MATH 165 "Linear Algebra with Differential Equations"

Course Number
 Time
 Location
 Instructor
 Office Hours
 E-mail
MATH 165-1 MW 10:25-11:40 Gavett 310 Anurag Sahay T 12:00-13:00, Hylan 910
F 12:00-13:00 via Zoom 		anuragsahay@rochester.edu
MATH 165-2 MW 12:30-13:45 Goergen 108 Minsik Han M 14:30-16:00, Hylan 908 minsik.han@rochester.edu
MATH 165-3 MW 9:00-10:15 Dewey 2162 Dan-Andrei Geba MW 11:50-12:50, Hylan 806 dangeba@math.rochester.edu
MATH 165-4 MW 14:00-15:15 Dewey 2162 Joshua Sumpter WF 12:00-13:00, Hylan 803 jsumpter@math.rochester.edu

Syllabus: First order differential equations. Matrices and systems of linear equations. Determinants. Vector spaces. Linear transformations. Eigenvalues and eigenvectors. Higher order linear differential equations. Systems of differential equations. For more information, see the course catalog.

Prerequisites: MATH 143, MATH 162, or MATH 172. These are strict prerequisites. MATH 162 and 165 cannot be taken concurrently. MATH 164 is not a prerequisite for MATH 165.

Textbook: Stephen Goode and Scott Annin, Differential Equations and Linear Algebra (4th edition), Pearson Prentice Hall, 2016. This book will also be on reserve at Carlson Library.

Course philosophy: This is a first college class on linear algebra and its applications to solving differential equations, which builds on the material covered in one year of real calculus. This course can be challenging at times and, especially in the beginning, it will move quite fast. It will require time commitment. Proficiency will be achieved only by hard work and massive problem solving. Please take full advantage of all the office hours offered in connection with this course. This means you can also attend the office hours of a MATH 165 instructor other than the one of your regular section.

Grading: Webwork 25%, Midterm 1 20%, Midterm 2 20%, Final 35%.

Incomplete "I" grades are almost never given. The only justification is a documented serious medical problem or genuine personal/family emergency. Falling behind in this course or problems with workload on other courses are not acceptable reasons.

Webwork

To access Webwork, you should click on the "Webwork Link" item listed on the MATH 165 Course Home Page on the Blackboard site.

Webwork will be assigned weekly on Thursdays and it will be due the following week on Friday at 23:59. The only exception is Webwork 7 which is assigned on 3/2 and it is due in two weeks (because of the spring break) on 3/17. There are 12 Webwork sets and all will count toward your grade. The Webwork portion of the course grade will be based on the total number of Webwork questions completed.

All Webwork problems have a button to "Email Webwork TA". Click it to email the instructors and a "Webwork TA". The Webwork TA will respond within a day or so (and maybe sooner). You do not have to copy out the problem, the system automatically does this. If Webwork does not accept your answer, then you should include your answer and how you came up with it. It helps to give some idea of your thought process. Beware that any email sent after 17:00 on a Friday will almost certainly not get a reply before the set closes. Note that this should be used for Webwork feedback only. If you want to contact your instructor, then you should email him directly.

Exams

The location for both midterms is as follows:

- Lower Strong Auditorium for students in Prof. Sahay's, Prof. Sumpter's, and Prof. Geba's sections;

- Dewey 1101 for students in Prof. Han's section.

The first midterm took place on 2/16. It was based on material from sections 1.1-1.4, 1.6, 1.7, and 2.1-2.5.

Sample first midterms: Spring 2018, Fall 2018, Spring 2019, Fall 2019, Spring 2020.

The second midterm takes place on Tuesday, 3/28, between 8:00 and 9:15. It is based on material from sections 2.6, 3.4, and 4.1-4.6.

Sample second midterms: Spring 2018, Fall 2018, Spring 2019, Fall 2019, Spring 2020.

The final exam is on Monday, 5/1, between 16:00 and 19:00.

Sample finals: Spring 2018, Fall 2018, Spring 2019, Fall 2019, Spring 2020.

The Final Exam will have two parts: Part A will cover the material of both midterms, while Part B will cover only the material since second midterm. Part A accounts for 15% of your course grade and Part B accounts for 20% of your course grade. In addition, the Part A score will replace the lowest of the midterm scores (but not both) if it is better.

Note about the posted exams: the syllabus changes slightly from year to year, so the exams you will be administered might not matchup perfectly with the ones above in terms of topics. You should combine their study with the practice problems and Webwork.

Recitations

For this course, we conduct formal recitations, which will start during the week of 1/23-1/27. The attendance is not mandatory, yet strongly encouraged. During recitations, TAs will lead through practice problems assigned the previous week and will answer questions pertaining to both lectures and Webwork.

Time
 Location
 Teaching Assistant
 E-mail
Tuesday 11:05-12:20 Lattimore 210 Daniel Gotshall dgotshal@ur.rochester.edu
Tuesday 19:40-20:55 Dewey 2110D Daniel Gotshall dgotshal@ur.rochester.edu
Wednesday 18:15-19:30 Dewey 2110E Firdavs Rakhmonov frakhmon@ur.rochester.edu
Thursday 15:25-16:40 Goergen 109 Firdavs Rakhmonov frakhmon@ur.rochester.edu
Thursday 18:15-19:30 Hylan 101 Daniel Gotshall dgotshal@ur.rochester.edu
Friday 14:00-15:15 Wilmot 116 Firdavs Rakhmonov frakhmon@ur.rochester.edu

In addition to office hours and recitations, you can also seek help from:

- MATH 165 weekly study group on Fridays from 12:30 to 13:45 in Hylan 101 coordinated by Fariha Raisa (fraisa@u.rochester.edu);

- the regular Math Study Hall, run Mondays through Thursdays in Hylan 1104, 17:00-20:00. For more details, go here.

