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In particular, a class (lecture and/or discussion) can be moved to on-line mode on a very short notice, so please check your e-mail before every class.

Class number 39673

Math 445 in Fall 2025 semester: Key dates

  • August 25: first day of classes
  • September 1: Labor Day, no class
  • September 12: Last day to drop without a W AND with refund
  • October 8: Midterm Exam 1
  • October 9,10: Fall Break
  • October 10: Last day to drop without a W, BUT WITH NO refund
  • October 24: Computer project 1 is due
  • November 11: no class  (Veterans Day)
  • November 14: Last day to drop with a W
  • November 19: Midterm Exam 2
  • November 26-30: Thanksgiving Break
  • December 5: Computer project 2 is due; Last day of classes
  • December 17: Final exam (11am-1pm, in KAP 144)

Class Schedule
Homework problems
Some homework answers
Computer Projects
Crank-Nicolson scheme for the heat equation
Implicit method for the wave equation

Extended summary

  • Instructor: Dr. Sergey Lototsky
    Office: KAP 248D.
    Phone: 213–740-2389.
    E-mail: lototsky (at) USC (dot) edu
    URL: https://dornsife.usc.edu/sergey-lototsky/
    Lectures:  MWF 1-1:50pm, KAP 144
    Office hours: MWF    TBD

    Please do not hesitate to talk to me about your problems, questions, or concerns in this class. We can always arrange a special zoom meeting.

  • Teaching Assistant:  
    E-mail:   [at] usc (dot) edu
    Discussions: Tuesday  1-1:50pm
    Office hours:  in Math Center (KAP 263)

Beside the discussion sections, the TA is responsible for administering and grading quizzes and collecting and grading homeworks.

  • Textbook: “Advanced Engineering Mathematics” by E. Kreyszig, Wiley. Any edition will work. The official version is the custom USC edition.
  • Supplement: “Mathematics of Physics and Engineering” by Edward K. Blum and Sergey V. Lototsky, World Scientific, 2006 (ISBN-13: 978-9-812-56621-8)
  • The Ultimate Alternative: “Mathematical Methods for Physics and Engineering: A Comprehensive Guide” by K. F. Riley, M. P. Hobson, and S. J. Bence:  3rd Edition 0f a 1300+ page textbook, published by Cambridge University Press, 2006 (paperback ISBN-13: 978-0-521-67971-8)
  • Course goal: To realize that there is a lot of beautiful and useful mathematics out there beyond calculus and ordinary differential equations. In particular, we will cover all the material promised in the catalogue description of the course (Vector field theory; theorems of Gauss, Green, and Stokes; Fourier series and integrals; complex variables; linear partial differential equations; series solutions of ordinary differential equations), although not necessarily in this order. Here is an alternative look at it.
  • Two very interesting books closely connected with the second half of the course:
    • Nicholas J. Giordano, Physics of the piano. Oxford University Press, Oxford, 2010. 184 pp.
    • Barry Mazur and William Stein, Prime numbers and the Riemann hypothesis. Cambridge University Press, Cambridge, 2016. xi+142 pp.

Save the dates! There will be two in-class one-hour exams (October 8 and November 19, both Wednesday, during regular lecture time). The two-hour final exam is Wednesday, December 17, 11am-1pm, in the regular lecture room KAP 144.

Note: You might need a PDF Scanner, to submit your (mostly likely handwritten) work to Gradescope
in PDF format (one PDF per assignment or exam). There are many free phone apps that you can use
to scan your work to make a PDF, for instance Adobe Scan.

Homework, Quizzes, etc.: There will be 10 weekly quizzes (most Thursdays, administered by the Teaching Assistant), 11 homeworks (usually due  on Tuesdays), and two computer projects (due Friday, October 24 and Friday, December 5). You should understand every solution to every homework problem and be ready to reproduce most of those solutions on your own and in reasonable time. You are welcome to use any help whatsoever with the homework problems and the projects, but not with the quizzes. For best results, do not copy the solutions you did not produce yourself; those include my notes from the top of the page, anything by your fellow students, and whatever an AI system might generate. 

