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
Tu  noon  –1pm  Gross Hall 104 
W  1:30  –3:30pm  Gross Hall 111 
Tu  5:30  –6:45pm  Math & Physics 113 
Th  1  –2:15pm  Zoom (see Sakai) 
Lecture  Instructor  Location  Time 

218D1 (001)  Joe Rabinoff  Math & Physics 130  TTh 10:15–11:30am 
218D1 (002)  Eylem Yildiz  Math & Physics 130  TTh 3:30–4:45pm 
Problem Session  Instructor  Location  Time 
218D1 (01D)  Bowen Li  Social Sciences 119  F 8:30–9:45am 
218D1 (02D)  Bowen Li  Perkins 071  F 10:15–11:30am 
218D1 (03D)  Edna Jones  LSRC A247  F noon–1:15pm 
218D1 (04D)  Edna Jones  Social Sciences 119  F 3:30–4:45pm 
Access Gradescope by clicking on the tab in Sakai.
For practicing row reduction when you're allergic to fractions.
A complement to Strang's book written by Joe.
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. 

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: 1/16  Solving Equations: Elimination (2.2)  Joe's Notes 
Homework #2 Due 1/25 11:59pm Solutions 

Gauss–Jordan Algorithm (2.2, 2.5) 
Joe's Notes Gauss–Jordan Slideshow Rabinoff's Reliable Row Reducer 

Problem Session  Quiz  
Week 3: 1/23  LU Decomposition (2.3, 2.6)  Joe's Notes 
Homework #3 Due 2/1 11:59pm Solutions 

Parametric Form 
Joe's Notes Demo: Parameterized Line Demo: Parameterized Plane 

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 R^{2} Demo: Linear combinations of two vectors in R^{3} Demo: Linear combinations of three vectors in R^{3} Demo: Span of 1 vector in R^{2} Demo: Span of 2 vectors in R^{2} Demo: Span of 1 vector in R^{3} Demo: Span of 2 vectors in R^{3} Demo: Span of 3 vectors in R^{3} 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 

Subspaces (3.1, 3.2) 
Joe's Notes Demo: Column and Null Space 

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 R^{2} 
Homework #5 Due 2/15 11:59pm Solutions 

Fundamental Subspaces (3.4, 3.5) 
Joe's Notes Demo: Ranknullity: n=3, r=0 Demo: Ranknullity: n=3, r=1 Demo: Ranknullity: n=3, r=2 Demo: Ranknullity: n=3, r=3 

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 R^{2} 
Homework #6 Due 2/22 11:59pm Solutions 

Orthogonal Projections (4.2) 
Joe's Notes Demo: Decomposition relative a line in R^{2} Demo: Decomposition relative a line in R^{3} Demo: Decomposition relative a plane in R^{3} Demo: Projection onto a plane Demo: Projection onto a line Demo: Projection onto a plane 

Friday, 2/17: MIDTERM 1 
Practice Midterm
and Solutions Midterm and Solutions 

Week 7: 2/20  Projection Matrices (4.2)  Joe's Notes 
Homework #7 Due 3/1 11:59pm Solutions 

Least Squares (4.3) 
Joe's Notes Demo: LeastSquares Demo: Bestfit line Demo: Bestfit parabola Demo: Bestfit trigonometric function Demo: Bestfit ellipse Demo: Bestfit ellipse: what is minimized? 

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 

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 

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 

Problem Session  Quiz  
SPRING BREAK  
Week 10: 3/20  Diagonalization: Vector Form (6.2)  Joe's Notes 
Homework #10 Due 3/29 11:59pm 

Diagonalization: Geometry (6.2) 
Joe's Notes Dynamics demos: 

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 

AM/GM and Diagonalizability (6.2) 
Joe's Notes Supplement: Proof of the AM≥GM theorem AM/GM demos: Dynamics with a Complex Eigenvalue 

Systems of ODEs (6.3)  Joe's Notes  
Friday, 3/31: MIDTERM 2 
Practice Midterm
and Solutions 

Week 12: 4/3  Spectral Theorem (6.4) 
Homework #12 Due 4/12 11:59pm 

LDL^{T}; Quadratic Optimization (2.7, 6.5)  
Problem Session  
Week 13: 4/10  Quadratic Optimization II (6.5) 
Homework #13 Due 4/19 11:59pm 

SVD: Outer Product Form (7.1, 7.2)  
Week 14: 4/17  SVD: Matrix Form (7.3) 
Homework #14 Due 4/26 11:59pm 

PCA I (7.3, 7.4)  
Problem Session  
4/25  PCA II (7.3) 
Homework #15 (Not collected) 

Final exams:
