University of Rhode Island Department of Mathematics Fall 2018

**MTH 243-02 Calculus for Functions of Several Variables**

**Instructor**: Prof. Orlando Merino, merino@uri.edu, Lippitt 200F, 874 4442

**Text**: Mc Callum, Hughes-Hallet, et al, *Calculus Multivariable* 6th edition, Wiley, with *WileyPlus*.

**Prerequisites**: MTH 142 or equivalent

**About the course** MTH 243 is a third calculus course, with focus on functions of several variables, and extensions of the ideas of elementary calculus to higher dimension. The concepts and ideas in this class apply in many fields of study, for example economics, finance, epidemiology, quantum mechanics, planetary motion, optimization, all engineering fields, physical chemistry. In this course we will use the Mathematica software, which is available for URI students. Also, we will be using WileyPlus online homework system this semester. To sign up for the WileyPlus system, you will need a WileyPlus registration code. If you buy a copy of our textbook at the URI Bookstore, a registration code for WileyPlus will be included with the book at no additional cost. If you buy a copy somewhere else and it does not include WileyPlus code, you will need to purchase a WileyPlus code separately.

At the conclusion of this semester you will be able to:

- Read and interpret 3d plots and 2d/3d contour diagrams, read and interpret tables of functions of several variables, and plot by hand the graph of simple functions of 2 variables, and simple contour plots of 2 or 3 variables.
- Do calculations with vectors that involve the concepts of addition, scalar multiplication, dot product, cross product, magnitude, projection, and use these concepts in geometry and physics applications.
- Calculate partial and directional derivatives, gradients and differentials of function of several variables, use local linearization to approximate functions,
- Calculate critical points, use the second derivative test to determine local extrema and saddle points (for functions of two variables only), use these concepts to solve unconstrained optimization problems, and use Lagrange multipliers to solve constrained optimization problems.
- Calculate double and triple integrals algebraically, change variables in integrals from rectangular coordinates to polar, cylindrical, spherical coordinates and viceversa.
- Use the concept of parametrization.
- Represent and interpret plots of vector fields (including flow lines)
- Use vector valued functions to do calculations of line integrals, and apply Green's theorem.

**Evaluation** There will be two exams and a comprehensive final exam. The course grade will be computed as follows:

**Course grade = ( 100 E1 + 100 E2 + 150 FE + 75 CW +75 WP) / 500**

Key: **E1** and **E2** correspond to Exams, **FE** = Final Exam, **CW** = Class Homework or quizzes, **WP** = WileyPlus hw.

Class Work may include collected homework, quizzes, Mathematica assignments or special projects.

The course material discussed after the second exam will be heavily represented in the final exam.

**Special Accomodations** Students who need special accomodations and who have documentation from Disability Services (874-2098) should make arrangements with the instructor as soon as possible.

**Letter grades** will be distributed based on the following scale: Grade A 93.00-100.00, A- 90.00-92.99, B+ 87.00-89.99, B 83.00-86.99, B- 80.00-82.99, C+ 77.00-79.99, C 73.00-76.99, C- 70.00-72.99, D+ 67.00-69.99, D 60.00-66.99, F 59.99 and lower

**Expectations:** 1. You are expected to attend every lecture, and to submit your work on time. 2. It is your responsibility to communicate clearly in writing up solutions for homework, quizzes, 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. Precise communication and neatness count! 3. 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.

**Exam Makeup Policy**: Makeup exams may be scheduled in the event you are unable to attend the evening exams under the following conditions. In particular, if you must miss the exam because of a scheduling conflict, you must notify your instructor before, not after, the exam, and emergencies require you to contact your instructor within 24 hours. 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), or (ii) a responsibility to an employer that cannot be rescheduled (with documentation from your employer), 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 documentation), 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 exams 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.