Math 218D-1 Spring 2022


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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Joe Rabinoff
Joe Rabinoff

Joe Rabinoff
Math & Physics 243
Office Hours:
M10–noonGross Hall 105
Th1:30–2:30pmPerkins LINK 079
 (Seminar 3)
Alex Wagner
Alex Wagner

Alex Wagner
Gross Hall Desk 68
Office Hours:
W1:30–3:30pmGross Hall 324
Th12–1pmGross Hall 318
Eylem Yildiz
Eylem Yildiz

Eylem Yildiz
Math & Physics 114
Office Hours:


Lecture Instructor Location Time
218D-1 (001) Joe Rabinoff Math & Physics 130 TTh 10:15–11:30am
218D-1 (002) Alex Wagner Math & Physics 130 TTh 3:30–4:45pm
Problem Session Instructor Location Time
218D-1 (01D) Eylem Yildiz Reuben-Cooke 127 F 8:30–9:45am
218D-1 (02D) Eylem Yildiz Social Sciences 119 F 10:15–11:30am
218D-1 (03D) Eylem Yildiz Math & Physics 235 F 12:00–1:15pm
218D-1 (04D) Eylem Yildiz Reuben-Cooke 127 F 3:30–4:45pm


Access Gradescope by clicking on the tab in Sakai


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.


Office Hours
Your first stop for help should be office hours! Joe, Alex, and Eylem 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!


  Topic and Section Materials Homework
Week 1: 1/3 Introduction Joe's Notes  ●  Alex's Notes
Demo: Best fit ellipse
Demo: Rabbit population
Demo: A Plane
Demo: Two Planes
Homework #1
Due 1/10


Note: HW#1 covers the recorded lecture.
Vectors and Matrices (Ch. 1, 2.4, 2.7) Joe's Notes

Recorded: Watch on WarpWire (on Sakai) before the second lecture.
Problem Session
Week 2: 1/10 Solving Equations: Elimination (2.2) Joe's Notes  ●  Alex's Notes Homework #2
Due 1/17

Gauss–Jordan Algorithm (2.2) Joe's Notes  ●  Alex's Notes
Gauss–Jordan Slideshow
Rabinoff's Reliable Row Reducer
Problem Session Worksheet and Solutions
Week 3: 1/17 Inverse and Elementary Matrices (2.3, 2.5) Joe's Notes Homework #3
Due 1/24

LU Decomposition (2.6) Joe's Notes
Problem Session Worksheet
Week 4: 1/24 Parametric Form Demo: Parameterized Line
Demo: Parameterized Plane
Homework #4
Due 1/31

Spans (3.2, 3.3)
Problem Session
Week 5: 1/31 Subspaces (3.1, 3.2) Homework #5
Due 2/9

Linear Independence and Basis (3.4, 3.5)
Week 6: 2/7 Fundamental Subspaces (3.4, 3.5) Homework #6
Due 2/14

Orthogonal Complements (3.5, 4.1)
Problem Session
Week 7: 2/14 The Big Picture (3.5, 4.1) Homework #7
Due 2/21

Orthogonal Projections (4.2)
Problem Session
Week 8: 2/21 Least Squares (4.3) Homework #8
Due 2/28

Gram–Schmidt and QR (4.4)
Problem Session
Week 9: 2/28 Determinants I (5.1, 5.3) Homework #9
Due 3/14

Determinants II (5.2)
Week 10: 3/14 Eigenvalues and Eigenvectors (6.1) Homework #10
Due 3/21

Diagonalization (6.2)
Problem Session
Week 11: 3/21 Complex Numbers; Euler's Formula (9.1) Joe's Notes

Recorded: Watch on WarpWire (on Sakai) before Tuesday's lecture.
Homework #11
Due 3/28

AM/GM and Diagonalizability (6.2)
Systems of ODEs (6.3)
Problem Session
Week 12: 3/28 Spectral Theorem (6.4) Homework #12
Due 4/4

LDLT; Quadratic Optimization (2.7, 6.5)
Problem Session
Week 13: 4/4 Quadratic Optimization II (6.5) Homework #13
Due 4/13

SVD: Outer Product Form (7.1, 7.2)
Week 14: 4/11 SVD: Matrix Form (7.3) Homework #14
Due 4/19

PCA I (7.3, 7.4)
Problem Session
4/19 PCA II (7.3) Homework #15
(Not collected)
Final exams:
218D-1 (001):Wednesday, 4/27, 9am–noon
218D-1 (002):Friday, 4/29, 7–10pm