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.
| Instructor | Office Hours | ||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|
| Joe Rabinoff | jdr@math.duke.edu |
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| Jesse Silliman | jesse.silliman@duke.edu |
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| Lecture | Instructor | Time |
|---|---|---|
| 218D-001 | Joe Rabinoff | MW 12:00–12:50pm |
| 218D-002 | Joe Rabinoff | TTh 3:30–4:20pm |
| Problem Session | Instructor | Time |
| 218D-01D | Jesse Silliman | F 10:15–11:05am |
| 218D-02D | Jesse Silliman | F 12:00–12:50pm |
| 218D-03D | Jesse Silliman | F 1:45–2:35pm |
| 218D-04D | Jesse Silliman | F 3:30–4:20pm |
| 218D-05D | Joe Rabinoff | M 10:15–11:05am |
Links:
The official text for the course is Introduction to Linear Algebra (5th Ed) by Gilbert Strang, Wellesley–Cambridge Press/SIAM (2016). However, we will follow Strang only loosely. Another good reference is the online text Interactive Linear Algebra, by Dan Margalit and Joe Rabinoff.
Your first stop for help should be office hours! Joe and Jesse will be holding plenty (times listed above), and you should not hesitate to show up with questions and chat with the other students there.
Ask questions on Piazza! Your instructors and fellow students are happy to post answers for everyone to see.
The Math Department operates several Help Rooms to provide assistance to students in lower-level courses. Students are invited to drop by the Help Rooms whenever they are open. No appointment is necessary. If you can't make the scheduled office hours, send us an email and we'll set up a meeting.
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| Topic | Materials | Remarks | Homework | |
|---|---|---|---|---|
| Week 1: 8/17 |
Vectors and Matrices (Ch. 1; 2.4) |
Joe's Notes Demo: A vector Demo: Scalar multiplication Demo: Vector addition Demo: Vector subtraction Demo: Linear combos in R2 Demo: Linear combos in R3 Demo: Linear combos in R3 |
Pre-recorded: watch here before the second lecture |
HW#1 Due 8/25 11:59pm Note: Problems 1–21 are about the material in the pre-recorded lecture. |
| Introduction |
Joe's Notes Jesse's Notes Demo: Best fit ellipse Demo: Rabbit population Demo: A Plane Demo: Two Planes |
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| Elimination (2.2) |
Joe's Notes Jesse's Notes |
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| Problem Session | Worksheet and Solutions | |||
| Week 2: 8/24 |
Gauss–Jordan (2.2) |
Joe's Notes Jesse's Notes Gauss–Jordan Slideshow Rabinoff's Reliable Row Reducer |
HW#2 Due 9/1 11:59pm |
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| LU Factorization (2.3, 2.5, 2.6, 2.7) |
Joe's Notes Jesse's Notes |
Supplement: PA=LU | ||
| Problem Session | Worksheet and Solutions | |||
| Week 3: 8/31 |
Parametric Form |
Joe's Notes Demo: Parameterized Line Demo: Parameterized Plane Demo: Column Picture: consistent Demo: Column Picture: inconsistent |
HW#3 Due 9/8 11:59pm |
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| Vector Equations (2.1, 3.2, 3.3) |
Joe's Notes 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: Row/col picture: full row rank Demo: Row/col picture: not full row rank |
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| Problem Session | Worksheet and Solutions | |||
| Week 4: 9/7 |
Transposes (2.7), Rank (3.2), Subspaces (3.1, 3.2) | Joe's Notes |
HW#4 Due 9/17 11:59pm |
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| Subspaces (3.1, 3.2, 3.3) |
Joe's Notes Demo: Column and Null Space |
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| Problem Session | Worksheet and Solutions | |||
| Week 5: 9/14 |
Tuesday, 9/15: Midterm 1 |
Practice Midterm
and Solutions Midterm and Solutions |
HW#5 Due 9/22 11:59pm |
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| Linear Independence (3.4) |
Joe's Notes Demo: Coplanar vectors Demo: Lin. (In)dep. of 1 vector Demo: Lin. (In)dep. of 2 vectors Demo: Lin. (In)dep. of 3 vectors |
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| Basis and Dimension (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 |
Supplement: full rank matrices | ||
| Problem Session | Worksheet and Solutions | |||
| Week 6: 9/21 |
Orthogonality (4.1) |
Joe's Notes Demo: Ortho complements in R2 Demo: Ortho complements in R3 Demo: Ortho complements in R3 |
HW#6 Due 9/29 11:59pm |
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| Projections (4.2) |
Joe's Notes Demo: Projection onto a line Demo: Projection onto a plane Demo: Decomp. relative a line Demo: Decomp. relative a plane |
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| Problem Session | Worksheet and Solutions | |||
| Week 7: 9/28 |
Least Squares (4.3) |
Joe's Notes Demo: Least-Squares Demo: Best-fit line Demo: Best-fit parabola |
See ILA for other least-squares examples. |
HW#7 Due 10/6 11:59pm |
| Gram–Schmidt (4.4) |
Joe's Notes Demo: Projection Formula |
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| Problem Session | Worksheet and Solutions | |||
| Week 8: 10/5 |
Determinants I (5.1, 5.3) |
Joe's Notes |
HW#8 Due 10/15 11:59pm |
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| Determinants II (5.2) |
Joe's Notes |
Supplement: cofactor matrix | ||
| Problem Session | Worksheet and Solutions | |||
| Week 9: 10/12 |
Tuesday, 10/13: Midterm 2 |
Practice Midterm
and Solutions Midterm and Solutions |
HW#9 Due 10/20 11:59pm |
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| Eigenvalues (6.1) |
Joe's Notes Demo: Rabbits Multiply Demo: Eigenspaces of a 2x2 Demo: Eigenspaces of a 3x3 Demo: Eigenspaces of a projection Demo: Eigenspaces of a rotation Demo: Eigenspaces of a shear |
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| Diagonalization (6.2) | Joe's Notes |
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| Problem Session | Worksheet and Solutions | |||
| Week 10: 10/19 |
Complex Numbers (9.1) | Joe's Notes |
Pre-recorded; watch before the first lecture |
HW#10 Due 10/27 11:59pm |
| Complex Diagonalization (6.2) |
Joe's Notes Dynamics demos: |
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| ODEs (6.3) | Joe's Notes | |||
| Problem Session | Worksheet and Solutions | |||
| Week 11: 10/26 |
Spectral Theorem (6.4) |
Joe's Notes Demo: Eigenspaces of a symmetric matrix |
HW#11 Due 11/5 11:59pm |
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| Quadratic Forms (6.5) |
Joe's Notes |
Supplement: LDLT and Cholesky | ||
| Problem Session | Worksheet and Solutions | |||
| Week 12: 11/2 |
SVD I (7.1, 7.2) | Joe's Notes |
HW#12 Due 11/12 11:59pm |
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| SVD II (7.2) | Joe's Notes | |||
| Problem Session | Worksheet and Solutions | |||
| Week 13: 11/9 |
Geometry of the SVD (7.4) | Joe's Notes |
HW#13 (Not collected) |
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| SVD and PCA (7.3) | Joe's Notes | |||
| Problem Session | ||||
| Monday, 11/16: Midterm 3 |
Practice Midterm
and Solutions Midterm and Solutions |
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| Monday, 11/23, 2–5pm / Tuesday, 11/24, 2–5pm: Final Exam |
Practice Final and Solutions | |||