Math 240 schedule
Tuesday Thursday
August 27

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. A brief introduction to Markov Processes
  6. Systems of linear equations (DELA section 2.3)
  7. The geometry of linear systems (DELA section 2.3)

Associated Reading:
  • DELA Sections 2.1 - 2.2


Homework:
  1. Homework #1 due week of Sept. 16
  2. Core homework problem list (not to turn in)


Important Note: There will be no recitations this week. Next week
there will be no recitation on Monday because of Labor Day.
So next week, students in Monday recitations should try to go to
one of the Wednesday recitations listed below.
  1. Wed. 8-9 a.m., DRL 2N36
  2. Wed. 9 - 10 a.m.,Towne Hall 313

Only recitations numbered 211, 212, 213 and 214 are running this term.
There will be no quiz in recitation this week or next week.
The first quiz in Wednesday recitations will be on September 11.
The first quiz in in Monday recitations will be on September 9.

August 29

In Lecture:
  1. The Wikipedia article on the pagerank algorithm
    The part of this article I will explain in class begins with the section title "Algorithm" and
    stops with the last displayed equation in the section titled "Damping Factor".
    We will eventually be able to talk about the later parts of the article.
  2. Writing systems of linear differential equations in matrix form (DELA section 2.2)
  3. Row reduction of matrices, echelon and reduced echelon forms (DELA section 2.4)
  4. Solving systems of linear equations. (DELA section 2.5)

Associated Reading:
  • DELA Sections 2.3 - 2.5


Homework:
  1. Homework #1 due week of Sept. 16
  2. Core homework problem list (not to turn in)

Sept. 3

In Lecture:
  1. Ranks of matrices (DELA section 2.4)
  2. Pivot variables and free variables, existence and uniqueness of solutions to systems of linear equations (DELA section 2.5)

Associated Reading:
  • DELA Sections 2.4, 2.5, 2.6, 3.1 - 3.5



Important Note:
There will be no recitation on Monday because of Labor Day.
So students in Monday recitations should try to go to
one of the Wednesday recitations listed below.

  1. Wed. 8-9 a.m., DRL 2N36
  2. Wed. 9 - 10 a.m.,Towne Hall 313

The first quiz in Wednesday recitations will be on September 11.
The first quiz in in Monday recitations will be on September 9.
The quizzes on these days will be on core problems of the kind in sections 2.1, 2.2, 2.3, 2.4 and 2.5



Homework:

  1. Homework #1 due week of Sept. 16
  2. Core homework problem list (not to turn in)
September 5

In Lecture:
  1. Inverses of matrices (DELA section 2.6)

Associated Reading:
  • DELA Sections 2.6, 3.1 - 4.2



Homework:

  1. Homework #1 due week of Sept. 16
  2. Core homework problem list (not to turn in)

Sept. 10

In Lecture:
  1. The heat equation as a source of large linear systems of equations
  2. Determinants and their properties (DELA sections 3.1 - 3.5)

Associated Reading:
  • DELA Sections 4.1 - 4.5


Homework:

September 12

In Lecture:
  1. Polynomial time algorithms
  2. Determinants, continued

Associated Reading:


Quizzes

  • The quiz for the week of Sept. 16 - 20 may have problems similar to the Core Problem list from sections 3.1 - 3.5.


Homework:

September 17

In Lecture:
  1. Definition of a vector space, examples (DELA section 4.1 - 4.2)
  2. Subspaces (DELA section 4.3)
  3. Error Correction
  4. Spanning sets (DELA section 4.4)

Associated Reading:
  • Notes on error correcting codes The material in section 14.2 up through Theorem 14.1 is useful in understanding the assigned homework.
  • DELA Sections 4.1 - 4.9


Quizzes

  • The quiz for the week of Sept. 16 - 20 may have problems similar to the Core Problem list from sections 3.1 - 3.5. The quiz next week may have problems similar to the Core Problems from sections 3.1 - 3.4 and from sections 4.1, 4.2 and 4.3.


Homework:

Sept. 19

In Lecture:
  1. Linear dependence and independence continued (DELA section 4.5 )
  2. Bases and dimension (DELA Section 4.6)
  3. The row space and column space of a matrix (DELA section 4.8)
  4. Finding a basis for the row space. (DELA section 4.8)

Associated Reading:
  • DELA Sections 4.1 - 4.9


Homework:

September 24

In Lecture:
  1. The row space and column space of a matrix, continued (DELA section 4.8)
  2. Rank Nullity theorem (DELA section 4.9)

Associated Reading:
  • DELA Sections 4.1 - 4.9


Quizzes and next week's midterm.

