Math 240 schedule

Tuesday Thursday
August 29

In Lecture:
  1. Overview of the course and of the text, "Differential equations and Linear Algebra" = DELA.
  2. Adding and multiplying matrices (DELA Section 2.1)
  3. Transpose and trace of a matrix (DELA Section 2.2)
  4. Triangular, symmetric and skew symmetric matrices (DELA section 2.2)
  5. Systems of linear equations (DELA section 2.3)
  6. The geometry of linear systems (DELA section 2.3)

Associated Reading:
  • DELA Sections 2.1 - 2.2

Core homework problem list
Important Note: There are no Monday recitations this week and next
due to the start of classes being on Tuesday and because of Labor Day.
So this week only, students in Monday recitations should try to go to
one of the Wednesday recitations listed below.
The DRL classrooms are larger than those in Williams Hall, so these may be less crowded.
  1. Wed. 8-9 a.m., DRL 2C6
  2. Wed. 9 - 10 a.m., DRL 2C6
  3. Wed. 8-9 a.m., Williams Hall 304 (a smaller classroom)
  4. Wed. 9 - 10 a.m., Williams Hall 304 (a smaller classroom)

There will be no quiz in recitation this week.
The first quiz in Wednesday recitations will be on September 6.
The first quiz in in Monday recitations will be on September 11.


Video of class (downloadable)

August 31

In Lecture:
  1. Row reduction of matrices, echelon and reduced echelon forms (DELA section 2.4)
  2. Solving systems of linear equations. (DELA section 2.5)

Associated Reading:
  • DELA Sections 2.3 - 2.5

Core homework problem list
Video of class (downloadable)
Sept. 5

In Lecture:
  1. Ranks of matrices (DELA section 2.4)
  2. Pivot variables and free variables, existense and uniqueness of solutions to systems of linear equations (DELA section 2.5)
  3. Writing systems of linear differential equations in matrix form (DELA section 2.2)
  4. Inverses of matrices (DELA section 2.6)

Associated Reading:
  • DELA Sections 2.6, 3.1 - 3.5


Quizzes

  • The first quiz in Wednesday recitations will be on September 6.
  • The first quiz in in Monday recitations will be on September 11.


Homework:


Video of class (downloadable)
September 7

In Lecture:
  1. Determinants and their properties (DELA sections 3.1 - 3.5)

Associated Reading:
  • DELA Sections 3.1 - 4.2

Quizzes
  • The second quiz in Wednesday recitations will be on September 13.
  • The first quiz in in Monday recitations will be on September 11.
  • The quizzes next week will be on the Core Problems associated to the material listed on the schedule up to and including section 3.5.


Homework:


Video of class (downloadable) - to be posted
Sept. 12

In Lecture:
  1. The formula for determinants as a sum over permutations
  2. Definition of a vector space, examples (DELA section 4.1 - 4.2)

Associated Reading:
  • DELA Sections 4.1 - 4.5


Quizzes

  • The quizzes this week will be on the Core Problems associated to the material listed on the schedule up to and including section 3.5.


Homework:


Video of class (downloadable)
September 14

In Lecture:
  1. Subspaces (DELA section 4.3)
  2. Error Correction
  3. Spanning sets (DELA section 4.4)

Associated Reading:
Quizzes
  • The quiz for the week of Sept. 18 - 22 will be about Core Problems from sections 4.1, 4.2, 4.3 and 4.4.


Homework:


Video of class (downloadable)
Sept. 19

In Lecture:
  1. Linear dependence and independence continued (DELA section 4.5 )
  2. Bases and dimension (DELA Section 4.6)

Associated Reading:
  • DELA Sections 4.1 - 4.9


Quizzes

  • The quizzes this week will be on the Core Problems associated to sections 4.1, 4.2, 4.3 and 4.4.


Homework:


Video of class (downloadable)
September 21

In Lecture:
  1. Change of basis (DELA Section 4.7)
  2. The row space and column space of a matrix (DELA section 4.8)
  3. Rank Nullity theorem (DELA section 4.9)

Associated Reading:
  • DELA Sections 4.1 - 4.9

Quizzes and next week's midterm.
  • The quiz next week will on core problems from sections 4.5, 4.6, 4.7, 4.8 and 4.9 of the text.
  • The mid-term next Thursday will cover the material on the sections listed on this course schedule from chapters 2, 3 and 4 of the text. It will also deal with the same linear algebra topics when one works with linear equations, matrices and vector spaces over Z/2.
  • You can bring with you to the exam one two-sided handwritten page of notes. No calculators, phones or other references can be used during the exam. Now is a good time to begin preparing your two pages of notes.


