Section MFI:

Dr. Paul Jensen
IGB 3137
Office Hours: Email Appointment

Teaching Assistant: Dikshant Pradhan,; Office Hours: Monday (11am-12pm), DCL 3211

Section B:

Dr. Gregory Underhill
3236 DCL
Office Hours: Email Appointment

Teaching Assistant: Hyeon Ryoo,; Office Hours: Thursday (11:30am-12:30pm), DCL 3211


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.


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 6: Applied Linear Regression in Matlab (updated 2/22)
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)




3 in-class exams (2/13, 3/15, 5/1).  Exams are open-book (open-notes) and during the normal lecture period.


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:


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.

Week Of



Homework Due


Introduction, Fields & Vectors (1.1-1.5)

Norms and Inner Products (1.6-1.8)

Lecture 2- Example Problems



Matrix Multiplication(Ch. 2.1 - 2.4)

Lecture 3- Example Problems 

Gaussian Elimination(Ch. 2.4 - 2.6)

Lecture 4- Supplemental Slides

Lecture 4- Example Problems

Homework #1 Due Thursday 1/25

Matlab files (HW1 m-file; HW1 mat-file)

Homework #1 Solution


The Finite Difference Method (Ch. 3)

Lecture 5- Supplemental Slide

Lecture 5- Example Problems

Matrix Inverse (Ch. 4)

Lecture 6- Example Problems



Solvability and Rank (Ch. 4)

Lecture 7- Example Problems

Last day of material for Exam 1.

Linear Models

Lecture 8- Supplemental Slide

Homework #2 Due Thursday 2/8

Homework #2 Solutions


Exam #1

(Tues. 2/13)

Practice Exam #1

Practice Exam #1 Solutions

Linear Regression



Applied Linear Regression- Model Formulation

Lecture 10- Lecture Slides

Lecture 10- Additional Example Problem

Applied Linear Regression II- Logistic Regression

Lecture 11- Supplemental Slides

Lecture 11- Additional Lecture Notes



Optimization and Convexity (Ch. 7)

Linear Programming I- Hyperplanes (Ch. 7)

Lecture 13- Example Problems



Linear Programming II-
Simplex Method

Lecture 14- Supplemental Slides

Lecture 14- Example Problem

Linear Programming III- Flux Balance Analysis

Lecture 15- Supplemental Slides

Lecture 15- Example (Matlab) Problem

Homework #3 Due Tuesday 3/6

Matlab file (HW3 mat-file)

Homework #3 Solutions


Support Vector Machines

SVM Notes

Exam #2

(Thurs. 3/15)

Practice Exam #2

Practive Exam #2 Solutions

Homework #4 Due Tuesday 3/13

Files (HW4 mat-file; HW4 png-file)

Homework #4 Part I Solutions (update 3/14)

Homework #4 Part II Solutions


Spring Break Spring Break  


Applied Support Vector Machines- Cross Validation

Lecture 17- Lecture Slides

Basis Vectors

Lecture 18- Example Problems



Lecture 19- Example Problem

Eigenvalues and Eigenvectors

Lecture 20- Example Problems



Eigenvalues II- Determinant

Lecture 21- Example (Network Centrality)

Matrix Decomposition- Singular Value Decomposition


SVD II- Principal Components Analysis

Lecture 23- Example (PCA in Matlab)

Principal Component Regression

Lecture 24- Example (PCR)

Homework #5 Due Thursday 4/19

File (HW5 mat-file)

Homework #5 Solutions


Partial Least Squares Regression

Lecture 25- Supplemental Slides

Vector Transformation & Practice Exam Review

Homework #6 Due Thursday 4/26

File (HW6 mat-file)

Homework #6 Solutions


Exam #3

(Tues. 5/1)

Practice Exam #3

Practice Exam #3 Solutions

No Class


Finals Week



* No Final- No Assignments Due During Finals Week