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 | Office Hours | |||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|
| Joe Rabinoff | jdr@math.duke.edu | Math & Physics 243 |
|
||||||||
| Spencer Leslie | lesliew@math.duke.edu | Math & Physics 222 |
|
||||||||
| Jesse Silliman | jesse.silliman@duke.edu | Math & Physics 106 |
|
||||||||
| Bowen Li | bowen.li200@duke.edu | Gross Hall 326 |
|
| Lecture | Instructor | Location | Time |
|---|---|---|---|
| 218D-1 (001) | Joe Rabinoff | LSRC A247 | TTh 12:00–1:15pm |
| 218D-1 (002) | Spencer Leslie | LSRC A247 | TTh 3:30–4:45pm |
| Problem Session | Instructor | Location | Time |
| 218D-1 (01D) | Spencer Leslie | Math & Physics 235 | F 10:15–11:30am |
| 218D-1 (02D) | Jesse Silliman | Math & Physics 235 | F 12:00–1:15pm |
| 218D-1 (03D) | Jesse Silliman | Allen 326 | F 1:45–3:00pm |
| 218D-1 (04D) | Bowen Li | Math & Physics 259 | F 3:30–4:45pm |
| 218D-1 (05D) | Bowen Li | Math & Physics 047 | F 8:30–9:45am |
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, Spencer, Jesse, and Bowen 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 Ed Discussion. Your instructors and fellow students are happy to post answers for everyone to see, and usually do so much more quickly than someone can respond to an email message.
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.
The Academic Resource Center (ARC) offers free services to all students during their undergraduate careers at Duke. Services include Learning Consultations, Peer Tutoring, Learning Communities, ADHD/LD Coaching, Outreach Workshops, GRE/MCAT Prep, Study Connect, and more. Because learning is a process unique to every individual, we work with each student to discover and develop their own academic strategy for success at Duke. Contact the ARC to schedule an appointment. Undergraduates in any year, studying any discipline can benefit!
| Topic and Section | Materials | Homework | |||||
|---|---|---|---|---|---|---|---|
| Week 1: 8/23 | Introduction |
Joe's Notes Demo: Best fit ellipse Demo: Rabbit population Demo: A Plane Demo: Two Planes |
Homework #1 Due 8/30 11:59pm Note: Problems 1–22 are about the material in the pre-recorded lecture. |
||||
|
Vectors and Matrices (Ch. 1; 2.4, 2.7) Recorded: Watch on WarpWire before the second lecture. (If this link doesn't work, use the tab on the Sakai page.) |
Joe's Notes and Erratum (fixed in the 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 |
||||||
| Solving Equations: Elimination (2.2) | Joe's Notes | ||||||
| Problem Session | Worksheet and Solutions | ||||||
| Week 2: 8/30 | Gauss–Jordan Algorithm (2.2, 2.5) |
Joe's Notes Gauss–Jordan Slideshow Rabinoff's Reliable Row Reducer |
Homework #2 Updated 9/2 Due 9/6 11:59pm |
||||
| LU Factorization (2.3, 2.5, 2.6) | Joe's Notes | ||||||
| Problem Session | Worksheet and Solutions | ||||||
| Week 3: 9/6 | Maximal Partial Pivoting; PA=LU (2.6, 2.7) | Joe's Notes |
Homework #3 Updated 9/8 Due 9/13 11:59pm |
||||
| Parametric Form of Solutions |
Joe's Notes Demo: Parameterized Line Demo: Parameterized Plane Demo: Column Picture: consistent Demo: Column Picture: inconsistent |
||||||
| Problem Session | Worksheet and Solutions | ||||||
