MA 262, Fall 2025: 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: M/W/F 12:30pm–1:30pm, or by appointment.
Office: ET 314 (Purdue in Indianapolis)
Email: daniel84 , followed by "at" and purdue dot edu

Shabaz Khan: TA for the 11:30am lecture class (Section 990)
Website
Email: khan456, followed by "at" and purdue dot edu

Chrisil Ouseph: TA for the 2:30pm lecture class (Section 880)
Email: couseph, followed by "at" and purdue dot edu

Lecture and recitation sections and times


Lectures:
  M/W/F 11:30am–12:20pm, in room ET 202. (Section 990)
  M/W/F 2:30pm–3:20pm, in room ET 202. (Section 880)

Recitations for students in the 11:30am lecture:
  Thu 10:30am–11:20am, room ET 329. TA: Shabaz Khan (Section 992)
  Thu 11:30am–12:20pm, room ET 329. TA: Shabaz Khan (Section 991)

Recitations for students in the 2:30pm lecture:
  Thu 12:30pm–1:20pm, in room ET 308. TA: Chrisil Ouseph (Section 881)
  Thu 1:30pm–2:20pm, room ET 308. TA: Chrisil Ouseph (Section 882)

Course docs and other pages


Course-wide syllabus
Past Exam Archive for MA-262

Exam 1 review questions
  – Review solutions
Exam 1 Answer Keys

Exam 2


Date/Time: Tuesday, Nov. 11, 6:30pm-7:30pm
Location: LE 100
 Covers lessons [L15]–[L26]; 11 multiple choice questions (9 pts each) plus 1 free point.
Exam 2 review questions
   – Review solutions
 Review session 11/11: Video Notes

Piazza Forum

Some Graphing Tools


Desmos Basics
Slope Field Plotter

Notes and Extras


Ch. 1: Basics; 1st-order ODEs


[L1] Intro
[L2] General Solutions
  – Handling unknown constants
[L3] Slope Fields
[L4] Separable Eqs
  – Note on implicit solutions
  – Solutions vocab chart
[L5] 1st-order Linear ODEs
[L6] Mixture Problems
  – Mathematica notebook: here
[L7] Substitution
  – Extra notes on substitutions
[L8] Exact Eqs and Reduction

Ch. 2: Populations; Stability


[L9] Population Models
[L10] Stability and equilibrium
[L11] Euler's Method

Ch. 3: Systems of linear eqs; Matrices


[L12] Review of linear systems
[L13] Matrices and Elimination
[L14] Reduced Echelon Form
[L15] Matrix Operations
  – (Note: pay special attention to the last section, "vector equations").
  – What are row operations?
[L16] Inverses
  – Matrix Eqs
[L17-1] Determinants (pt 1)
[L17-2] Determinants (pt 2)

Ch. 4: Vectors, Vector Spaces, and Subspaces


Outline for Ch.4
Vocab summary for linear in/dependence

[L18] Span and Independence in R^2 and R^3
  – 3Blue1Brown: Span and Independence ; Matrices acting on R^2
[L19] Subspace examples for R^n
[L20-21] Linear independence and bases
  – Determinant and Independence
[L22] Row and Column Space

Ch. 5: 2nd-order linear ODEs


[L23] 2nd order linear ODEs
[L24] General sols to linear ODEs
[L25] Homog. eqs with const. coeffs. (part 1)
[L26] Homog. eqs with const. coeffs. (part 2)
  – Complex numbers basics
  – Repeated complex roots: Notes Video
[L27] Mechanical vibrations: Notes Video
[L28(1)] Undetermined coeffs (part 1): Notes Video
[L28(2)] Undetermined coeffs (part 2): Notes Video
[L29] Variation of parameters: (notes and video to be added)

Clarifying the Wronksian: Notes

Ch. 6+7: Eigenvectors and systems of ODEs


[L30] Eigenvectors: Notes 3Blue1Brown video

(Extra) Least Squares


IPython notebook

Course Calendar


Colors:
   - Lessons
   - HW & Quizzes
   - Exams

Notes:

Lessons are listed as
  [L〈#〉] Sec. 〈#〉, 〈Topics〉,
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., [L:1-14].