MA 262, Spring 2026: Differential Equations and Linear Algebra
This is a page to keep copies of some course documents and share some useful links.
Contacts and Office Hours
Dr. Taylor Daniels: Course instructor
Office Hours: 2:00pm–3:00pm, or by appointment.
Office: ET 314 (Purdue in Indianapolis)
Email: daniel84 followed by "at" and purdue dot edu
Chrisil Ouseph: TA for the 10:30am lecture class (Section 610)
Email: couseph followed by "at" and purdue dot edu
Shabaz Khan: TA for the 11:30am lecture class (Section 611)
Email: khan456 followed by "at" and purdue dot edu
Website: here
Lecture and recitation sections and times
Lectures:
M/W/F 10:30am–11:20am, room LE 105. (Section 610)
M/W/F 11:30am–12:20pm, room LE 105. (Section 611)
Recitations for students in the 10:30am lecture:
Thu 10:30am–11:20am, room SL 108. TA: Chrisil Ouseph (Section 612)
Thu 11:30am–12:20pm, room SL 108. TA: Chrisil Ouseph (Section 615)
Recitations for students in the 11:30am lecture:
Thu 1:30pm–2:20pm, room SL 108. TA: Shahbaz Khan (Section 614)
Thu 2:30pm–3:20pm, room SL 108. TA: Shahbaz Khan (Section 613)
Course docs and other info and pages
Syllabus
University course page
Past Exam Archive for MA-262
Exam 1
Date/Time: Thursday, Feb. 19, 8:00pm–9:00pm
Location: LE 100
Covers lessons [L1]–[L14]; 11 multiple choice questions (9 pts each) plus 1 free point.
Exam 1 review questions
– Review solutions
Exam 2
Date/Time: Tuesday, Apr. 14, 8:00pm–9:00pm
Location: LE 100
Covers lessons [L15]–[L28]; 11 multiple choice questions (9 pts each) plus 1 free point.
Final Exam
Date/Time: Tuesday, May 5, 10:30am–12:30pm
Location(s): ET 202 and ET 310. NOTE: I will inform you/the class about which specific rooms you will have.
Covers all lessons*, [L1]–[L36]; 20 multiple choice questions worth 10pts each.
*The exam questions will be evenly balanced between all topics; there is no "bias" toward newer material.
– Some review problems
Notes
Chapter Summaries
[Ch 1,2,3 (1st part)] Exam 1 Notes
[Ch 3 (2nd part)] Matrices
[Ch 4] Vector Spaces
[Ch 5] Linear ODEs
[Ch 6,7] Eigenvalues, systems of 1st order ODEs
Ch. 1: Basics; 1st-order ODEs
[L1] Intro to diff eq: Notes (class), Notes (html)
[L2-3 (1)] Slope fields and solutions: Notes (class), Notes (html)
[L2-3 (2)] More on solutions: Notes (class), Notes (html)
– (Extra) Handling unknown constants: Notes
[L4] Separable eqs: Notes (class), Notes (html)
– Solutions vocab chart: Notes
[L5] 1st-order linear eqs (part 1): Notes (class), Notes (html)
[L6] 1st-order linear eqs (part 2): Notes (class), Notes (html)
[L7] Substitution Methods: Notes (class), Notes (html)
[L8] Exact eqs, Reducible eqs: Notes (class), Notes (html)
Ch. 2: Populations; Stability
[L9] Population models: Notes (class), Notes (html),
Extra: Working out two full examples (from HW 9): Video [the pages are in the notes]
[L10] Stability and equilibrium: Notes (class), Notes (html)
[L11] Euler's method: Notes (class), Notes (html)
– Geogebra app: link
Ch. 3: Systems of linear eqs; Matrices
[L12] Review of linear systems: Notes
[L13] Matrices and elimination: Notes
[L14] Reduced echelon form: Notes
[L15] Matrix Operations: Notes
– What are row operations? Notes
[L16] Inverses: Notes
– How to compute inverses: Notes
– Solving systems using inverses: Notes
– Matrix equations: Notes
[L17(1)] Determinants: Notes
– Solving systems with Cramer's Rule: Notes
[L17(2)] Determinants (cont.): Notes
[★] Vocab & concept summary/list: Notes
Ch. 4: Vector Spaces and Subspaces
[L18] Intro to vector spaces: Notes
– 3Blue1Brown: Span and Independence
Independence and subspace definitions: Notes
More on subspaces (video+notes): Notes, Video
Bases and null space: Notes
Dimension: Notes
Row/Column space and rank: Notes
[★] Vocab & concept summary/list: Notes
Ch. 5: 2nd-order linear ODEs
[L23] 2nd order linear ODEs: Notes
[L24] Higher order linear ODEs: Notes, Video
[L25] Homog. eqs with const coeffs (part 1): Notes
[L26] Homog. eqs (part 2) (Complex numbers): Notes
– Repeated complex roots: Video; Notes
– (Extra) Complex numbers basics:Notes
[L27] Mechanical vibrations: Notes, Video
– Python app graphing some damped spring systems: damped_motion.py
[L28(1)] Nonhomogeneous eqs (part 1 -- Undetermined Coeffs): Notes
[L28(2)] Nonhomogeneous eqs (part 2): Notes
[L28(3)] Nonhomogeneous eqs (part 3 -- Removing Duplication): Notes
[★L29] Variation of parameters: Notes, Video
[★] Read/watch this and do Hw 29 by end of semester.
[★] Summary of Linear ODEs: Notes
Clarifying the Wronksian: Notes
Ch. 6+7: Eigenvectors and systems of ODEs
[L30] Eigenvectors: Notes 3Blue1Brown video
[★] Vector ODEs and their solution curves: Notes, Video
[The notes contain two extra pages than what appears in the video]
[L31-32] Systems of 1st-order eqs: Notes, Video
[L33] The "eigenvalue method" for vector diff. eqs.: Notes, Video
[L34(1)] Chain eigenvectors examples: Notes
[L34(2)] Repeated eigenvalues: Notes
[★ Read for HW34] Defect d=2 notes and example: Notes
[L35-36] Phase plane portraits: Notes
– "Phase plane" plotter: GeogebraLink [I take no credit for this]
[★] Summary of systems of 1st-order linear ODEs: Notes
Course Calendar
Colors:
■ - Lessons
■ - HW & Quizzes
■ - Exams
Notes:
Lessons are listed as
[L〈#〉] 〈book section #〉 〈topic(s)〉,
and HW #'s indicate the material's corresponding lesson number. Some lessons have parts (1) and (2), but there is still only one homework associated to the lesson. Some book sections/topics are spread over more than one lesson.
Quiz topics are shown using
[Q 〈#〉],
where 〈#〉 lists the lesson/homework numbers covered by the quiz.
Exams list the lessons covered, e.g., [L1-14].