Instructors
Section MFI:
Dr. Paul Jensen
pjens@illinois.edu
IGB 3137
217-265-7110
Office Hours: Email Appointment
Teaching Assistant: Dikshant Pradhan, dpradha2@illinois.edu; Office Hours: Monday (11am-12pm), DCL 3211
Section B:
Dr. Gregory Underhill
gunderhi@illinois.edu
3236 DCL
217-244-2169
Office Hours: Email Appointment
Teaching Assistant: Hyeon Ryoo, hryoo2@illinois.edu; Office Hours: Thursday (11:30am-12:30pm), 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 linear-system 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 9:30-10:50am in 106B1 Engineering Hall.
Section B: meets TR 9:30-10:50am 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 1-4.
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 in-class exams (2/13, 3/15, 5/1). Exams are open-book (open-notes) and during the normal lecture period.
Homeworks
Approximately 6-7 homework sets. Homeworks are due by the end of class on the assigned date. Homework assignments will typically include both analytical problems plus Matlab-based exercises. Written answers to the analytical problems are due in-class 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/lab-information/remote-connections.
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
- Least-squares approximations
- Case Study: Linear regression
- Regularized least-squares
- Case Study: The Lasso
- Linear programming
- Case Study: Flux Balance Analysis
- Quadratic programming
- Case Study: Support Vector Machines
- Mixed-integer programming
- Case Study: Gene Regulatory Networks
- Gaussian elimination
- Matrix analysis
- Basis vectors
- Eigenvectors and eigenvalues
- Case Study: Protein-protein 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 (1.1-1.5) |
Norms and Inner Products (1.6-1.8) |
|
|
1/22 |
Matrix Multiplication(Ch. 2.1 - 2.4) |
Gaussian Elimination(Ch. 2.4 - 2.6) |
Matlab files (HW1 m-file; HW1 mat-file) |
| 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 mat-file) |
|
3/12 |
Classification- |
Exam #2 (Thurs. 3/15) |
Files (HW4 mat-file; HW4 png-file) |
|
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 mat-file) |
| 4/23 |
Partial Least Squares Regression |
Vector Transformation & Practice Exam Review |
File (HW6 mat-file) |
|
4/30 |
Exam #3 (Tues. 5/1) |
No Class |
|
|
Finals Week |
|
|
* No Final- No Assignments Due During Finals Week |
