Vector Calculus 5th edition, by J. E. Marsden and A. J. Tromba

MTH 437 Advanced Calculus and Application I

Fall 2016 - Course Webpage
James Baglama
Office: Lippitt Hall 200
Department of Mathematics
Phone: 401.874.2709

Vector Calculus 5th edition, by J. E. Marsden and A. J. Tromba


MTH 437 Syllabus

MTH 437 Fall 2016 Course Calendar



Course and Section number: MTH 437 Section 01
Course Title: Advanced Calculus and Application I
Semester and Year: Fall 2016
Class Day(s)/Time:: MWF, 10:00am to 10:50am
Class Location: Lippitt Hall 204
Instructor: James Baglama
Office Location: Lippitt Hall 200
Office Hours: MW 11:00am to 11:50am
Contact Information Phone:401.874.2709 and

Course Description: LEC: (3 crs.) Sequences, limits, continuity, differentiability, Riemann integrals, functions of several variables, multiple integrals, space curves, line integrals, surface integrals, Green's theorem, Stokes' theorem, series, improper integrals, uniform convergence, Fourier series, Laplace transforms. Applications to physics and engineering emphasized.

Prerequisite(s): MTH 243, credit or concurrent enrollment in MTH 215 or 362

General Education Area(s) and Outcome(s): None

Credit Hours: 3

Required Textbook(s): Vector Calculus 5th edition by J. E. Marsden and A. J. Tromba

Other Required Material(s): You may use a calculator for homework and exams to do routine calculations. You will need to use Octave or Matlab for the project(s). Octave online:

Course Goals: This course is intended for students to become proficient with vector calculus operations in order to solve problems in mathematical sciences, engineering, and physics.

Learning Outcomes: At the end of the course the student should be able to:

  1. perform the vector calculus operations (addition, subtraction, scalar multiplication, dot product, and cross product);
  2. interpret and create 3d plots and 2d/3d contour diagrams;
  3. calculate partial and directional derivatives, gradients and differentials of function of several variables;
  4. calculate critical points, use the second derivative test to determine local extrema and saddle points;
  5. solve unconstrained optimization problems and use Lagrange multipliers to solve constrained optimization problems;
  6. represent and interpret plots of vector fields and compute the flow of a vector field;
  7. calculate the curl of a vector field;
  8. calculate double and triple integrals algebraically and change variables in integrals as needed;
  9. use technology to analyze methods, perform calculations, and produce graphical representation of functions to investigate their properties;
  10. communicate effectively in written form mathematical ideas and conclusions, by stating in a complete, clear, concise, and organized manner steps, calculations, solution strategy, conclusions, and when appropriate, interpreting results in practical or applied terms.

Grade Distribution:
10% Project(s) Details for project(s) will be in Sakai
10% Homework See calendar below
50% Exams Two exams (10/19 and 12/7)
30% Final Exam Monday Dec. 19 from 8am - 11am in Lippitt 204

Letter Grade Distribution:
94.00 - 100.00 A 73.00 - 76.99 C
90.00 - 93.99 A- 70.00 - 72.99 C-
87.00 - 89.99 B+ 67.00 - 69.99 D+
83.00 - 86.99 B 60.00 - 66.99 D
80.00 - 82.99 B- 0.00 - 59.99 F
77.00 - 79.99 C+

Instructor Policies for the Course:

  • Assignments
    Homework will be assigned for section of the textbook we cover. A list of homework problems is posted on this website. Do NOT email your homework to me! Homework must have
    • your name
    • chapter and section number
    • list of problems assigned
    • complete solution (answers only will be given no credit)
    • multiple pages stapled
    If I cannot read it or follow the solution, then it is marked incorrect. I will not accept ANY late or incomplete homework assignments.
  • Attendance
    Attendance is a vital and necessary part of this course. While there is no formal attendance policy, we cover a lot of information at a rapid pace; missing a class will result in a large amount of material missed. Students are responsible for all missed work, regardless of the reason for absence. It is also the absentee's responsibility to get all missing notes or materials.
  • Expectations
    • You are expected to attend every lecture, and to submit your work on time. Late homework is not accepted.
    • It is your responsibility to communicate clearly in writing up solutions for homework, projects, and exams. Your results must display your understanding well and be written in a correct, complete, coherent, and well organized fashion. The rules of language still apply in mathematics, and they apply even when symbols are used in formulas, equations, etc.
    • The rapid pace of the class requires that you spend time every day doing homework, reviewing notes, reading the textbook, and working out extra problems, all in addition to the time spent in class.
  • Makeup Policy
    Makeup exams may be scheduled in the event you are unable to attend exams under the following conditions. In particular, if you must miss the exam because of a scheduling con ict, you must notify your instructor before, not after, the exam, and emergencies require you to contact your instructor within 24 hours. See University Manual sections 8.51.10 to 8.51.14 for guidelines.
    • If your reason for missing the exam as scheduled is (i) a University sanctioned event for which verifiable documentation can be provided (including another scheduled class), (ii) a responsibility to an employer that cannot be rescheduled (with documentation from your employer), or (iii) Religious holidays, then you MUST INFORM YOUR INSTRUCTOR 48 HOURS IN ADVANCE OF THE EXAM AND PROVIDE DOCUMENTATION IF REQUESTED. Makeup exams will be scheduled after the actual exam, and preferably before the class period when exams are to be handed back, but no later than one week after the original date.
    • If the reason for missing the exam as scheduled is due to (i) illness (with verifiable documentation from a medical provider), or (ii) an emergency (with appropriate doc- umentation), then you MUST INFORM YOUR INSTRUCTOR WITHIN 24 HOURS OF THE EXAM and provide documentation upon your return. Failure to notify your instructor within 24 hours will result in a 0 for the exam. No exceptions. Makeup ex- ams may be scheduled no later than a week after the original date, unless the illness or emergency precludes this, in which case the makeup exam will be given on a common date during the last two weeks of the semester.
    Students that miss course work (not exams) under the same the conditions mentioned above will be given the opportunity to make up the course work.
  • Electronic Devices
    Cell phones, ipads, ipods, etc. should be turned off during class. Excepted from this are electronic pads used for notetaking.
  • Other Policies
    • All class materials (e.g. notes, projects, exams, lectures, etc.) are property of URI and the instructor. Copying, video taping, taking pictures, or posting this material is not allowed without consent of the instructor and URI.
    • Please come to class prepared by reading over the text to be covered and by bringing your book, notebook and pencil. Pencils only please.
    • You are here to learn, so please give class your full attention, ask questions if you do not understand and be respectful and courteous to your fellow students and professor.

