Course Number 
Time 
Location 
Instructor 
Office Hours 
Email 
29716  MW 14:0015:15  Hutchison 140  DanAndrei Geba  MW 11:5012:50 or by appointment, Hylan 806  dan.geba@rochester.edu 
29727  MW 16:5018:05  Bausch & Lomb 109  Evan Dummit  T 15:0017:00, Hylan 908  edummit@ur.rochester.edu 
29875  TR 11:0512:20  Hylan 201  Irina Bobkova  T 15:2517:25, Hylan 801  ibobkova@ur.rochester.edu 
29881  MW 10:2511:40  Meliora 203  Tamar Friedmann  M 15:3016:45 and W 9:0010:05, Hylan 1006  tfriedma@ur.rochester.edu 
77749  MW 12:3013:45  Dewey 2110D  Saul Lubkin  MF 10:1511:30 or by appointment, Hylan 705  saul.lubkin@rochester.edu 
Syllabus: First order differential equations. Matrices and systems of linear equations. Determinants. Vector spaces. Linear transformations. Higher order differential equations. Systems of differential equations. For more information, see the course catalog.
Prerequisites: MTH 143, MTH 162, or MTH 172.
Textbook: Stephen Goode and Scott Annin, Differential Equations and Linear Algebra (3rd Edition),
Pearson Prentice Hall, 2007. This book will be also 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, recitations, and study halls offered in connection with this course.
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 will be assigned weekly on Fridays and it will be due the following week on Saturday morning at 9:00 am. The only exception is Webwork 7 which is assigned on 3/4 and it is due in two weeks (because of the spring break) on 3/19. There are 12 Webworks from which the best 10 will count towards your grade. As a result, no extension for any Webwork will be granted.
All Webwork problems have a button to "Email Webwork TA". Click it to email the instructors and a "Webwork TA". The Webwork TA, Yingzhong Chen, 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 them directly.
For Webwork problems pertaining to Section 1.3 in the textbook, you might find useful the following software: Java & Matlab programs for plotting direction fields dfield and pplane. See also Mathematica's builtin VectorPlot and StreamPlot commands.
For this course, we have both formal recitations and a MTH 165 study hall, the latter being exclusively for MTH 165 students. The recitations and the study hall will start during the week of 1/181/23. Though optional, you are strongly encouraged to attend. In addition, one can also seek help from the regular Math Study Hall, run Mondays through Fridays in Hylan 1104, between 17:00 and 20:00.
Recitations will be held:
During recitations, TAs will lead through practice problems assigned the previous week and will answer questions pertaining to both lectures and Webwork.
MTH 165 Study Hall will be held:
During MTH 165 Study Hall, TAs will be on hand to answer any type of questions related to the course. Feel free to come by anytime during the hours listed.
The first midterm (which covers the sections 1.11.4, 1.61.7, and 2.12.5) was on 2/25, while the second one (which covers the sections 2.6, 3.13.3, 4.14.6) was on 3/31.
Sample first midterms: Fall 2014 (Solutions), Spring 2015 (Solutions), Fall 2015 (Solutions; Note: there is a mistake in the solution to problem 3, the constant C being 300000 instead of 300000.).
Sample second midterms: Fall 2014 (Solutions), Spring 2015 (Solutions), Fall 2015 (Solutions).
The final exam (which is comprehensive and covers all the sections discussed in chapters 1 through 7) is on 5/2, 12:3015:30, and its location is:
 Lower Strong Auditorium for students in sections taught by Bobkova, Friedmann, and Lubkin;
 Hutchison 141 for students in sections taught by Dummit and Geba.
Sample finals: Fall 2014 (Solutions), Spring 2015 (Solutions), Fall 2015 (Solutions).
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 lecture notes, practice problems, and Webwork.
1. There will be no makeup exams. If you miss a midterm with a valid excuse (e.g., illness or emergency), you must notify the instructor and provide supporting documentation verifying your excuse as soon as possible. For such an instance, the final exam will count as your makeup test (i.e., the percentage of the missed exam will be added to the percentage of the final). If you miss an exam without a valid excuse, you will receive a score of 0 on that test.