Homework:

  • Core homework problem list (For use in preparing for quizzes; this is not graded).There is a mix-up involving sections 4.8 and 4.9 on the core problems list. These sections and their core problems should be listed in the following way:
    1. Section 4.8 Row space and Column Space. Do True and False questions b and c and then Problems 8, 9 and 14.
    2. Section 4.9 Rank Nullity Theorem. Do True and False questions b, c, f, g and h and then Problems 3,4,7, 15, 16 and 17.
  • Graded Homework assignment 1 (due in recitation the week of Sept. 18-22. )

Video of class (downloadable)
Sept. 26

In Lecture:
  1. Linear maps between vector spaces (DELA section 6.1)
  2. Matrices of linear maps (DELA section 6.5)
  3. Change of basis matrices, continued (DELA section 4.7)

Associated Reading:
  • DELA Sections 6.1 - 6.5 and Sections 7.1 - 7.3.


Quizzes and this week's midterm.

  • The quiz this week will on core problems from sections 4.5, 4.6, 4.7, 4.8 and 4.9 of the text.
  • This week's mid-term will cover the material on the sections listed on this course schedule from chapters 2, 3 and 4 of the text. It will also deal with the same linear algebra topics when one works with linear equations, matrices and vector spaces over Z/2.
  • You can bring with you to the exam one two-sided handwritten page of notes. No calculators, phones or other references can be used during the exam.


Homework:


Video of class (downloadable)
September 28

In Lecture: Mid-Term 1
  • The mid-term will cover the material on the sections listed on this course schedule from chapters 2, 3 and 4 of the text. It will also deal with the same linear algebra topics when one works with linear equations, matrices and vector spaces over Z/2.
  • You can bring with you to the exam one two-sided handwritten page of notes. No calculators, phones or other references can be used during the exam.
  • The topics for the quizzes next week will be listed here after class on September 26.


Homework:

  • Core homework problem list (For use in preparing for quizzes; this is not graded).There is a mix-up involving sections 4.8 and 4.9 on the core problems list. These sections and their core problems should be listed in the following way:
    1. Section 4.8 Row space and Column Space. Do True and False questions b and c and then Problems 8, 9 and 14.
    2. Section 4.9 Rank Nullity Theorem. Do True and False questions b, c, f, g and h and then Problems 3,4,7, 15, 16 and 17.
  • Graded Homework assignment 2 (due in recitation the week of Oct. 16 -20. )
Oct. 3

In Lecture:
  1. Motivation: Quantum computers
  2. Matrices of linear maps (DELA section 6.5)
  3. Jordan block matrices (DELA section 7.6)
  4. Jordan canonical forms (DELA section 7.6)

Associated Reading:
  • DELA Sections 6.1 - 6.5 and Sections 7.1 - 7.6.


There will be no quiz this week.


Homework:


Video of class (downloadable)
October 5

No class: Fall Break!
Oct. 10

In Lecture:
  1. Eigenvalues and eigenvectors (DELA sections 7.1 and 7.2)
  2. Diagonalization (DELA section 7.3)

Associated Reading:
  • DELA Sections 6.1 - 6.5 and Sections 7.1 - 7.6.


The quiz this week will be on matrices of linear maps and change of basis matrices.


Homework:


Video of class (downloadable)
Oct. 12

In Lecture:
  1. Bases of eigenvectors, with applications (DELA section 7.2)
  2. Diagonalization (DELA section 7.3)
  3. Jordan canonical forms (DELA section 7.6)

Associated Reading:
  • DELA Sections 7.1 - 7.6, 8.1 - 8.3


The quiz next week will be on eigenvalues, eigenvectors and diagonizable matrices.


Homework:


Video of class (downloadable)
Oct. 17

In Lecture:
  1. Jordan canonical forms (DELA section 7.6)

Associated Reading:


The quiz this week will be on eigenvalues, eigenvectors and diagonizable matrices


Homework:


Video of class (downloadable)
Oct. 19

In Lecture:
  1. Perron Frobenius Theorem and the Google page rank algorithm
  2. Linear differential equations (DELA section 8.1)
  3. Constant coefficient homogenous linear systems of differential equations (DELA section 8.2)

Associated Reading:
  • DELA 8.1 - 8.4


The quiz next week will be Jordan canonical forms and their applications


Homework:


Video of class (downloadable)
Oct. 24

In Lecture:
  • Bases of solutions of linear constant coefficient O.D.E.'s (DELA sections 8.1 and 8.2)
    Associated Reading:
    • DELA 8.1 - 8.4


    The quiz this week will be Jordan canonical forms and their applications


    Homework:


    Video of class (downloadable) - this is a recap from class on October 31 of what was discussed on October 24
  • Oct. 26

    In Lecture: Second mid-term exam.
    1. The mid-term will cover the material on the sections listed on this course schedule from chapters 6 and 7 of the text. Note that we have not talked about matrix exponentials, so there will be no questions about this.
    2. You can bring with you to the exam one two-sided handwritten page of notes. No calculators, phones or other references can be used during the exam.

