![[circular math logo]](/images/fractal-1978534_640.jpg)
Updates/Revisions to the Math 251 Course Webpages
- Please note the date change for Test 3 on the Tests page.
Links to other Math 251 Sites
- You can find more resources on the Math 251 websites for the following
Camosun instructors:
- Gilles Cazelais, especially his Course Notes and Resources page.
- Leah Howard, including a complete set of course notes and also lecture videos
- George Ballinger, who has sample tests and useful documents and links
- (You'll find some redundancy because we do share resources.)
Study Plan
Week 1: Sept 7 to Sept 10
- Section 1.1: The Geometry and Algebra of Vectors
- My Old Lecture Notes: Part 1, Part 2 – these are skeleton notes from last year's lecture class. For my current notes, see the Lectures page. For more detailed notes, please check out Gilles Cazelais' Math 251 Course Notes Page.
- Handout: Section 1.1: Properties of Vectors
- We are omitting Binary Vectors and Modular Arithmetic from Section 1.1.
- Leah's Videos: 1.1 Intro to Vectors (2 mins) and 1.1 Intro to Linear Combinations (4 mins)
- Section 1.2: Length and Angle: The Dot Product
- My Old Lecture Notes: Part 1, Part 2, Part 3, Part 4 (can leave Parts 3 and 4 until next week and still be on track)
- Leah's Videos: 1.2 A Proof about The Dot Product (5 mins) and 1.2 Scaling Vectors (4 mins)
- Conceptual Videos: Zach Star's video on applications of the dot product: watch the first 2:30 min
- WeBWorK Assign0, which is due the following week
Week 2: Sept 13 to Sept 17
- Finish up Section 1.2
- Exploration: The Cross Product
- Start looking at Section 1.3: Lines and Planes
- My Old Lecture Notes: Part 1, Part 2, Part 3, Part 4, Part 5 (can leave Parts 3 to 5 until next week and still be on track)
- Handout: Section 1.3: Lines and Planes
- Leah's Videos: 1.3 General and Normal Form (3 mins), 1.3 Vector and Parametric Form (6 mins), 1.3 Distance Between a Point and a Line (9 mins)
- WeBWorK Assign1, which is due the following week
Week 3: Sept 20 to Sept 24
- Finish up Section 1.3
- Section 2.1: Introduction to Systems of Linear Equations
- Start working on Section 2.2: Direct Methods for Solving Linear Systems
- My Old Lecture Notes: Part 1, Part 2, Part 3, Part 4
- Handout: Section 2.2: Homogeneous Systems
- Leah's Videos: 2.2 Gaussian Elimination (12 mins), 2.2 Gauss-Jordan Elimination (13 mins)
- Conceptual Videos: LeiosOS's video on Gaussian Elimination has a neat visualization of what Gaussian elimination is actually doing
- Conceptual Videos: watch the first 2:23 minutes of Zach Star's video on matrix manipulation for two different ways to think about what it means to solve a system of equations
- WeBWorK Assign2, which is due the following week
- Fun link of the week: Mad Engineers
Week 4: Sept 27 to Oct 1
- Finish up Section 2.2
- Test 1 covers the material up to this point. Here is a brief review of the topics covered.
- Section 2.3: Spanning Sets and Linear Independence
- My Old Lecture Notes: Part 1, Part 2, Part 3, Part 4
- Leah's Videos: 2.3 Span (7 mins) , 2.3 Linear Independence (11 mins)
Week 5: Oct 4 to Oct 8
- Section 2.4: Applications
- Revised lecture notes coming soon!
- Leah does not have videos for this section.
- Section 3.1: Matrix Operations
- My Old Lecture Notes: Part 1, Part 2
- Leah's Videos: 3.1 Matrix Operations (9 mins), 3.1 Powers of a Matrix (10 mins)
- Conceptual Videos: Zach Star's video on applications of matrices: from 1:15 to 4:36 to see why we can use the inverse of matrix A to solve Ax=b
- Test 1 is tentatively scheduled for Tuesday of this week.
