Welcome to Math 218D! I will post almost all course materials on this page. Please check back for information about homework assignments, exams, and additional resources. You should probably read the syllabus.
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Tu | noon | –1pm | Gross Hall 104 |
W | 1:30 | –3:30pm | Gross Hall 111 |
Tu | 5:30 | –6:45pm | Math & Physics 113 |
Th | 1 | –2:15pm | Zoom (see Sakai) |
Lecture | Instructor | Location | Time |
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218D-1 (001) | Joe Rabinoff | Math & Physics 130 | TTh 10:15–11:30am |
218D-1 (002) | Eylem Yildiz | Math & Physics 130 | TTh 3:30–4:45pm |
Problem Session | Instructor | Location | Time |
218D-1 (01D) | Bowen Li | Social Sciences 119 | F 8:30–9:45am |
218D-1 (02D) | Bowen Li | Perkins 071 | F 10:15–11:30am |
218D-1 (03D) | Edna Jones | LSRC A247 | F noon–1:15pm |
218D-1 (04D) | Edna Jones | Social Sciences 119 | F 3:30–4:45pm |
Access Gradescope by clicking on the tab in Sakai.
For practicing row reduction when you're allergic to fractions.
A complement to Strang's book written by Joe.
Topic and Section | Materials | Homework | |||||
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Week 1: 1/9 | Introduction |
Joe's Notes Demo: Best fit ellipse Demo: Rabbit population Demo: A Plane Demo: Two Planes |
Homework #1 Due 1/18 11:59pm Solutions Note: HW#1 covers the recorded lecture. |
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Vectors and Matrices (Ch. 1, 2.4, 2.7) |
Joe's Notes Recorded: Watch on WarpWire (on Sakai) before the second lecture. |
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Problem Session | |||||||
Week 2: 1/16 | Solving Equations: Elimination (2.2) | Joe's Notes |
Homework #2 Due 1/25 11:59pm Solutions |
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Gauss–Jordan Algorithm (2.2, 2.5) |
Joe's Notes Gauss–Jordan Slideshow Rabinoff's Reliable Row Reducer |
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Problem Session | Quiz | ||||||
Week 3: 1/23 | LU Decomposition (2.3, 2.6) | Joe's Notes |
Homework #3 Due 2/1 11:59pm Solutions |
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Parametric Form |
Joe's Notes Demo: Parameterized Line Demo: Parameterized Plane |
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Problem Session | Quiz | ||||||
Week 4: 1/30 | Spans (3.2, 3.3) |
Joe's Notes Demo: A vector Demo: Scalar multiplication Demo: Vector addition Demo: Vector subtraction Demo: Linear combinations of two vectors in R2 Demo: Linear combinations of two vectors in R3 Demo: Linear combinations of three vectors in R3 Demo: Span of 1 vector in R2 Demo: Span of 2 vectors in R2 Demo: Span of 1 vector in R3 Demo: Span of 2 vectors in R3 Demo: Span of 3 vectors in R3 Demo: Column Picture for Consistency: Consistent Demo: Column Picture for Consistency: Inconsistent Demo: Row/column picture: parallel lines Demo: Row/column picture: sometimes inconsistent |
Homework #4 Due 2/8 11:59pm Solutions |
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Subspaces (3.1, 3.2) |
Joe's Notes Demo: Column and Null Space |
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Problem Session | Quiz | ||||||
Week 5: 2/6 | Linear Independence and Basis (3.4, 3.5) |
Joe's Notes Demo: Coplanar vectors Demo: Redundant parameterization Demo: Linearly dependent vectors Demo: Linearly independent vectors Demo: Linear (In)dependence of 1 vector Demo: Linear (In)dependence of 2 vectors Demo: Linear (In)dependence of 3 vectors Demo: Linear Dependence of 3 vectors in R2 |
Homework #5 Due 2/15 11:59pm Solutions |
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Fundamental Subspaces (3.4, 3.5) |
