CRN 11547

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  • Time and Place. TR 13:30-14:50 in LART 206
  • Office Hours. TR 15:00-16:30, or by appointment.
  • Teaching Assistant: Mr. Bethuel Khamala. Office hours: T 14:00-15:00 and W 8:00-9:00 in PHYS 123.
  • Prerequisites. I will assume that you have a thorough knowledge of the material covered in the three courses of the Calculus sequence.
  • Course Content. The course will cover the following material:
    • Vector Differential Calculus. Grad, Div, Curl.
    • Vector Integral Calculus. Integral Theorems.
    • Complex Numbers and Functions. Complex Differentiation and Integration.
  • Homework. I will regularly assign homework. Some homework will be turned in and (at least partially) graded. Other homework will be presented in class by student volunteers. Homework will account for 10%+15%=25% of your grade.
  • Tests. Exams will be given on the following dates: Thursday, October 5, and Tuesday, November 21. Each exam counts 25% of your grade.
  • Make-up Exams. Make-up tests will only be given under extraordinary circumstances, and only if you notify the instructor prior to the exam date.
  • Final exam. The final on Thursday, December 14, 13:00-15:45, is mandatory and comprehensive. It counts 25% of your grade.
  • Grades. Your grade will be based on the percentage of the total points that you earn during the semester. You need at least 90% of the points to earn an A, at least 80% for a B, at least 70% for a C, and at least 60 % for a D.
  • Calculators. You may use a non-graphing calculator (not a cell phone, tablet, etc.) during tests and the final. If you have doubts about whether your calculator qualifies, ask me before the first test.
  • Time Requirement. I expect that you spend an absolute minimum of six hours a week outside of class on reading the textbook, preparing for the next class, reviewing your class notes, and completing homework assignments. Not surprisingly, it has been my experience that there is a strong correlation between class grade and study time.
  • Attendance. You are strongly encouraged to attend class every day. I expect you to arrive for class on time and to remain seated until the class is dismissed.
  • Drop Policy. The class schedule lists Friday, November 3, as the last day to drop with an automatic "W". After the deadline, I can only drop you from the course with a grade of "F". All students at any Texas public college or university are limited to six course withdrawals (drops) during their academic career. Drops include those initiated by students or faculty and withdrawals from courses at other institutions! This policy does not apply to courses dropped prior to census day or to complete withdrawals from the university.
  • Students with Disabilities. If you have a disability and need classroom accommodations, please contact The Center for Accommodations and Support Services (CASS) at 747-5148, or by email to, or visit their office located in UTEP Union East, Room 106. For additional information, please visit the CASS website at
  • Academic Integrity. All students must abide by UTEP's academic integrity policies, see for details. Please note that you may not leave the classroom during a test.

Written Homework

  • due 12/7: 2-16; 3-12,15; 4-7,9
  • due 10/31: 163-3,4; 164-7,9,11
  • due 10/26: 149-8,9; 155-2,4,10
  • due 10/3: 82-22,26,27; 142-14,15
  • due 9/28: 58-10,12,14; 63-6,12
  • due 9/19: 19-20,26; 29-14;30-27;39-20

Homework (in class)

Open Problems: 142-10; 155-9; 164-6; 1-2,3,5,9a,10,12; 2-5,8,10,14

  • 11/30: 3-1,3,4,9,11,12,16b,17; 4-1,6
  • 11/28: 1-1,2,3,5,7ae,9a,10,12; 2-5,8,10,14
  • 11/14: Find a potential for the vector field \((y z^2)\, \vec{\imath} +(x z^2-2 y z+2)\, \vec{\jmath} +(2 x y z-y^2-2 z)\, \vec{k}\).
  • 11/2: 176-2,4,10,12
  • 10/19: 163-2,164-6,8
  • 10/12: 155-2,5,6,8,9
  • 9/28: 149-2,4,7
  • 9/26: 142-2,4,8,10
  • 9/21: 63-2,4; 82-5,12,16,26
  • 9/12: 46-2,5,6,10,13; 50-2,4,6,8,12; 57-2,6; 58-16
  • 9/5: 39-2,5,8,10,11,17,19,21
  • 8/31: 29-1,2,5,8,12,16,23,28
  • 8/29: page 8-5;14-1hj,4,6; 18-2; 19-4,10,18,22,25


Formula sheet for Test 2 | Planimeter I | Planimeter II | Formula sheet for Test 1 | Parametrization by Arclength PDF version | Quadric Surfaces PDF version


Advanced References

  • Lars Ahlfors. Complex Analysis, McGraw-Hill, 3rd edition.
  • Henri Cartan. Elementary Theory of Analytic Functions of One or Several Complex Variables, Dover.
  • Bruce P. Palka. An Introduction to Complex Function Theory, Springer.
  • Michael Spivak. Calculus on Manifolds: A Modern Approach To Classical Theorems Of Advanced Calculus, Westview Press.
  • Dirk Struik. Lectures on Classical Differential Geometry, Dover, 2nd edition.
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