Extra note on quizzes. Because of the recent reduction in the number of discussions per week, we will need to develop a fresh approach to quizzes. Tentatively, the quizzes will be during weeks 2,3,4,5,6,9,10,11,12,and 13. The details will be worked out by the TA and adjusted as necessary.

Note on Use of AI
You are welcome to use  artificial intelligence (AI) powered programs as a help with homework problems and computer projects, but not with quizzes and exams. While AI tools can help you brainstorm ideas or revise work you have already written, AI text generation tools may present incorrect information, biased responses, and incomplete analyses. To adhere to our university values, you must cite any AI-generated material (such as text or images) included or referenced in your work and provide the prompts used to generate the content.  I will not be using any AI tools in grading your work.

Grading:

  • Quizzes 15% total
  • Homeworks, 15% total
  • The projects, 10% total [5% each]
  • Two Mid-Term Exams, 30% total [15% each]
  • Final Two-Hour Exam, 30%

Approximate Grading Scheme. A: 90 and up; B: 80-89; C: 70-79. Pluses/minuses (As in A-, B+, etc.) will mostly be decided on a case-by-case basis.

Missed work. The general rule: no make-up exams or quizzes, and no late submissions of homeworks or the project (but early submissions, especially in electronic format, are welcome). Emergencies will be handled on a case-by-case basis. If you miss the final exam, with a valid excuse, you get an incomplete in the class; an incomplete is a major inconvenience for a number of people, including yourself, so, please, do not miss the final.

To encourage and reward consistent performance throughout the semester, I will not automatically drop any scores (such as the two lowest quizzes, etc.)

Students Requiring Special Accommodation
Any student requesting academic accommodations based on special needs is required to register with Office Of Student Accessibility Services (OSAS) each semester. A letter of verification for approved accommodations can be obtained from OSAS. Please be sure the letter is delivered to me (or to TA) as early in the semester as possible. OSAS is located in GFS 120. To contact OSAS: (213) 740-0776 [tel.], OSASFrontDesk@usc.edu [e-mail], on the web.

Academic Integrity
USC seeks to maintain an optimal learning environment. General principles of academic honesty include the concept of respect for the intellectual property of others, the expectation that individual work will be submitted unless otherwise allowed by an instructor, and the obligations both to protect one’s own academic work from misuse by others as well as to avoid using another’s work as one’s own. All students are expected to understand and abide by these principles. Scampus (the Student Guidebook) contains the Student Conduct Code in Section 11.00, while the recommended sanctions are in Appendix A.

FINAL EXAMINATION POLICIES

Student Scheduling Conflicts
No student is permitted to omit or take the final examination before the rest of the class and no instructor is authorized to permit a student to do so.

Students should plan in advance to avoid scheduling conflicts in their final examinations. If a student is scheduled for two final examinations at the same time, the student should request to take one of the examinations on a different day or time. If a student is scheduled for more than two final examinations in one calendar day, the student may request to take one of the exams on a different day or time. In either situation, the student must contact the professors involved no later than two weeks prior to the scheduled examination date and request an accommodation. If an accommodation cannot be arranged, the student should contact USC Testing Services at testing@usc.edu or (213) 740-7166 for assistance.

Ggrades are due 96 hours after the university-scheduled final examination day and time. Therefore, it might not be possible to accommodate late student requests for an alternate, makeup final examination after the published examination period.

Academic Support The Kortschak Center for Learning and Creativity

Supplementary materials

Sample exams

Earlier MT1s     MT1-S2022   MT1-F2022  MT1-F2024

Earlier MT2s    MT2-S2022   MT2-F2022  MT2-F2024

Earlier Finals    Final-S2022  Final-F2022 Final-F2024

Other materials

My notes

Other Notes and Illustrations

More

USC Math Department Homepage