Joe's Notes Demo: Rank-nullity: n=3, r=0 Demo: Rank-nullity: n=3, r=1 Demo: Rank-nullity: n=3, r=2 Demo: Rank-nullity: n=3, r=3 |
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Problem Session | Quiz | ||||||
Week 6: 2/13 | Orthogonal Complements (3.5, 4.1) |
Joe's Notes Demo: Closest vector to b Demo: Orthogonal complement of one vector Demo: Orthogonal complement of two vectors Demo: Orthogonal complements in R2 |
Homework #6 Due 2/22 11:59pm Solutions |
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Orthogonal Projections (4.2) |
Joe's Notes Demo: Decomposition relative a line in R2 Demo: Decomposition relative a line in R3 Demo: Decomposition relative a plane in R3 Demo: Projection onto a plane Demo: Projection onto a line Demo: Projection onto a plane |
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Friday, 2/17: MIDTERM 1 |
Practice Midterm
and Solutions Midterm and Solutions |
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Week 7: 2/20 | Projection Matrices (4.2) | Joe's Notes |
Homework #7 Due 3/1 11:59pm Solutions |
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Least Squares (4.3) |
Joe's Notes Demo: Least-Squares Demo: Best-fit line Demo: Best-fit parabola Demo: Best-fit trigonometric function Demo: Best-fit ellipse Demo: Best-fit ellipse: what is minimized? |
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Problem Session | |||||||
Week 8: 2/27 | Gram–Schmidt and QR (4.4) |
Joe's Notes Demo: Projection formula |
Homework #8 Due 3/8 11:59pm Solutions |
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Determinants I (5.1, 5.3) | Joe's Notes | ||||||
Problem Session | Quiz | ||||||
Week 9: 3/6 | Determinants II (5.2) |
Joe's Notes Supplement: cofactor matrix |
Homework #9 Due 3/22 11:59pm Solutions |
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Eigenvalues and Eigenvectors (6.1) |
Joe's Notes Demo: Rabbits Multiply Demo: Eigenspaces of a flip Demo: Eigenspaces of a shear Demo: Eigenspaces of a rotation Demo: Eigenspaces of the rabbit matrix Demo: Eigenspaces of a 3x3 matrix Demo: Eigenspaces of a projection matrix |
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Problem Session | Quiz | ||||||
SPRING BREAK | |||||||
Week 10: 3/20 | Diagonalization: Vector Form (6.2) | Joe's Notes |
Homework #10 Due 3/29 11:59pm |
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Diagonalization: Geometry (6.2) |
Joe's Notes Dynamics demos: |
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Problem Session | Quiz | ||||||
Week 11: 3/27 | Complex Numbers; Euler's Formula (9.1) |
Joe's Notes Recorded: Watch on WarpWire (on Sakai) before Tuesday's lecture. |
Homework #11 Due 4/5 11:59pm |
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AM/GM and Diagonalizability (6.2) |
Joe's Notes Supplement: Proof of the AM≥GM theorem AM/GM demos: Dynamics with a Complex Eigenvalue |
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Systems of ODEs (6.3) | Joe's Notes | ||||||
Friday, 3/31: MIDTERM 2 |
Practice Midterm
and Solutions |
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Week 12: 4/3 | Spectral Theorem (6.4) |
Homework #12 Due 4/12 11:59pm |
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LDLT; Quadratic Optimization (2.7, 6.5) | |||||||
Problem Session | |||||||
Week 13: 4/10 | Quadratic Optimization II (6.5) |
Homework #13 Due 4/19 11:59pm |
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SVD: Outer Product Form (7.1, 7.2) | |||||||
Week 14: 4/17 | SVD: Matrix Form (7.3) |
Homework #14 Due 4/26 11:59pm |
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PCA I (7.3, 7.4) | |||||||
Problem Session | |||||||
4/25 | PCA II (7.3) |
Homework #15 (Not collected) |
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Final exams:
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