Course policies

1. Make-up exams will be very rare and only administered for extreme emergencies with formal documentation. If a student misses a midterm whether it be for medical or other reason, they would be expected to use Part A of the final as its replacement.

2. The use of any electronic devices (including calculators), books, notes, or formula cards/sheets is prohibited during any of the exams.

3. If you have an academic need related to a disability, arrangements can be made to accommodate most needs. For information, please contact the Office of Disability Resources. To be granted alternate testing accommodations, you (the student) must fill out forms with this office at least seven days before each and every exam. These forms are not sent automatically. Instructors are not responsible for requesting alternative testing accommodations for you, and they are not obligated to make any accommodations without prior approval from the Office of Disability Resources.

4. You are responsible for knowing and abiding by the University of Rochester's academic honesty policy. Any violation of academic integrity will be pursued according to the specified procedures.

5. This course follows the College credit hour policy for four-credit courses. This course meets 3 academic hours per week. Students may also be expected to deepen their understanding of the course material through close examination/evaluation of the readings assigned in the course.

Tentative weekly schedule:


Week of Topic Practice problems Webwork
1/9 1.1: Differential equations everywhere;
1.2: Basic ideas and terminology.		 1.1: 1, 3, 5, 9, 11, 15, 17, 19, 21, 23;
1.2: 2, 4, 5, 8, 13, 14, 16, 18, 19, 22, 23, 27, 32, 37, 41.		 Webwork 0 (tutorial, not graded)
1/16 1.3: The geometry of first-order differential equations;
1.4: Separable differential equations.		 1.3: 2, 3, 6, 11, 17, 19, 22, 24;
1.4: 4, 7, 9, 12, 14, 20, 24, 27, 28, 30.		 Webwork 1 (due 1/27) (in dealing with slope fields, you may find useful the following plotter)
1/23 1.6: First-order linear differential equations;
1.7: Modeling problems using first-order linear differential equations.		 1.6: 3, 6, 7, 11, 13, 16, 19, 22, 28, 29;
1.7: 1, 3, 5, 6, 7, 8.		 Webwork 2 (due 2/3)
1/30 2.1: Matrices (definitions and notations);
2.2: Matrix algebra;
2.3: Terminology for systems of linear equations.		 2.1: 4, 7, 11, 14, 20, 24, 25, 28, 30;
2.2: 1, 3, 8, 9, 11, 13, 16, 42, 44, 46;
2.3: 3, 6, 9, 11, 12, 18, 21.		 Webwork 3 (due 2/10)
2/6 2.4: Row-echelon matrices and elementary row operations;
2.5: Gaussian elimination.		 2.4: 1, 2, 4, 7, 10, 12, 18, 21, 26;
2.5: 4, 8, 12, 14, 17, 20, 23, 26, 36, 38, 46, 48, 52, 56. 		Webwork 4 (due 2/17)
2/13 2.6: The inverse of a square matrix;
3.4: Summary of determinants.		 2.6: 5, 9, 10, 16, 23, 25, 29;
3.1: 9, 11, 13, 15, 17, 21;
3.2: 5, 7, 9, 13, 15, 21, 23, 37, 39;
3.3: 5-19 odd.		 Webwork 5 (due 2/24)
2/20 4.1: Vectors in R^n;
4.2: Definition of a vector space;
4.3: Subspaces.		 4.1: 1, 3, 4;
4.2: 1, 3, 5, 7, 11, 13;
4.3: 3, 5, 7, 9, 15, 19, 21. 		Webwork 6 (due 3/3)
2/27 4.4: Spanning sets;
4.5: Linear dependence and linear independence.		 4.4: 1, 3, 5, 9, 13, 15, 17, 23, 27;
4.5: 1, 3, 7, 9, 13, 15, 21, 23, 27, 31, 33, 35, 39. 		Webwork 7 (due 3/17)
3/13 4.5: Linear dependence and linear independence;
4.6: Bases and dimension.		 4.5: 1, 3, 7, 9, 13, 15, 21, 23, 27, 31, 33, 35, 39;
4.6: 3, 5, 11, 13, 15, 21, 23, 27, 33. 		Webwork 8 (due 3/24)
3/20 4.6: Bases and dimension;
4.8: Row space and column space;
4.9: The rank-nullity theorem;
6.1: Definition of a linear transformation.		 4.6: 3, 5, 11, 13, 15, 21, 23, 27, 33;
4.8: 1, 3, 5, 7, 9;
4.9: 1, 3, 7, 9, 11, 13, 17;
6.1: 1, 6, 7, 9, 13, 15, 17, 19, 23, 25, 27, 30. 		Webwork 9 (due 3/31)
3/27 Webwork 10 (due 4/7)
4/3 Webwork 11 (due 4/14)
4/10 Webwork 12 (due 4/21)
4/17
4/24

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