Academic Honesty Policy: Cheating is defined in the University Manual section 8.27.10 as the claiming of credit for work not done independently without giving credit for aid received, or any unauthorized communication during examinations. Students are expected to be honest in all academic work. The resolution of any charge of cheating or plagiarism will follow the guideline set forth in the University Manual 8.27.10-8.27.21,

Special Needs: Any student with a documented disability should contact your instructor early in the semester so that he or she may work out reasonable accommodations with you to support your success in this course. Students should also contact Disability Services for Students: Office of Student Life, 330 Memorial Union, 401-874-2098. They will determine with you what accommodations are necessary and appropriate. All information and documentation is confidential.

Incomplete Grade: University of Rhode Island regulations concerning incomplete grades will be followed. See University Manual sections 8.53.20 and 8.53.21 for details.

Religious holidays: It is the policy of the University of Rhode Island to accord students, on an individual basis, the opportunity to observe their traditional religious holidays. Students desiring to observe a holiday of special importance must provide written notification to each instructor.

Standards of behavior: Students are responsible for being familiar with and adhering to the published Community Stan- dards of Behavior: University Policies and Regulations" which can be accessed in the University Student Handbook ( If you must come in late, please do not disrupt the class. Please turn off all cell phones or any electronic devices.


Fall 2016 Course Calendar

The weekly coverage might change as it depends on the progress of the class. Homework problems are required to be handed in and will be graded.

Week Content Homework Problems
Week 1 (9/7 - 9/9)
First Day 9/7
  • Section 1.1: 1, 4, 6, 9, 12, 14, 16, 18, 19 Due: 9/14
Week 2 (9/12 - 9/16)
  • Section 1.2: 3, 5, 6, 10, 14, 18, 21, 23 Due: 9/19
  • Section 1.3: 4, 6, 7, 9, 10, 15c, 16c, 20 Due: 9/23
Week 3 (9/19 - 9/23)
  • Section 1.4: 1, 8 Due: 9/28
  • Section 1.5: 1, 2a, 7, 17 Due: 9/28
Week 4 (9/26 - 9/30)
  • Section 2.1: 1, 2a, 5, 9, 11, 14 Due: 10/3
  • Section 2.2: 5, 6bc, 10, 16a Due: 10/12
Week 5 (10/3 - 10/7)
Friday Oct. 7
Q&A on homework
No lecture
  • Section 2.3: 1, 2b, 5, 7c, 15 Due: 10/17
  • Section 2.4: 2, 3, 7, 9, 16Due: 10/19
Week 6 (10/10 - 10/14)
No Classes 10/10
  • Section 2.5: 5b, 9, 10, 11 Due: 10/26
Week 7 (10/17 - 10/21)
Last day drop 10/19
  • Section 2.6: 2a, 3a, 4a, 6a, 12, 15 Due: 10/28
Week 8 Friday 10/28
Adjusted schedule
  • Section 2.6: 2a, 3a, 4a, 6a, 12, 15 Due: 11/2
Week 9 (10/31 - 11/4)
  • Section 3.1: 2, 3, 5, 9, 19 Due: 11/4
    (#24 - +5pts extra credit added to homework)
  • Section 3.2: 2, 5 Due: 11/9
Week 10 (11/7 - 11/11)
No Classes 11/11
  • Section 3.3: 1, 3, 8, 12, 23, 33 Due: 11/17
Week 11 (11/14 - 11/18)
  • Section 3.4: 2, 4, 12, 23ab(only) Due: 11/23
  • Section 4.1: 1, 5, 7, 11 Due: 11/30
    (#20 - +5pts extra credit added to homework)
Week 12 (11/21 - 11/25)
No Classes 11/24-11/25
  • Section 4.2: 3, 5, 7 Due: 12/2
Week 13 (11/28 - 12/2)
Adjusted schedule
  • Section 4.2: 3, 5, 7 Due: 12/2
  • Section 4.3: 5, 6, 11 Due: 12/7
Week 14/15 (12/5 - 12/9, 12/12)
Last Day 12/12
  • Section 4.4: 3, 9, 14, 21 Due: 12/9
  • Section 5.2: 1c, 2a, 6
Final Exam Monday Dec. 19 from 8am - 11am in Lippitt 204