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MATH 528 Mathematical Methods for the Physical Sciences I Fall 2015 Instructor: Daniel M. Harris E-mail: [email protected] Office: Phillips 307A Office Hours: MW 2:00 - 4:00 pm, and by appointment Website: harris.web.unc.edu/teaching/math528/ Course Meets: TR 11:00 am - 12:15 pm in Phillips 381 Text: E. Kreyszig, Advanced Engineering Mathematics, Tenth Edition. Prerequisites: MATH 383 (Differential Equations). Grades: Homework = 20% (10% for completion, 10% graded questions) Two Midterm Exams = 50% (25% each) Cumulative Final Exam = 30% Optional Course Project = Up to 5% extra credit Homework Policy: Assignments will be posted on the course website and collected on the specified due date at the beginning of lecture. The lowest individual homework score will be dropped. Late homework is devalued by 50% if handed in within one week of the due date, and not accepted one week past the due date. Exceptions are made for university-sponsored activities and documented health or personal reasons. Collaboration on homework is allowed and encouraged, however, each student must submit an individual assignment. Any collaborators must be listed on the first page of your assignment. Exam Policy: There will be two in-class midterm exams, and one final exam. Your final exam score will replace the lower of your two midterm exam scores if it is to your advantage. No make-up examinations will be given. If you have an excused absence from one midterm exam then you will be given the score that you earn on the final exam. You will be allowed two 8.5 × 11 00 sheets of notes (both sides) for each midterm, and four 8.5 × 11 00 sheets for the final exam. No calculators or other electronics allowed. Optional Course Project: For up to 5% added to your overall course grade, you may submit a short report (no more than 5 pages) discussing any application of ODEs in a physical system that you find interesting. The topic or model does not need to be excessively complex. This can be an original topic, or a review of an existing application. To receive credit, the topic must first be approved by the course instructor via email. A digital and paper copy of the report should be submitted to the course instructor anytime before the last regular lecture of the course. Points will be awarded based on the technical discussion as well as overall creativity. Be certain to appropriately cite any references.

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Page 1: MATH 528 Mathematical Methods for the Physical Sciences …harris.web.unc.edu/files/2015/08/528-syllabus.pdf · MATH 528 Mathematical Methods for the Physical Sciences I Fall 2015

MATH 528Mathematical Methods for the Physical Sciences I

Fall 2015

Instructor: Daniel M. HarrisE-mail: [email protected]: Phillips 307AOffice Hours: MW 2:00 - 4:00 pm, and by appointment

Website: harris.web.unc.edu/teaching/math528/

Course Meets: TR 11:00 am - 12:15 pm in Phillips 381

Text: E. Kreyszig, Advanced Engineering Mathematics, Tenth Edition.

Prerequisites: MATH 383 (Differential Equations).

Grades:Homework = 20% (10% for completion, 10% graded questions)Two Midterm Exams = 50% (25% each)Cumulative Final Exam = 30%Optional Course Project = Up to 5% extra credit

Homework Policy: Assignments will be posted on the course website and collectedon the specified due date at the beginning of lecture. The lowest individual homeworkscore will be dropped. Late homework is devalued by 50% if handed in within one weekof the due date, and not accepted one week past the due date. Exceptions are made foruniversity-sponsored activities and documented health or personal reasons. Collaborationon homework is allowed and encouraged, however, each student must submit an individualassignment. Any collaborators must be listed on the first page of your assignment.

Exam Policy: There will be two in-class midterm exams, and one final exam. Yourfinal exam score will replace the lower of your two midterm exam scores if it is to youradvantage. No make-up examinations will be given. If you have an excused absence fromone midterm exam then you will be given the score that you earn on the final exam. Youwill be allowed two 8.5 × 11′′ sheets of notes (both sides) for each midterm, and four8.5 × 11′′ sheets for the final exam. No calculators or other electronics allowed.

Optional Course Project: For up to 5% added to your overall course grade, you maysubmit a short report (no more than 5 pages) discussing any application of ODEs ina physical system that you find interesting. The topic or model does not need to beexcessively complex. This can be an original topic, or a review of an existing application.To receive credit, the topic must first be approved by the course instructor via email. Adigital and paper copy of the report should be submitted to the course instructor anytimebefore the last regular lecture of the course. Points will be awarded based on the technicaldiscussion as well as overall creativity. Be certain to appropriately cite any references.

Page 2: MATH 528 Mathematical Methods for the Physical Sciences …harris.web.unc.edu/files/2015/08/528-syllabus.pdf · MATH 528 Mathematical Methods for the Physical Sciences I Fall 2015

Important Dates:Midterm 1: Thursday, October 1 (in class)Last day to drop a class: Monday, October 12Fall break: Thursday, October 15 (no class)Midterm 2: Thursday, November 12 (in class)Thanksgiving: Thursday, November 26 (no class)Optional course project due: Tuesday, December 1Final exam: Thursday, December 10 at 12pm

Course Topics:

• Overview of Ordinary Differential Equations (Ch. 1, 2)

• Introduction to Numerical Methods for ODEs (Ch. 21.1-3)

• Linear and Nonlinear Systems of ODEs (Ch. 4)

• Laplace Transform Methods (Ch. 6)

• Series Solutions and Special Functions (Ch. 5)

• Fourier Series Methods (Ch. 11)

The website will be updated regularly with the specific topics and sections covered in eachlecture.

Honor System: It is expected that each student in this class will conduct herself orhimself within the guidelines of the Honor System. All academic work should be donewith the complete honesty and integrity that this University demands. In this regard,you may work with others on the homework, but the written work you turn in must beyour own.

The instructor reserves the right to make changes to the syllabus. Any changes will beannounced as early as possible.