  • The quiz this week may have problems similar to the Core Problems from sections 3.1 - 3.4 and from sections 4.1, 4.2 and 4.3. The quiz next week may contain problems similar to Core problems from sections 4.1 through 4.6 or 4.8 and 4.9 of the text.
  • The mid-term on Oct. 3 will cover the material on the sections listed on this course schedule from chapters 2, 3 and 4 of the text,
  • The mid-term 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 , 4.9 and 4.10 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.
    3. Section 4.10 Invertible Matrix Theorem. Do True and False questions a, c, e and h.
  • Graded Homework assignment 2 (to be turned in to Flora's mailbox by noon on October 21. )
Sept. 26

In Lecture:
  1. Finding a basis for the nullspace of a matrix (DELA , Proof of Theorem 4.9.1)
  2. Linear maps between vector spaces (DELA section 6.1)
  3. Matrices of linear maps (DELA section 6.5)
  4. Change of basis matrices, continued (DELA section 4.7)

Associated Reading:
  • DELA Sections 6.1 - 6.5, Section 4.7 and Sections 7.1 - 7.3.


Quizzes

  • The quiz this week may have problems similar to the Core Problems from sections 3.1 - 3.4 and from sections 4.1, 4.2 and 4.3. The quiz next week may contain problems similar to Core problems from sections 4.1 through 4.6 or 4.8 and 4.9 of the text.


Homework:

  • Core homework problem list (For use in preparing for quizzes; this is not graded). There is a mix-up involving sections 4.8, 4.9 and 4.10 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.
    3. Section 4.10 Invertible Matrix Theorem. Do True and False questions a, c, e and h.
  • Graded Homework assignment 2 (to be turned in to Flora's mailbox by noon on October 21. )
October 1

In Lecture:
  1. Invertible matrix theorem (DELA section 4.10)
  2. Linear maps between vector spaces (DELA section 6.1)
  3. Matrices of linear maps (DELA section 6.5)
  4. Change of basis matrices, continued (DELA section 4.7)

Associated Reading:
  • DELA Sections 4.1 - 4.10


Quizzes and this week's midterm.

  • The quiz this week may have problems similar to the Core Problems from sections 3.1 - 3.4 and from sections 4.1, 4.2 and 4.3. There will be no quiz next week.
  • The mid-term on Oct. 3 will cover the material on the sections listed on this course schedule from chapters 2, 3 and 4 of the text,
  • The mid-term 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, 4.9 and 4.10 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.
    3. Section 4.10 Invertible Matrix Theorem. Do True and False questions a, c, e and h.
  • Graded Homework assignment 2 (to be turned in to Flora's mailbox by noon on October 21. )
October 3

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.


Homework:

  • Core homework problem list (For use in preparing for quizzes; this is not graded).There is a mix-up involving sections 4.8, 4.9 and 4.10 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.
    3. Section 4.10 Invertible Matrix Theorem. Do True and False questions a, c, e and h.
  • Graded Homework assignment 2 (to be turned in to Flora's mailbox by noon on October 21. )
Oct. 8

In Lecture:
  1. Matrices of linear maps (DELA section 6.5)
  2. Characteristic polynomials of matrices (DELA section 7.1 - 7.2)
  3. Bases of eigenvectors, diagonalizable matrices (DELA section 7.3)

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


There will be no quiz this week.


Homework:

October 10

No class: Fall Break!
Oct. 15

In Lecture:
  1. Non-defective and defective matrices (DELA section 7.2)
  2. Jordan canonical forms (DELA section 7.6)

Associated Reading:
  • Notes on Jordan canonical forms Sections 1 through 7 are important to understand. Section 8 is optional, in case you would like to see how to find the appropriate bases in general.
  • DELA Sections 7.1 - 7.6, Section 8.1 - 8.2


The quiz next week will be on eigenvalues, eigenvectors, diagonalizable matrices and Jordan canonical forms


Homework:

Oct. 17

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

Associated Reading:


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


Homework:

Oct. 22

In Lecture:
  1. End of Jordan Canonical forms, with applications to the google page rank algorithm (DELA section 7.6)
  2. Linear differential equations (DELA section 8.1)
  3. Constant coefficient homogenous linear systems of differential equations (DELA section 8.2)
  4. Bases of solutions of linear constant coefficient O.D.E.'s (DELA sections 8.1 and 8.2)

Associated Reading:


The quiz this week will be on eigenvalues, eigenvectors and diagonalizable matrices. The quiz next week will be on Jordan canonical forms.


