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Differential Equations Homework Problems For Physics

Differential Equations for Engineering and Physics (Math 244), Sections 1-3, Fall 2013 (Rutgers, NB)

(Last Update: Jan. 6, 2013)
  • Textbook: Elementary Differential Equations (9th ed.) by William E. Boyce and Richard C. DiPrima
    [Note: ANY edition (older or newer) is fine!, the section numberings may be different, though]
  • Instructor: Dr. Doron ZEILBERGER ("Dr. Z").
  • Teaching Assistant: Mr. Fei Qi (fq15 at math dot rutgers dot edu)
  • Dr.Z's Email: zeilberg at math dot rutgers dot edu (MUST have DiffEqsRock in the subject!)
  • Place and Times of Lectures: Mondays and Thursdays, 1st period, 8:40-10:00am, PH-115 (Busch Campus)
  • Place and Times of Recitations:
    • Section 1: Thursdays 1:55-2:50pm, SEC 202 (Busch Campus)
    • Section 2: Thursdays 3:35-4:30pm, SEC 217 (Busch Campus)
    • Section 3: Thursdays 5:15-6:10pm, SEC 220 (Busch Campus)
  • Free Tutoring: Mondays and Thursdays 7:40-8:30am, PH 115.
  • Mr. Fei Qi's Office Hour: Wed. 5:00-6:00pm, Hill 624.
  • Dr. Z.'s Additional Office Hours: Mondays and Thursdays, 12:00-1:00pm, Hill 704.
  • Dr. Z.'s Class Policy

Here are the answers to the homework problems.
Added Oct. 7, 2013: How do design your very own Practice Exams for Exam 1.
Added Oct. 15, 2013: Here is Exam 1, and here are the Full Solutions to Exam 1.
Added Oct. 19, 2013: People who did not do as well as they should have are welcome to join the Second Chance Club for Exam I.
Added Nov. 19, 2013: How do design your very own Practice Exams for Exam 2.
Added Nov. 30, 2013: Here is Exam 2, and here are the Full Solutions to Exam 2.
Added Dec. 2, 2013: People who did not do as well as they should on Exam 2 have are welcome to join the Second Chance Club for Exam II.
Added Dec. 9, 2013: Instead of a practice Final, here are All the homework assignments, in one file. If you can do them all (correctly!) you would ace the final.
Added Dec. 23, 2013: Here is the Final Exam Without Solutions, and here is Meredith Taghon's Perfect Solutions,
P.S. Congratulations to Meredith, who won a $25 gift card at .

Optional Marathon Review

  • Thurs. Dec. 12, 9:00am-1:00pm, our usual classroom (PH-115)
Final Exam
  • Fri. Dec. 20, 2013, 4:00-7:00pm (in our classroom [PH-115])

Added Dec. 24, 2013: Here is the list of top scorers on the final exam (out of 210 points):
  • Adal Arnell: 210
  • Efren Deasis: 210
  • Meredith Taghon: 210
  • Kevin Albertson: 209
  • Samantha Jeng : 208
  • Kelsey Hickey: 207
  • Alok Shroff: 207
  • Jonathan Chang: 206
  • Guan Yu Chen: 206
  • Wesley Chin: 205
  • Colleen Engler: 205
  • Kolung Chan: 204
  • Sanatha Heller: 203
  • Mehul Salhotra: 203
  • Xiao Cheng: 202
  • Irina Limaico Suarez: 202
  • Elias Bull: 200
  • Cody Hewitt: 200
  • Xiaoyu (Sharon) Zhang: 200

Added Jan. 6, 2014: Here are the students' evaluations .

Doron Zeilberger's teaching page

Math 0290: Differential Equations

Instructor: Catalin Trenchea
Lectures: MWF 10:00-10:50pm, G30 Benedum Hall

Office Hours: Tue. 2:00pm-3:30pm, Th. 9:00am-10:30am and by appointment
Office: Thackeray 606
Phone: (412) 624-5681


Differential equations are an important branch of mathematics. They have a rich mathematical formalization, as well as a very successful history of being applied to important problems in physics, chemistry, engineering, and biology. This course will introduce primarily linear, first and second order differential equations. Solution techniques for separable equations, homogeneous and inhomogeneous equations, as well as an intuition for modeling-based applications will be presented. The application of Laplace transforms to differential equations, systems of linear differential equations, linearization of nonlinear systems, and phase plane methods will be introduced. Fourier series and their application to simple partial differential equations will be treated. MATLAB based numerical solution and visualization will be briefly covered.


  • Polking, Boggess and Arnold, Differential Equations with Boundary Value Problems, second edition, Pearson Prentice-Hall
  • Polking and Arnold, Ordinary Differential Equations using MatLab, Third Edition, Pearson Prentice-Hall
These two items will be packaged together in the Pitt Bookstore.

Other Materials

You will need some MatLab add-on software for differential equations. It can be downloaded from at Rice University.


Your course grade will be determined as follows:
  • Two midterm exams 40% (20% each)
  • Final exam 40%
  • Homework 20%
Assignments: Ten assignments will be given throughout the term. The best eight assignments will be used to compute the final assignment grade. The assignment grade will be 20% of the course grade.

Midterm Exams: There will be two in class midterm examinations given. The second midterm will not be cumulative to the first. In other words, the second midterm will only cover course material not covered by first midterm exam. Each midterm exam grade will be 20%(x2) of the course grade.

Final Exam: The final exam grade will be 40% of the course grade and will take place during exams week. Your course grade will not exceed your final exam grade by more than one letter grade.

A/A-:90-100%, B/B±: 80-89%, C/C±: 70-79%, D/D+: 60-69%, F: < 60%

Some sections may deviate slightly from this recipe. Any deviations will be announced by your instructor at the beginning of the term.