    Associated Reading:


    There will be no quiz next week in recitations


    Homework:

    Oct. 31

    In Lecture:
  • Oscilatory motion (DELA section 8.5)
  • Undetermined coefficients, annihilators (DELA section 8.3)
    Associated Reading:
    • DELA 8.1 - 8.4


    There will be no quiz this week in recitation


    Homework:


    Video of class (downloadable)
  • Nov. 2

    In Lecture:
    1. Complex valued trial solutions (DELA section 8.4)
    2. Forced oscillation (DELA section 8.5)
    3. Reduction of order (DELA section 8.9)

    Associated Reading:
    • DELA 8.2 - 8.5, 8.9


    The quiz next week will be on finding solutions of constant coefficient linear ordinary differential equations.


    Homework:


    Video of class (downloadable)
    Nov. 7

    In Lecture:
    1. Variation of Parameters (DELA section 8.7)

    Associated Reading:
    • DELA 8.7


    The quiz this week will be on finding solutions of constant coefficient linear ordinary differential equations.


    Homework:


    Video of class (downloadable)
    Nov. 9

    In Lecture:
    1. Reduction of order (DELA section 8.9)
    2. Systems of linear differential equations (DELA sections 9.1 and 9.2)

    Associated Reading:
    • DELA 8.7, 8.9, 9.1, 9.2


    The quiz next week will be the variation of parameters method


    Homework:


    Video of class (downloadable) Note: There were some typos in the computation on the board around 22 minutes in. These were corrected starting at the 40 minute mark.
    Nov. 14

    In Lecture:
    1. Solving linear systems of differential equations (DELA sections 9.2, 9.3, 9.4, 9.5, 9.8)

    Associated Reading:
    • DELA 9.2, 9.3, 9.4, 9.5, 9.8


    The quiz this week will be on the variation of parameters method


    Homework:


    Video of class (downloadable)
    Nov. 16

    In Lecture:
    1. Solving linear systems of differential equations (DELA sections 9.2, 9.3, 9.4, 9.5, 9.8). Note: My approach will be to emphasize how to use the matrix exponential in section 9.8 as a computational tool. The text tries to avoid this but ends up discussing many ad hoc and somewhat confusing special cases. The theory makes more sense with the matrix exponential, and this is really quite effective in calculating explicit solutions.

    Associated Reading:
    • DELA 9.2, 9.3, 9.4, 9.5, 9.8


    Recitations will meet next week to discuss solving linear systems of differential equations, but there will be no quiz in recitation next week. Happy Thanksgiving!


    Homework:


    Video of class (downloadable)
    Nov. 21

    No lecture today. Instead, please have a look at this Video about Zombie Epidemic models from Math 210 in the spring of 2017. Please ignore the reference to office hours at the beginning of the video - there will not be office hours this week. Math 210 will run again in the spring of 2018.

    Associated Reading:


    Recitations will meet this week to discuss solving linear systems of differential equations, but there will be no quiz this week. Happy Thanksgiving!


    New week (Nov. 27 - Dec. 1) there will be a quiz in recitation on solving systems of differential equations. I suggest reviewing the lecture on Nov, 16 and doing homework problems from sections 9.2, 9.3 9.4, 9.5 and 9.8 of the text in order to prepare for the quiz. The quiz will be on a problem similar those listed on the course syllabus for section 9.4.


    Homework:

    Nov. 23

    No class - Thankgiving
    Nov. 28

    In Lecture:
    1. Review of Solving linear systems of differential equations (DELA sections 9.2, 9.3, 9.4, 9.5, 9.8).

    Associated Reading:
    • DELA 9.2, 9.3, 9.4, 9.5, 9.8, 9.9

    The quiz in recitation this week will be on solving systems of differential equations. I suggest reviewing the lecture on Nov, 16 and doing homework problems from sections 9.2, 9.3 9.4, 9.5 and 9.8 of the text in order to prepare for the quiz. The quiz will be on a problem similar those listed on the course syllabus for section 9.4.


    Homework:

    Nov. 30

    In Lecture:
    1. Phase Plane for linear autonomous systems (DELA section 9.9)

    Associated Reading:
    • DELA 9.9

    The quiz next week will be on phase plane analysis


    Homework:

    Dec. 5

    In Lecture:
    1. Nonlinear Systems (DELA section 9.10).

    Associated Reading:
    • DELA 9.10

    The quiz in recitation this week will be on phase plane analysis.


    Homework:

    Dec. 7

    In Lecture:
    1. End of non-linear systems
    2. Review of the course

    Associated Reading:
    • All the sections of the text listed on the course schedule

    There will be no quiz or recitations next week!


    Homework:

    Dec. 12

    No Class!
    Dec. 14

    Final Exam
    1. Our exam will take place from 9 to 11 a.m. on Dec. 14 in room G17 of Claudia Cohen Hall. The abbreviation for this building is COHN. Please note that math 240 has a Special exam schedule. The exam schedule for all other courses meeting at the same time as our course does not apply.
    2. You can bring on two-sided handwritten page of notes to the exam. Apart from this, please bring only the pens and pencils you will use. No calculators, books or other aids will be allowed.

    Homework:

    Last updated: 11/30/17
    Send e-mail comments to: ted@math.upenn.edu