Week 6: Oct 12 to Oct 15
- Section 3.2: Matrix Algebra
- My Old Lecture Notes: Part 1, Part 2, Part 3
- Handout: Chapter 3: Matrix Properties
- Leah's Videos: 3.2 Span of a Set of Matrices (12 mins), 3.2 A Proof about the Transpose (3 mins)
- Section 3.3: The Inverse of a Matrix
- My Old Lecture Notes: Part 1, Part 2, Part 3, Part 4
- Leah's Videos: 3.3 The Inverse of a Matrix (8 mins), 3.3 Elementary Matrices (10 mins)
Week 7: Oct 18 to Oct 22
- Section 3.4: The LU Factorization
- My Old Lecture Notes: Part 1, Part 2
- Leah's Videos: 3.4 LU Factorization (8 mins), 3.4 Solving using LU (6 mins)
- Section 3.5: Subspaces, Basis, Dimensions, and Rank
- My Old Lecture Notes: Part 1, Part 2, Part 3, Part 4, Part 5,
- Handout: Section 3.5: Change of Basis
- Leah's Videos: 3.5 Subspaces (9 mins), 3.5 Rowspace, Columnspace and Nullspace (8 mins)
- Conceptual Videos: Zach Star's video on matrix manipulation explains the null space, row space, and column starting at 2:25 and ending at 9:00
Week 8: Oct 25 to Oct 29
- Section 3.6: Introductions to Linear Transformations
- My Old Lecture Notes: Part 1, Part 2, Part 3
- Leah's Videos: 3.6 Standard Matrix of a Linear Transformation (8 mins), 3.6 Image Under a Linear Transformation (7 mins)
- Test 2 covers the material up to this point. Here is a brief review of the topics covered: Part 1, Part 2.
Week 9: Nov 1 to Nov 5
- Appendix C: Complex Numbers (Appendix C)
- My Old Lecture Notes: Part 1, Part 2, Part 3
- Leah's Videos: Appendix C: The Algebra of Complex Numbers (3 mins)
- Test 2 is tentatively scheduled for Tuesday of this week.
Week 10: Nov 8 to Nov 12
- Section 4.1: Introduction to Eigenvalues and Eigenvectors
- My Old Lecture Notes: Part 1, Part 2
- Leah's Videos: 4.1 Eigenvalues and Eigenvectors (9 mins), 4.1 The Geometry of Eigenvectors (7 mins)
- Conceptual Videos: Zach Star's video on eigenvectors and eigenvalues: watch the first 2:56 min for a nice conceptualization, including complex eigenvectors
- Section 4.2: Determinants
- My Old Lecture Notes: Part 1, Part 2, Part 3
- Leah's Videos: 4.2 Cramer's Rule (7 mins), 4.2 The Adjoint Formula for an Inverse Matrix (7 mins)
Week 11: Nov 15 to 19
- Section 4.3: Eigenvalues and Eigenvectors of n × n matrices
- My Old Lecture Notes: Part 1, Part 2, Part 3 – Josh M. was my substitute lecturer for Part 2
- Leah's Videos: 4.3 Geometric Multiplicity (6 mins) , 4.3 Algebraic Multiplicity (13 mins) , 4.3 A Proof about Eigenvectors (5 mins) , Appendix C: Complex Eigenvalues and Eigenvectors (12 mins)
- Conceptual Videos: 3Blue1Brown's video on eigenvectors and eigenvalues
- Section 4.4: Similarity and Diagonalization
- My Old Lecture Notes: Part 1, Part 2, Part 3 – these are notes from 2017 since I had a substitute during this section in 2018
- Leah's Videos: 4.4 Diagonalization (7 mins), 4.4 Powers of a Matrix and Diagonalization (8 mins)
- Start working on Section 5.1: Orthogonality in Rn
- My Old Lecture Notes: Part 1, Part 2, Part 3
- Leah's Videos: 5.1 Calculations with an Orthogonal Basis (3 mins), 5.1 Orthogonal Matrices (4 mins)
Week 12: Nov 22 to Nov 26
- Finish up Section 5.1
- Section 5.2: Orthogonal Complements and Orthogonal Projections
- My Old Lecture Notes: Part 1, Part 2
- Leah's Videos: 5.2 Orthogonal Complements (7 mins), 5.2 Orthogonal Decompositions (8 mins)
- Section 5.3: The Gram-Schmidt Process and the QR Factorization
- My Old Lecture Notes: Part 1, Part 2
- Leah's Videos: 5.3 The Gram-Schmidt Process (7 mins) , 5.3 QR Factorization (9 mins)
- Test 3 covers the material up to this point. Here is a brief review of the topics covered: Review for Test 3
Week 13: Nov 29 to Dec 3
- Section 5.4: Orthogonal Diagonalization of Symmetric Matrices
- My Old Lecture Notes: Part 1, Part 2
- Leah's Videos: 5.4 Orthogonal Diagonalization (11 mins), 5.4 The Spectral Decomposition (6 mins)
- Test 3 is tentatively scheduled for Tuesday of this week
Week 14: Dec 6 to Dec 10
- Section 7.3: Least Squares Approximation
- My Old Lecture Notes: Part 1, Part 2, Part 3
- Leah's Videos: 7.3 Least Squares Approximation (8 mins)