2. The use of electronic devices (including calculators), books, 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 Center for Excellence in Teaching and Learning. To be granted alternate testing accommodations, you (the student) must fill out forms with CETL at least seven days before each and every exam. These forms are not sent automatically. Instructors are not responsible for requesting alternative testing accommodations at CETL, and they are not obligated to make any accommodations on their own.
4. You are responsible for knowing and abiding by the University of Rochester's academic integrity code. Any violation of academic integrity will be pursued according to the specified procedures.
Here are lecture notes for E. Dummit's lecture. These lecture notes are not a replacement for attending lecture! They may not be completely exhaustive and may not cover topics in the same order.
Handout  Contents 
Chapter 1: FirstOrder Differential Equations (12pp, version 2.10, updated 1/24) (changes from 2.01: updated section 1.5.1) 
Introduction and Terminology Qualitative Analysis (ExistenceUniqueness Theorem, Slope Fields) Separable FirstOrder Equations Linear FirstOrder Equations Applications of FirstOrder Equations (Population Modeling, Mixing Problems, Physics) 
Chapter 2: Matrices and Systems of Linear Equations (18pp, version 2.01, posted 1/26) 
Systems of Linear Equations (Matrix Formulation, Echelon Forms, Gaussian Elimination) Matrix Operations: Addition and Multiplication Determinants and Inverses Matrices and Systems of Linear Equations Revisited 
Chapter 3: Vector Spaces and Linear Transformations (29pp, version 2.30, updated 3/21) (changes from 2.15: added proposition and examples to 3.4.4, added proposition and examples to 3.5.1, edited nullityrank proof in 3.5.2) 
Review of Vectors in R^n The Formal Definition of a Vector Space Subspaces (The Subspace Criterion, Additional Examples) Linear Combinations and Span, Linear Independence and Linear Dependence, Bases and Dimension, Finding Bases Linear Transformations (Definition and Examples, Kernel and Image, Isomorphisms of Vector Spaces, Matrices Associated to Linear Transformations) 
Chapter 4: Eigenvalues and Eigenvectors (9pp, version 2.00, posted 3/24) 
Eigenvalues, Eigenvectors, Characteristic Polynomials Eigenspaces Additional Results About Eigenvalues 
Chapter 5: Linear Differential Equations (15pp, version 2.00, posted 4/1) 
General Linear Differential Equations (Classification, Solution Structure and ExistenceUniqueness Theorem) Homogeneous Linear Equations with Constant Coefficients NonHomogeneous Linear Equations with Constant Coefficients (Undetermined Coefficients, Variation of Parameters) Applications of SecondOrder Equations (Mechanical Oscillations, Resonance and Forcing) 
Chapter 6: Systems of FirstOrder Linear Differential Equations (7pp, version 2.00, posted 4/15) 
General Theory of (FirstOrder) Linear Systems Eigenvalue Method (Nondefective Coefficient Matrices) 
Appendix: Complex Numbers (6pp, version 2.15, posted 1/21) 
Arithmetic with Complex Numbers Complex Exponentials, Polar Form, and Euler's Theorem 
Week of  Topic  Practice Problems (to be discussed in Recitations the following week)  Webwork 
1/11  1.1 (How differential equations arise) 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) 
1/18  1.2 (Basic ideas and terminology) 1.3 (The geometry of firstorder differential equations) 
1.2: 2, 4, 5, 8, 13, 14, 16, 18, 19, 22, 23, 27, 32, 37, 41; 1.3: 2, 3, 6, 11, 17, 19, 22, 24. 
Webwork 1 (due 1/30) 
1/25  1.3 (The geometry of firstorder differential equations) 1.4 (Separable differential equations) 1.6 (Firstorder linear differential equations) 1.7 (Modeling problems using firstorder linear differential equations) 
1.3: 2, 3, 6, 11, 17, 19, 22, 24; 1.4: 1, 3, 6, 10, 13, 15, 18, 22, 24; 1.6: 3, 6, 7, 11, 13, 16, 19, 22, 28, 29; 1.7: 1, 5, 6, 9, 11, 13. 