Homework:

Oct. 24

In Lecture:
  1. Constant coefficient linear systems, continued. (DELA section 8.2)

Associated Reading:
  • DELA 8.1 - 8.4


The quiz this week will be on eigenvalues, eigenvectors, diagonalizable matrices. The quiz next week will be on Jordan canonical forms.


Homework:

Oct. 29

In Lecture:
  • Constant coefficient linear systems, continued. (DELA sections 8.1 and 8.2)
  • Undetermined coefficients, annihilators (DELA section 8.3)
    Associated Reading:
    • DELA 8.1 - 8.4


    The quiz this week will be on Jordan canonical forms. The quiz next week will be on constant coefficient linear systems and the undetermined coefficient method.


    Homework:

    		• Oct. 31

    In Lecture:
    1. Undetermined coefficients, annihilators (DELA section 8.3)
    2. Complex trial solutions (DELA section 8.4)
    3. Oscillating systems (DELA section 8.5)

    Associated Reading:
    • DELA 8.2 - 8.5


    The quiz this week will be on Jordan canonical forms. The quiz next week will be on constant coefficient linear systems and the undetermined coefficient method.


    Homework:

    Nov. 5

    In Lecture:
    1. Review for Mid-Term 2. The mid-term will involve problems similar
      to the core problems for the sections of the course covered between
      Oct. 8 and Oct. 29, inclusive.
    2. Forced oscillation (DELA section 8.5)
    3. Complex valued trial solutions (DELA section 8.4)
    4. Variation of Parameters (DELA section 8.7)

    Associated Reading:
    • DELA 8.5, 8.4, 8.7


    The quiz this week will be on will be on constant coefficient linear systems and the undetermined coefficient method. The quiz next week will be on oscillating systems.


    Homework:

    		Nov. 7

    In Lecture: Mid-Term 2
    • The mid-term will cover the material on the sections listed on this course
      schedule starting on October 8 and ending on October 29.
    • 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 quiz this week will be on will be on constant coefficient linear systems and the undetermined coefficient method. The quiz next week will be on oscillating systems.


    Homework:

    Nov. 12

    In Lecture:
    1. Complex valued trial solutions (DELA section 8.4)
    2. Variation of Parameters (DELA section 8.7)

    Associated Reading:
    • DELA 8.4, 8.7


    The quiz this week will be on will be on on oscillating systems. The quiz next week will be on the variation of parameter method.


    Homework:

    		Nov. 14

    In Lecture:
    1. Reduction of order (DELA section 8.9)
    2. Solving linear systems of differential equations (DELA sections 9.1, 9.2, 9.3, 9.4, 9.5, 9.8)

    Associated Reading:
    • DELA 8.9, 9.1 - 9.5, 9.8


    The quiz this week will be on will be on on oscillating systems. The quiz next week will be on the variation of parameter method.


    Homework:

    Nov. 19

    In Lecture:
    1. Solving linear systems of differential equations, continued (DELA sections 9.1, 9.2, 9.3, 9.4, 9.5, 9.8)

    Associated Reading:
    • DELA 9.1 - 9.5, 9.8


    The quiz this week will be the variation of parameters method. The quiz next week will be on the reduction of order method.


    Homework:

    		Nov. 21

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

    Associated Reading:
    • DELA 9.9


    The quiz this week will be the variation of parameters method. The quiz next week will be on the reduction of order method.


    Homework:

    Nov. 26

    In Lecture:
    1. Phase Plane for linear autonomous systems (DELA section 9.9)
    2. Nonlinear Systems (DELA section 9.10).

    Associated Reading:
    • DELA 9.9, 9.10

    The quiz this week will be on the reduction of order method. The next week will be on solving systems of differential equations.


    Homework:


    		Nov. 28

    No class - Thankgiving
    Dec. 3

    In Lecture:
    1. End of Nonlinear Systems (DELA section 9.10).
    2. Beginning of review of the entire course.

    Associated Reading:
    • DELA 9.10

    The quiz in recitation this week will be on solving systems of differential equations.


    Homework:

    		Dec. 5

    In Lecture:
    1. 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:

    Last updated: 11/24/19
    Send e-mail comments to: ted@math.upenn.edu