| Week 4: 9/13 | Spans (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: Is a vector contained in a span? Demo: Row/column picture: parallel lines Demo: Row/column picture: sometimes inconsistent |
Homework #4 Due 9/20 11:59pm |
||||
| Subspaces (3.1, 3.2) |
Joe's Notes Demo: Column and Null Space |
||||||
| Problem Session | Worksheet and Solutions | ||||||
| Week 5: 9/20 | 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 |
Homework #5 Due 9/29 11:59pm |
||||
| Column Rank and Row Rank (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 |
||||||
| MIDTERM 1 |
Practice Midterm
and Solutions Midterm and Solutions |
||||||
| Week 6: 9/27 | Orthogonality (3.5, 4.1) |
Joe's Notes Demo: Closest vector to b Demo: An orthogonal complement in R3 Demo: An orthogonal complement in R3 Demo: Orthogonal complements in R2 |
Homework #6 Due 10/6 11:59pm |
||||
| Orthogonal 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 |
||||||
| Problem Session | Worksheet and Solutions | ||||||
| Week 7: 10/4 | Fall Break |
Homework #7 Due 10/11 11:59pm |
|||||
| Projection Matrices (4.2) |
Joe's Notes |
||||||
| Problem Session | Worksheet and Solutions | ||||||
| Week 8: 10/11 | 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? |
Homework #8 Due 10/18 11:59pm |
||||
| Gram–Schmidt and QR (4.4) |
Joe's Notes |
||||||
| Problem Session | Worksheet and Solutions | ||||||
| Week 9: 10/19 | Determinants I (5.1, 5.3) | Joe's Notes |
Homework #9 Updated 10/24 Due 10/27 11:59pm |
||||
| Determinants II (5.2) |
Joe's Notes Supplement: cofactor matrix |
||||||
| MIDTERM 2 |
Practice Midterm
and Solutions Midterm and Solutions |
||||||
| Week 10: 10/25 | 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 |
Homework #10 Due 11/3 11:59pm |
||||
| Diagonalization (6.2) |
Joe's Notes |
||||||
| Problem Session | Worksheet and Solutions | ||||||
| Week 11: 11/1 |
Complex Numbers; Euler's Formula (9.1) Recorded: Watch on WarpWire before Tuesday's lecture. (If this link doesn't work, use the tab on the Sakai page.) |
Joe's Notes |
Homework #11 Due 11/8 11:59pm |
||||
| Complex Diagonalization (6.2) |
Joe's Notes Dynamics demos: |
||||||
| AM/GM; Ordinary Differential Equations I (6.3) |
Joe's Notes Demo: Eigenspaces of a non-diagonalizable 3x3 matrix Demo: Eigenspaces of a diagonalizable 3x3 matrix |
||||||
| Problem Session | Worksheet and Solutions | ||||||
| Week 12: 11/8 | Ordinary Differential Equations II (6.3) | Joe's Notes |
Homework #12 Updated 11/11 Due 11/15 11:59pm |
||||
| Spectral Theorem (6.4) |
Joe's Notes Demo: Eigenspaces of a 3x3 symmetric matrix Demo: Dynamics of a 2x2 symmetric matrix |
||||||
| Problem Session | Worksheet and Solutions | ||||||
| Week 13: 11/15 | Quadratic Optimization (6.5) | Joe's Notes |
Homework #13 Due 11/24 11:59pm |
||||
| Quadratic Optimization continued; LDLT |
Joe's Notes Supplement: LDLT and Cholesky |
||||||
| MIDTERM 3 |
Practice Midterm
and Solutions Midterm and Solutions |
||||||
| Week 14: 11/22 | SVD (7.1–7.3) On Zoom (see Sakai announcements). |
Joe's Notes |
Homework #14 Due 12/1 11:59pm |
||||
| Thanksgiving | |||||||
| Thanksgiving | |||||||
| Week 15: 11/29 | SVD: Matrix Form (7.3) |
Joe's Notes |
Homework #15 (Not collected) |
||||
| SVD: Application to PCA (7.3) |
Joe's Notes |
||||||
| Problem Session | |||||||
Final exams:
|
Practice Final and Solutions | ||||||