MATLAB component: The study of differential equations often uses computer algorithms to gain solutions to relevant problems in physics, biology, chemistry, and engineering. Several assignment problems will taken from the problem sets in the MATLAB supplemental textbook. These problems will be of use to the student in both acquiring a visual sense of differential equations and their solutions, as well as give an introduction into standard-practice techniques currently used in many disciplines.

Homework policies

Students are required to complete the homework problems; very few students can learn this material without constant practice. Students are welcome to work together on homework. However, each student must turn in his or her own assignments, and no copying from another student's work is permitted. Deadline extensions for homework will not be given. Students are encouraged to discuss with your professor about homework problems if you'd like additional feedback.

Final Exam Policy

All day sections will take a departmental final exam at a time and place to be scheduled by the registrar. Evening sections will meet through final exam week, and the final exam will be given during the last one or two scheduled class periods.

Final Grade Policy

Your final grade should not exceed your final exam grade by more than one letter grade.

Office Hours

Your instructor will announce his office hours.

Academic Integrity

The University of Pittsburgh Academic Integrity Code is available at The code states that "A student has an obligation to exhibit honesty and to respect the ethical standards of the academy in carrying out his or her academic assignments." The website lists examples of actions that violate this code. Students are expected to adhere to the Academic Integrity Code, and violations of the code will be dealt with seriously.

On homework, you may work with other students or use library resources, but each student must write up his or her solutions independently. Copying solutions from other students will be considered cheating, and handled accordingly.

Disability Resource Services

If you have a disability for which you are or may be requesting an accommodation, you are encouraged to contact both your instructor and Disability Resources and Services, 140 William Pitt Union, 412-648-7890 or 412-383-7355 (TTY) as early as possible in the term. DRS will verify your disability and determine reasonable accommodations for this course.

Schedule and practice problems

Approximate schedule for lectures. References of the form a.b refer to sections in the main textbook. References of the form Ma refer to Chapter a of the MatLab supplement.

Week 1: August 27, 29, 31
Modeling with differential equations
First order initial value problems
Separation of variables
1.1 Number 1-11. Homework: 1,2,5,7,11
2.1 Number 1-6, 12-15. Homework: 1,3,5,12,13,15
2.2 Number 1-18, 33-35 Homework: 3,5,9,33
M1 Number 1

Week 2: September 5, 7
Models of motion
First order linear equations
Plotting with MatLab
2.3 Number 8-10 Homework: 9
2.4 Number 1-21 Homework: 5,15,19
M2 Number 15-20

Week 3: September 10, 12, 14
3.1 Number 10, 12, 13 Homework: 10,13
3.3 Number 3, 5 Homework: 3,5
M3 Number 1-12 Homework: 1

Week 4: September 17, 19, 21
Electrical circuits
Second order equations
Function m-files
3.4 Number 1-10 Homework: 1,3,5,7,11
4.1 Number 1-20 Homework: 1,3,9,17
4.3 Number 1-36 Homework: 1,9,17,35
M4 Number 1-8, 17, 18

Week 5: September 24, 26, 28
Second order equations (cont.)
4.4 Number 1-12 Homework: 1,7,11,12
4.5 Number 1-29 Homework: 1,5,11,15,19
4.6 Number 1-10 Homework: 1,3,5

Week 6: October 1, 3, 5
Forced Harmonic Motion
Review and Exam
4.7 Number 3-6, 12-15 Homework: 3,13
First midterm on October 5

Week 7:
Laplace Transform
5.1 Number 1-29 Homework: 7,13,15,29
5.2 Number 1-41 Homework: 5,11,19,29
5.3 Number 1-36 Homework: 3,7,11,19

Week 8: October 15, 17, 19
Laplace Transform (cont.)
5.4 Number 1-26 Homework: 7,11,21
5.5 Number 1-25 Homework: 1,3,11,17
5.6 Number 1-9 Homework: 2,3,5,7

Week 9: October 22, 24, 26
Numerical methods
Introduction to systems
5.7 Number 4-10 Homework: 6, 8, 10
6.1 Number 1-5 Homework: 3,5
8.1 Number 1-16 Homework: 5,7,13,15
M5 Number 1-6 Homework: 2,3

Week 10: October 29, 31, November 2
Systems (cont.)
Constant coefficient homogeneous 2x2 systems
8.2 Number 13-16 (use pplane 8) Homework: 11,13,15
8.3 Number 1-6 Homework: 1,3,5
9.1 Number 1-8, 16-23 Homework: 3,5,17,19

Week 11: November 5, 7, 9
Planar systems
Review and Exam
9.2 Number 1-27, 58, 59 Homework: 3,13,15,41,49
Second Midterm on November 9

Week 12: November 12, 14, 16
Phase plane
Inhomogeneous systems: Undetermined coefficients and variation of parameters
Nonlinear systems: equilibria, linearization
9.3 Number 1-23 Homework: 1,11, 13, 15, 17, 21, 23
9.9 Number 1-6, 12-15 Homework: 1, 3, 13, 15
10.1 Number 1-18 Homework: 3, 5, 7, 15

Week 13: November 19
Nonlinear systems: stability, nullclines
10.2 Number 1-4 Homework: 1,3

Week 14: November 26, 28, 30
Nonlinear systems: invariant sets, nullclines
Fourier series
10.3 Number 1-16 Homework: 3,7,11
12.1 Number 1-17 Homework: 5,7,13,17
12.3 Number 1-32 Homework: 3,7,19,31

Week 15: December 3, 5, 7
Heat equation
Separation of variables
13.1 Number 1-9
13.2 Number 1-18 Homework: 5, 13

The final exam's date: 2012/12/11, Tuesday. Exam time: 2:00PM - 3:50PM. Location: 120/121 Lawrence Hall.