Instructors
Section MFI:
Dr. Paul Jensen
pjens@illinois.edu
IGB 3137
2172657110
Office Hours: Email Appointment
Teaching Assistant: Dikshant Pradhan, dpradha2@illinois.edu; Office Hours: Monday (11am12pm), DCL 3211
Section B:
Dr. Gregory Underhill
gunderhi@illinois.edu
3236 DCL
2172442169
Office Hours: Email Appointment
Teaching Assistant: Hyeon Ryoo, hryoo2@illinois.edu; Office Hours: Thursday (11:30am12:30pm), DCL 3211
Description
The language of systems analysis is linear algebra. Whether it is mechanical or electrical devices, cells metabolizing and communicating, or modeling other linearsystem behavior with Matlab, the use of matrices is a fundamental engineering skill. This course introduces matrix methods with applications in medical instruments and systems biology that are core to bioengineering.
Section MFI: meets TR 9:3010:50am in 106B1 Engineering Hall.
Section B: meets TR 9:3010:50am in 106B8 Engineering Hall.
Textbook
No required text book. Course notes posted here will serve as the text.
Course Notes:
Table of Contents
Introduction (updated 1/15)
Chapter 1: Fields and Vectors (updated 1/17)
Chapter 2: Matrices (updated 1/31)
Chapter 3: The Finite Difference Method (updated 1/22)
Chapter 4: Inverses, Solvability, and Rank (updated 2/5)
Exam 1 covers material in Chapters 14.
Chapter 7: Optimization, Convexity, and Hyperplanes (updated 2/26)
Chapter 8: Vector Spaces, Span, and Basis (updated 4/2)
Chapter 9: Eigenvalues and Eigenvectors (updated 4/12)
Grading
Exams
3 inclass exams (2/13, 3/15, 5/1). Exams are openbook (opennotes) and during the normal lecture period.
Homeworks
Approximately 67 homework sets. Homeworks are due by the end of class on the assigned date. Homework assignments will typically include both analytical problems plus Matlabbased exercises. Written answers to the analytical problems are due inclass and Matlab solutions (plus code) must be uploaded using Compass (additional details regarding homework submission will be provided).
Note: Students may discuss homework problems, but students must complete their own work and write up solutions independently.
MATLAB is required for the course and can be accessed in a variety of ways:
1. EWS machines.
2. EWS machines can be accessed remotely in a number of ways: https://it.engineering.illinois.edu/ews/labinformation/remoteconnections.
Grading
Homeworks 30%
Exam #1 23.3%
Exam #2 23.3%
Exam #3 23.3%
Letter grade determination:
>97% = A+; >93% = A; >89.5% = A; >87% B+; >83% = B; >79.5% = B; >77% = C+; >73% = C; >67% = C
* Student gradebook:
Grades will be posted in Compass.
 Fundaments of vector spaces
 Fields, Vector algebra, Norms
 Inner products, Matrix multiplication
 Solution of linear systems
 Gaussian elimination
 Case Study: Finite difference solution of PDEs
 Matrix Inverse, Solvability, Linear Dependence, and Rank
 Leastsquares approximations
 Case Study: Linear regression
 Regularized leastsquares
 Case Study: The Lasso
 Linear programming
 Case Study: Flux Balance Analysis
 Quadratic programming
 Case Study: Support Vector Machines
 Mixedinteger programming
 Case Study: Gene Regulatory Networks
 Gaussian elimination
 Matrix analysis
 Basis vectors
 Eigenvectors and eigenvalues
 Case Study: Proteinprotein interaction networks
 Matrix Pseudoinverse
 Singular value decomposition
 Case Study: Signal processing/imaging?
 Principal Components analysis
 Case Study: Microbiome clustering
 Partial Least Squared regression
 Case Study: Cytokine profiles
Week Of 
Tuesday 
Thursday 
Homework Due 
1/15 
Introduction, Fields & Vectors (1.11.5) 
Norms and Inner Products (1.61.8) 

1/22 
Matrix Multiplication(Ch. 2.1  2.4) 
Gaussian Elimination(Ch. 2.4  2.6) 
Matlab files (HW1 mfile; HW1 matfile) 
1/29 
The Finite Difference Method (Ch. 3) 
Matrix Inverse (Ch. 4) 

2/5 
Solvability and Rank (Ch. 4) Last day of material for Exam 1. 
Linear Models 

2/12 
Exam #1 (Tues. 2/13) 
Linear Regression 

2/19 
Applied Linear Regression Model Formulation 
Applied Linear Regression II Logistic Regression 

2/26 
Optimization and Convexity (Ch. 7) 
Linear Programming I Hyperplanes (Ch. 7) 

3/5 
Linear Programming II 
Linear Programming III Flux Balance Analysis 
Matlab file (HW3 matfile) 
3/12 
Classification 
Exam #2 (Thurs. 3/15) 
Files (HW4 matfile; HW4 pngfile) 
3/19 
Spring Break  Spring Break  
3/26 
Applied Support Vector Machines Cross Validation 
Basis Vectors 

4/2 
Orthogonality 
Eigenvalues and Eigenvectors 

4/9 
Eigenvalues II Determinant 
Matrix Decomposition Singular Value Decomposition 

4/16 
SVD II Principal Components Analysis 
Principal Component Regression 
File (HW5 matfile) 
4/23 
Partial Least Squares Regression 
Vector Transformation & Practice Exam Review 
File (HW6 matfile) 
4/30 
Exam #3 (Tues. 5/1) 
No Class 

Finals Week 


* No Final No Assignments Due During Finals Week 