 13, 14, 15, 19, 21, 33, 34. Section 4.4: 3, 7, 9, 11, 13, 17, 27, 29, 31.

    Week 7:

  • Monday (02/28): Sections 4.4, 4.5 HW: Section 4.5: 3, 5, 7, 11, 13, 19, 21, 23, 24.
  • Wednesday (03/02): Sections 4.5, 4.6 HW: Section 4.6: 1, 3, 5, 9, 11, 13, 15, 19, 25.

    Handout 11 for Theorems in Sections 5.1-5.2

  • Friday (03/04): Sections 4.7, 5.1-5.2 HW: Section 4.7: 1, 5, 7, 9, 13, 19. Section 5.1: 5, 7, 9, 13, 19, 21, 25, 31, 32. Section 5.2: 1, 5, 9, 13, 17, 18, 19, 21.

    Week 7:

    Handout 12 for sufficient conditions for diagonalization in Sections 5.3

  • Monday (03/07): Section 5.1-5.2, 5.3 HW: Section 5.3: 1, 5, 9, 13, 19, 23, 25, 27, 31, 32.
  • Wednesday (03/09): Section 5.3, 5.4 HW: Section 5.4: 1, 5, 7, 9, 13, 19, 23, 25, 27, 31.
  • Friday (03/11): Section 5.5 HW: Section 5.5: 1, 3, 7, 8, 13, 19.

    Week 8: Spring Break

    Week 9:

    Handout 13 for Sections 6.2

  • Monday (03/21): Section 6.1-6.2 HW: Section 6.1: 5, 9, 11, 15, 17, 26, 29, 31. Section 6.2: 3, 5, 7, 9, 11, 13, 15, 17, 32, 33.

    Handout 14 for Sections 6.3

  • Wednesday (03/23): Section 6.2, 6.3. HW: Section 6.3: 5, 9, 11, 13, 15, 23.
  • Friday (03/25): Section 6.4. HW: Section 6.4: 3, 5, 11, 12, 15, 16.

    Week 10:

  • Monday (03/28): Section 6.5 HW: Section 6.5: 3, 5, 7, 10, 11, 13, 19.
  • Wednesday (03/30): ODE book, 1.1, 1.2 HW: 1.1: 1, 2 (draw by hand). 1.2: 1.
  • Friday (04/01): 1.3, 2.1. HW: 1.3: 1, 5, 6, 7, 11, 15, 17, 21, 22. 2.1: 1, 5, 11, 13, 15, 19, 21, 23, 31.

    Week 11:

  • Monday (04/04): Section 2.1, 2.2 HW: Section 2.2: 3, 6, 7, 9, 17, 19, 21, 23, 29.

    Sample modeling problems

  • Wednesday (04/06): Section 2.3 HW: Section 2.3: 3, 8, 9, 13, 16, 19, 29.

    Existence and Uniqueness Thm of 1st order DEs.

  • Friday (04/08): Section 2.4 HW: Section 2.4: 1, 3, 7, 11, 13, 15, 23.

    Week 12:

  • Monday (04/11): Section 2.4, 2.5 HW: Section 2.5: 3, 5, 7, 9, 15, 18, 20.
  • Wednesday (04/13): Section 2.6 HW: Section 2.6: 1, 3, 5, 7, 9, 11, 13, 15, 19, 25, 27, 28.

    Help section: HAYE 229, 6:30 - 7:30

  • Friday (04/15): Section 3.1 HW: Section 3.1: 1, 5, 9, 13, 17, 21, 23.

    Week 13:

  • Monday (04/18): Section 3.2 HW: Section 3.2: 1, 5,9, 11, 14, 17, 22, 29, 31, 35, 37, 38.

    Review session: DBRT 116, 8:00pm - 9:00pm

    Thm 3.2.5, 3.2.6.

  • Wednesday (04/20): Section 3.3, 3.4 HW: Section 3.3: 1, 3, 5, 7, 9, 13, 17, 19, 21, 29. Section 3.4: 1, 5, 7, 11, 13, 18, 19, 25, 27, 28.

    Week 14:

  • Wednesday (04/27): Section 3.4, 3.5
  • Friday (04/29): Section 3.5 HW: Section 3.5: 3, 5, 7, 9, 13, 15, 16, 17

    Week 15:

  • Monday (05/02): Section 3.6, 3.7 HW: Section 3.6: 1, 3, 5, 10, 11, 15, 17.
  • Wednesday (05/04): Section 3.7, 3.8, review
  • Thursday (05/05): Office hrs 3:00-4:00pm.

    Final exam week schedule

  • Monday, Wednesday, office hrs: 5:00pm-6:00pm.
  • Tuesday, review: 7:00pm- , Hayes-Healy 129.
  • Thursday, office hrs: 5:00pm-7:00pm