Math 213A
Introduction to Linear Algebra and
Ordinary Differential Equations

Ethan Bloch's home page

PDF summary version of this page

Updated list of homework assignments

Complex numbers handout
(from the Stewart calculus text)

Study Sheet for Midterm Exam

Study Sheet for Final Exam



Basic Information


  • Mon. 1:30-2:50
  • Wed. 1:30-2:50
  • Hegeman 102


  • Ethan Bloch
  • bloch "at" bard "dot" edu
  • Albee 317
  • 845-758-7266

Office Hours

  • Mon. 12:00-1:00
  • Tue. 1:30-2:50
  • Wed. 11:00-12:30


  • Edwards, C. H. & Penney, D. E., “Differential Equations and Linear Algebra,” 3rd ed., Prentice Hall


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Work for the Course


  • It is expected that students attend all classes. Bring the text to each class.


  • Homework will be assigned at the end of every class. Do the homework before the next class.
  • Every Monday, hand in the homework assignments from both classes of the previous week. Late assignments will not be accepted, except in emergency situations.
  • You are encouraged to work with other students in solving the homework problems. However, for the sake of better learning, as well as honesty, please adhere to the following guidelines:

    • Write up your solutions yourself.
    • Acknowledge in writing anyone with whom you work.
    • Acknowledge in writing any revisions of your work based upon solutions given in class.
  • Your solutions should be written clearly, with enough detail that another student in the class would be able to follow your reasoning.

Quizzes and Exams

  • All quizzes and exams will be in class, closed book.
    • Quiz #1: Mon., Feb. 13
    • Quiz #2: Wed., Feb. 29
    • Midterm Exam: Wed., Mar. 21
    • Quiz #3: Mon., Apr. 16
    • Quiz #4: Wed., May 2
    • Final Exam: Mon., May 21

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What is Math 213

  • This course is an introduction to two fields of mathematics, linear algebra and ordinary differential equations, that are of fundamental importance throughout mathematics and its applications, and that are related by the use of linear algebra in the study of systems of linear differential equations. Topics in linear algebra include n-dimensional Euclidean space, vectors, matrices, systems of linear equations, determinants, eigenvalues and eigenvectors; topics in ordinary differential equations include separable differential equations, higher order linear differential equations, systems of linear differential equations and applications.
  • The prerequisite is Calculus II (Math 142) or the equivalent.
  • If you are unsure whether Math 213 is an appropriate course for you, please talk to the instructor.
  • This course comes before Calculus III (Math 212).

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Office Hours

  • If you have any problems with the course, or any questions about the material, the assignments, the tests or anything else, please see the instructor about it. If you cannot make any of the scheduled office hours, do not hesitate make an appointment for some other time. To make an appointment, or to ask any questions, please talk to the instructor after class, or by phone or email, or just stop by his office.

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Computers and Calculators

  • For most of the course, pencil and paper will suffice. A scientific calculator (which has trigonometric, exponential and logarithmic functions) will be needed for some problems. Programmable and/or graphing calculators are not required.
  • Laptop computers may not be used during class.

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Mathematics Study Room

  • The Mathematics Study Room is open Sunday-Thursday, 7:00pm-10:00pm, in RKC 111.
  • The Mathematics Study Room is staffed by undergraduate mathematics majors who are available to answer your questions. You can go to the study room to work on your homework, and then ask for help when you get stuck.


  • If you need additional help beyond office hours and the Mathematics Study Room, you can request to meet with a tutor. To request a tutor, please contact Maria Belk at Bard Learning Commons.

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  • Grades are determined primarily by the quizzes and exams; assignments and class participation are taken into account, especially in cases of borderline grades. Grades are determined by work completed during the semester, except in cases of medical or personal emergency.

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  • Sage    A free open-source mathematics software system

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Online Linear Algebra Tools

  • Linear Algebra Toolkit    A website that has a number of useful toods for linear algebra, including elementary row operations on matrices
  • Online Matrix Calculator    A website that does a variety of matrix computations, including matrix multiplication, determinants, inverse matrices and eigenvalues and eigenvectors

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  • Flatland (Complete text)    Flatland (MP3 audio recording)    A minor classic, with heavy emphasis on both words. Flatland recounts the adventures of A SQUARE, who lives in a 2-dimensional world. The first part of the book, a satire of the Victorian society in which the author lived, describes the racist and sexist social order of the flat world of our hero. The second part of the book describes A SQUARE'S encounter with lower and higher dimensional beings, thus introducing the reader to some important ideas about the fourth dimension and higher. Neither great writing nor brilliant mathematics, Flatland straddles the fence so well that its place in the canon is assured. (Be careful with the introductions to various print editions of Flatland -- the one by Banesh Hoffmann in the Dover edition, and the one by Isaac Asimov in the HarperCollins edition, both entirely miss the point of the book.)

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