Math 218D-1 Spring 2022

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.

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Instructors

Joe Rabinoff
Joe Rabinoff

Joe Rabinoff

jdr@math.duke.edu
Math & Physics 243
Office Hours:
M10–noonGross Hall 105
Th2–3pmOn Zoom
Alex Wagner
Alex Wagner

Alex Wagner

awagner@math.duke.edu
Gross Hall Desk 68
Office Hours:
W1:30–3:30pmGross Hall 324
Th12–1pmGross Hall 318
Eylem Yildiz
Eylem Yildiz

Eylem Yildiz

eylem.yildiz@duke.edu
Math & Physics 114
Office Hours:
F2–3pmOn Zoom
Sa10–noonOn Zoom

Classes

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

Resources

Syllabus
Sakai Site
Ed Discussion
Gradescope help

Access Gradescope by clicking on the tab in Sakai

Textbook

Strang
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, 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!

Schedule

  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
11:59pm

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
11:59pm
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
11:59pm
LU Decomposition (2.6) Joe's Notes
Problem Session Worksheet and Solutions
Week 4: 1/24 Parametric Form Joe's Notes
Demo: Parameterized Line
Demo: Parameterized Plane
 Homework #4
Updated 1/26
Due 1/31
11:59pm
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
Problem Session Worksheet and Solutions
Week 5: 1/31 Subspaces (3.1, 3.2) Joe's Notes
Demo: Column and Null Space 		Homework #5
Due 2/9
11:59pm
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
MIDTERM 1 Practice Midterm and Solutions
Midterm and Solutions
Week 6: 2/7 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 		Homework #6
Due 2/14
11:59pm
Orthogonal Complements (3.5, 4.1) Joe's Notes
Demo: Closest vector to b
Demo: An orthogonal complement in R3
Demo: An orthogonal complement in R3
Problem Session Worksheet and Solutions
Week 7: 2/14 The Big Picture (3.5, 4.1) Joe's Notes
Demo: Orthogonal complements in R2
 Homework #7
Due 2/21
11:59pm
Orthogonal Projections (4.2) Joe's Notes
Demo: Projection onto a line
Demo: Projection onto a plane
Demo: Decomposition relative a line
Demo: Decomposition relative a plane
Problem Session Worksheet and Solutions
Week 8: 2/21 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 2/28
11:59pm
Gram–Schmidt and QR (4.4) Joe's Notes
Demo: Projection formula
Problem Session Worksheet and Solutions
Week 9: 2/28 Determinants I (5.1, 5.3) Joe's Notes Homework #9
Due 3/16
11:59pm
Determinants II (5.2) Joe's Notes
Supplement: cofactor matrix
MIDTERM 2 Practice Midterm and Solutions
Midterm and Solutions
SPRING BREAK
Week 10: 3/14 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 3/23
11:59pm
Diagonalization (6.2) Joe's Notes
Problem Session Worksheet and Solutions
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 3/30
11:59pm
AM/GM and Diagonalizability (6.2) Joe's Notes
Supplement: Proof of the AM≥GM theorem

Dynamics demos:
AM/GM demos:
Systems of ODEs (6.3) Joe's Notes
Problem Session Worksheet and Solutions
Week 12: 3/28 Spectral Theorem (6.4) Joe's Notes
Demo: Eigenspaces of a 3x3 symmetric matrix
Demo: Eigenspaces of a 3x3 symmetric matrix (GM=2)
Demo: Dynamics of a 2x2 symmetric matrix
 Homework #12
Updated 4/3 (fixed typo in #16)
Due 4/6
11:59pm
LDLT; Quadratic Optimization (2.7, 6.5) Joe's Notes
Supplement: LDLT and Cholesky
Problem Session Worksheet and Solutions
Week 13: 4/4 Quadratic Optimization II (6.5) Joe's Notes Homework #13
Due 4/15
11:59pm
SVD: Outer Product Form (7.1, 7.2) Joe's Notes
MIDTERM 3 Practice Midterm and Solutions
Midterm and Solutions
Week 14: 4/11 SVD: Matrix Form (7.3) Joe's Notes Homework #14
Due 4/20
11:59pm
PCA I (7.3, 7.4) Joe's Notes
Problem Session Worksheet and Solutions
4/19 PCA II (7.3) Joe's Notes Homework #15
(Not collected)
 
Final exams:
218D-1 (001):Wednesday, 4/27, 9am–noon
218D-1 (002):Friday, 4/29, 7–10pm
 Practice Final and Solutions