Webwork 2 (due 2/6) 
2/1  1.7 (Modeling problems using firstorder linear differential equations) 2.1 (Matrices: definitions and notation) 2.2 (Matrix algebra) 
1.7: 1, 5, 6, 9, 11, 13; 2.1: 3, 6, 8, 11, 15, 19, 20, 21, 23; 2.2: 2, 3, 5, 11, 13, 15, 17, 27, 32, 37, 39, 43. 
Webwork 3 (due 2/13) 
2/8  2.3 (Terminology for systems of linear equations) 2.4 (Elementary row operations and rowechelon matrices) 2.5 (Gaussian elimination) 
2.3: 3, 5, 6, 8, 9, 13, 15, 16; 2.4: 1, 4, 5, 8, 9, 11, 13, 17, 21, 25; 2.5: 1, 5, 9, 11, 14, 17, 20, 23, 33, 35, 43, 45, 49, 53. 
Webwork 4 (due 2/20) 
2/15  2.5 (Gaussian elimination) 2.6 (The inverse of a square matrix) 3.1 (The definition of the determinant) 3.2 (Properties of determinants) 
2.5: 1, 5, 9, 11, 14, 17, 20, 23, 33, 35, 43, 45, 49, 53; 2.6: 4, 8, 9, 15, 16, 19, 21, 25; 3.1: 9, 11, 13, 15, 17, 21; 3.2: 5, 7, 9, 13, 15, 21, 23, 37, 39. 
Webwork 5 (due 2/27) 
2/22  3.2 (Properties of determinants) 3.3 (Cofactor expansions) 4.1 (Vectors in R^n) 1st Midterm (2/25, 8:009:15) 
3.2: 5, 7, 9, 13, 15, 21, 23, 37, 39; 3.3: 519 odd; 4.1: 1, 3, 4. 
Webwork 6 (due 3/5) 
2/29  4.2 (Definition of a vector space) 4.3 (Subspaces) 4.4 (Spanning sets) 
4.2: 1, 3, 5, 7, 11, 13; 4.3: 3, 5, 7, 9, 15, 19, 21; 4.4: 1, 3, 5, 9, 13, 15, 17, 23, 27. 
Webwork 7 (due 3/19) 
3/14  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 3/26) 
3/21  4.8 (Row space and column space) 4.9 (The ranknullity theorem) 5.1 (Definition of a linear transformation) 5.3 (The kernel and range of a linear transformation) 
4.8: 1, 3, 5, 7, 9; 4.9: 1, 3, 7, 9, 11, 13, 17; 5.1: 1, 6, 7, 9, 13, 15, 17, 19, 23, 25, 27, 30; 5.3: 1, 3, 5, 12, 14, 15. 
Webwork 9 (due 4/9) 
3/28  5.3 (The kernel and range of a linear transformation) 5.6 (The eigenvalue/eigenvector problem) 5.7 (General results for eigenvalues and eigenvectors) 2nd Midterm (3/31, 8:009:15) 
5.3: 1, 3, 5, 12, 14, 15; 5.6: 925 odd; 5.7: 115 odd. 
Webwork 10 (due 4/16) 
4/4  6.1 (General theory for linear differential equations) 6.2 (Constantcoefficient homogeneous linear differential equations) 6.3 (The method of undetermined coefficients: annihilators) 
6.1: 912, 2127 odd, 31, 33; 6.2: 535 odd; 6.3: 111 odd, 17, 19, 21, 25, 27. 
Webwork 11 (due 4/23) 
4/11  6.3 (The method of undetermined coefficients: annihilators) 6.5 (Oscillations of a mechanical system) 7.1 (Firstorder linear systems) 7.2 (Vector formulation) 
6.3: 111 odd, 17, 19, 21, 25, 27; 6.5: 5, 7, 9, 2325, 28, 29; 7.1: 2, 5, 8, 10, 13, 14, 18; 7.2: 1, 4, 5, 7, 8, 12. 
Webwork 12 (due 4/30) 
4/18  7.2 (Vector formulation) 7.3 (General results for firstorder linear differential systems) 7.4 (Vector differential equations: nondefective coefficient matrix) 
7.2: 1, 4, 5, 7, 8, 12; 7.3: 1, 3, 5; 7.4: 115 odd. 

4/25  Review for the Final exam. 