Math 218D-1 Spring 2023
Welcome
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.
Jump to Week: 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
Instructors
Joe Rabinoff
jdr@math.duke.eduMath & Physics 243
Office Hours:
| Tu | noon | –1pm | Gross Hall 104 |
| W | 1:30 | –3:30pm | Gross Hall 111 |
Eylem Yildiz
eylem.yildiz@duke.eduMath & Physics 114
Office Hours:
| Tu | 5:30 | –6:45pm | Math & Physics 113 |
| Th | 1 | –2:15pm | Zoom (see Sakai) |
Classes
| Lecture | Instructor | Location | Time |
|---|---|---|---|
| 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 |
Resources
Access Gradescope by clicking on the tab in Sakai.
Rabinoff's Reliable Row Reducer
For practicing row reduction when you're allergic to fractions.
Interactive Linear Algebra
A complement to Strang's book written by Joe.
Textbook
Strang, Introduction to Linear Algebra
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.Help
Office Hours
Your first stop for help should be office hours! Joe, Eylem, Edna, 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.Ed Discussion
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.
Help Rooms
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
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!Schedule
| Topic and Section | Materials | Homework | |||||
|---|---|---|---|---|---|---|---|
| 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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