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Instructor Key

DF = Prof. Dan Frey
GS = Prof. Gilbert Strang

Session Key

L = Lecture
R = Recitation
E = Quiz or Exam

SES # TOPICS INSTRUCTORS KEY DATES
L1 Course introduction: What are differential equations and linear algebra? How do engineers use them? Four examples of first order differential equations. DF Problem Set 1
Assigned
L2 First-order equations: Constant source, step function (Heaviside), delta (Dirac), exponentials, real and complex sinusoids. GS  
R1 Recitation    
L3 First-order equations (continued): Separable equations, exact equations. GS

Problem Set 1 Due

Problem Set 2 Assigned

L4 Second-order equations: Second derivatives in engineering, complex numbers, constant coefficient equations. GS  
E1 Quiz 1
L5 Second-order equations (continued): Forced oscillations, examples in electrical and mechanical systems, Laplace transforms. GS Problem Set 3 Assigned
L6 Laplace transforms (continued): Graphical Methods: Direction fields, nonlinear equations, sources, sinks, saddles, and spirals. DF Problem Set 2 Due
R2 Recitation    
L7 Graphical and numerical methods: Linearization, stability, Euler’s method. DF  
L8 Linear systems of equations: Gaussian elimination, matrix multiplication. DF  
R3 Recitation    
L9 Linear systems of equations: Matrix inverse. Existence and uniqueness of solutions. Column, row, null space. DF

Problem Set 3 Due

Problem Set 4 Assigned

L10 Linear systems of equations (continued): Mechanical engineering examples. DF  
R4 Recitation    
E2 Quiz 2: Oral exams scheduled throughout the week.
L11 Eigenvalues and eigenvectors: The eigenvalue problem. Diagonalization, exponentiation of a matrix. DF

Problem Set 4 Due

Problem Set 5 Assigned

L12 Least squares and projection: Positive definite matrices. Singular value decomposition. DF Problem Set 5 Due
L13 Review session for the final exam. DF  
R5 Review session for the final exam (continued).    
E3 Final Exam

These are additional MATLAB® scripts that were used in the course.

MATLAB® Scripts

Direction Field Plotter (M)

A fish example

Truss Analysis (M)

A script that will make a matrix representation from a simpler representation of connectivity and angles

Shear Building (M)

An example of eigenvalues and eigenvectors

Circuit (M)

An example of eigenvalues and eigenvectors

Lateral Dynamics 747 (M)

An example of eigenvalues and eigenvectors

Note to OCW Users: MIT OpenCourseWare does not provide student access or discounts for MATLAB software. It can be purchased from The MathWorks®. For more information about MATLAB Pricing and Licensing, contact The MathWorks directly.

Professor Strang’s foundational course 18.06 Linear Algebra has long been one of the most popular courses on OCW. It has received more than 10 million visits since its first publication in 2002. Professor Strang also has a website dedicated to his linear algebra teaching.

A new version of Professor Strang’s classic Linear Algebra was released in 2011 in the innovative OCW Scholar format designed for independent learners. 18.06SC Linear Algebra includes 35 lecture videos and 36 short (and highly-praised) problem-solving help videos by teaching assistants.

Professor Strang has continued to offer new insights into key mathematics subjects. In 2014, he published the new textbook Differential Equations and Linear Algebra. In 2016, that textbook was developed into a series of 55 short videos supported by MathWorks, with parallel videos about numerical solutions by Dr. Cleve Moler, the creator of MATLAB®. The textbook and video lectures help students in a basic ordinary differential equations course. This new series, Learn Differential Equations: Up Close with Gilbert Strang and Cleve Moler, is also available on the MathWorks website.

In 2017, Professor Strang launched a new undergraduate course at MIT: 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning. Published on the OCW site in 2019, the course uses linear algebra concepts for understanding and creating machine learning algorithms, especially as applied to deep learning and neural networks. This course reviews linear algebra with applications to probability and statistics and optimization and, above all, a full explanation of deep learning. 

Professor Raj Rao was the inspiration for the course 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, and co-taught it with Professor Strang in the first year it was offered at MIT. Since then, he has developed a very successful course on computational linear algebra and machine learning at the University of Michigan. The website, Mynerva, describes this course, the online textbook, and future plans. Professor Rao’s textbook is complementary to Professor Strang’s new book, Linear Algebra for Everyone.

Strang, Gilbert. Introduction to Linear Algebra. 5th ed. 2016. Wellesley-Cambridge Press. ISBN: 9780980232776.

Strang, Gilbert. Linear Algebra and Learning from Data. 2019. Wellesley-Cambridge Press. ISBN: 9780692196380.

Strang, Gilbert. Linear Algebra for Everyone. 2020. Wellesley-Cambridge Press. ISBN: 9781733146630.

Strang, Gilbert. Differential Equations and Linear Algebra. 2014. Wellesley-Cambridge Press.ISBN: 9780980232790.

ZoomNotes for Linear Algebra (PDF). Professor Strang created these notes in 2020 and 2021 when many MIT classes were moved online (using Zoom) due to the COVID-19 Pandemic. He hopes that faculty who are planning a linear algebra course and students who are reading for themselves will see these notes.

Guest speaker at the weekly OLSUME (Online Seminar on Undergraduate Mathematics Education) on the topic Linear Algebra and Deep Learning (MP4)

“Linear Algebra, Teaching, and MIT OpenCourseWare” (YouTube) on Lex Fridman Podcast

Course Meeting Times

Lectures: 2 sessions / week, 1.5 hours / session

Recitations: 1 session / week, 1.5 hours / session

Course Description

This course is about the mathematics that is most widely used in the mechanical engineering core subjects: An introduction to linear algebra and ordinary differential equations (ODEs), including general numerical approaches to solving systems of equations. Topics covered include linear systems of equations, existence and uniqueness of solutions, Gaussian elimination. Initial value problems, 1st and 2nd order systems, forward and backward Euler, and the Runge-Kutta method (RK4). The course also covers eigenproblems: eigenvalues and eigenvectors, including complex numbers, functions, vectors and matrices. MATLAB® is used in this course.

Note to OCW Users: MIT OpenCourseWare does not provide student access or discounts for MATLAB software. It can be purchased from The MathWorks®. For more information about MATLAB Pricing and Licensing, contact The MathWorks directly.

Textbook

Strang, Gilbert. Differential Equations and Linear Algebra. Wellesley-Cambridge. 2014.

See the website for Prof. Strang’s textbook for more information, including samples of the text. In 2016, the textbook was developed into a series of 55 short videos, Learn Differential Equations: Up Close with Gilbert Strang and Cleve Moler.

Grading

Students can calculate their grade with this MATLAB script. (M)

ACTIVITIES PERCENTAGES
Homework (5 assignments, 6% each) 30%
Quizzes (2 quizzes, 20% each) 40%
Final Exam 30%

Late Policy

It is expected that completed assignments will be submitted on the due date and time noted on the assignment. The usual policy for late assignments is that a letter grade is lost per day late. If no arrangement is made ahead of time, that is going to be adhered to strictly. The teaching staff is well aware of the multiple time demands on students. In the case of unusual circumstances or unavoidable conflicts, students discussed the details with the professor and explored alternatives before the due date.

Course Info

As Taught In
Fall 2014
Learning Resource Types
Exams
Lecture Videos
Problem Sets
Programming Assignments with Examples