**Instructor**: Paul Jenkins

**Office**: 282 TMCB, 801-422-5868

**Email**: jenkins@math.byu.edu

**Lecture**: 2:00-2:50 PM MWF, 3104 JKB

**Office hours**: 1:00-1:50 PM MWF or by appointment

**Textbook**: Stewart, Multivariable Calculus, 8th edition, ISBN 978130526664-3 (hardcover) or 978130565423-5 (loose leaf).

Homework assistance is also available in the Math Lab, 159 TMCB.

**Grading**: Homework 30%, three midterms 15% each, final exam 25%. Grades will be available on BYU Learning Suite.

**Exams**: In the testing center on September 21-23, October 14-17, and November 9-11. The final exam will be in the testing center from December 10-15. The final exam will cover all material studied this semester.

**Homework**: Homework will be assigned each day throughout the semester, and will be due at 4:30 PM in the box outside my office on the class day after it is assigned. Homework assignments will be posted on the course webpage. Your homework should be neat and should include enough detail that another student from the class could follow your arguments. Homework that is not stapled, is excessively sloppy, or is written on paper torn from a spiral notebook may receive less than full credit. Late homework will not be accepted. Working in groups on homework is encouraged, but each student should write up each problem, without looking at other students’ written solutions. The lowest three homework assignments will be dropped.

**Electronic devices**: Do not use mobile phones or permit them to ring during class. Calculators may be used on homework; if you use a calculator or computer, you should indicate this.

**Prerequisites**: Math 113 (Calculus 2). In addition, you should be able to do the following without referring to calculators or written notes:

- Know trigonometric, logarithmic, exponential, and polynomial integration and differentiation.
- Know how to use the chain rule, product rule, etc.
- Be familiar with the following integration techniques: integration by parts, u-substitution, trigonometric substitution.
- Know how to compute determinants.
- Be familiar with elementary trigonometric identities.

**Minimal learning outcomes**: See https://www.math.byu.edu/wiki/index.php/Math_314:_Calculus_of_Several_Variables. Students should achieve mastery of the topics listed below. This means that they should know all relevant definitions, full statements of the major theorems, and examples of the various concepts. Further, students should be able to solve non-trivial problems related to these concepts, and prove simple theorems in analogy to proofs given by the instructor.

- Vectors and vector functions
- Compute vector operations
- Describe lines and planes in space
- Identify standard quadratic surfaces
- Describe parametric curves as vector functions
- Compute and interpret the derivative of a vector function
- Apply vector functions to curvilinear motion

- Derivatives of functions of several variables
- Compute and interpret partial derivatives
- Use the gradient to find directional derivatives and normal vectors
- Find local and global extrema
- Solve optimization problems involving several variables
- Use the method of Lagrange to find extrema under constraints

- Multiple integrals
- Know and apply Fubini’s theorem to express multiple integrals as iterated integrals
- Change the order of integration
- Transform integrals to polar, cylindrical, and spherical coordinates
- Use multiple integrals to find area, volume, mass, center of mass, and other applications
- Use the Jacobian of a coordinate change to transform integrals

- Line and surface integrals
- Evaluate line integrals
- Use line integrals to compute work and circulation
- Use surface integrals to compute surface area and flux
- Set up and use integrals over parametric surfaces

- Divergence and curl
- Explain and interpret divergence and curl
- Know and apply the divergence theorem
- Know and apply Stokes’ theorem
- Use the divergence and curl tests to describe properties of vector fields

This is a 3 credit class. The BYU Catalog states that “The expectation for undergraduate courses is three hours of work per week per credit hour for the average student who is appropriately prepared; much more time may be required to achieve excellence.” Thus, an average student should expect to spend at least 6 hours per week outside of lecture on working problems, reading the textbook, reviewing concepts, and completing assignments.

**Preventing Sexual Harassment**: Title IX of the Education Amendments of 1972 prohibits sex discrimination against any participant in an educational program or activity that receives federal funds. The act is intended to eliminate sex discrimination in education and pertains to admissions, academic and athletic programs, and university-sponsored activities. Title IX also prohibits sexual harassment of students by university employees, other students, and visitors to campus. If you encounter sexual harassment or gender-based discrimination, please talk to your professor, contact the Equal Employment Office at 801-422-5895 or 1-888-238-1062 (24 hours) or http://www.ethicspoint.com, or contact the Honor Code Office (4440 WSC) at 801-422-2847.

**Students with Disabilities**: BYU is committed to providing reasonable accommodation to qualified persons with disabilities. If you have any disability that may adversely affect your success in this course, please contact the University Accessibility Center office (2170 WSC) at 801-422-2767. Services deemed appropriate will be coordinated with the student and instructor by that office.

**Honor Code**: In keeping with the principles of the BYU Honor Code, students are expected to be honest in all of their academic work. Academic honesty means, most fundamentally, that any work you present as your own must in fact be your own work and not that of another. Violations of this principle may result in a failing grade in the course and additional disciplinary action by the university. Students are also expected to adhere to the Dress and Grooming Standards. It is the university's expectation, and my own expectation in class, that each student will abide by all Honor Code standards. Please call the Honor Code Office (4440 WSC) at 801-422-2847 if you have questions about those standards.