Eastern Iowa Community College District

EASTERN IOWA COMMUNITY COLLEGE DISTRICT CLINTON COMMUNITY COLLEGE

MATH 219 SECTION NUMBER 45022

MEETING TIMES: 8:00 - 10:00am MTWTHF ROOM 140

INSTRUCTOR: Elizabeth Wood OFFICE: 156 G PHONE: (563) 244 - 7134 EMAIL: [email protected]

WEBSITE: http://faculty.eicc.edu/bwood

OFFICE HOURS: 1:00 – 2:00 p.m. MTWTHF AND BY APPOINTMENT COURSE DESCRIPTION: Continuation of Calculus and Analytical Geometry II. The final course in the series. Topics include vector-valued functions, solid analytic geometry, moments, partial derivatives, and multiple integrals. Graphic calculator required.

PRE-REQUISITE: Math 155, Calculus and Analytic Geometry II

CO-REQUISITE none

REQUIRED TEXT: Thomas’ Calculus, 11 th ed., by Weir, Hass, Giordana

OTHER MATERIALS: TI- 82 / TI - 83 or TI- 85 / TI - 86 calculator (The TI - 89 / TI- 92 calculator can be used in this course.)

GENERAL COURSE GOALS: Upon the completion of this course, the student will be able to: 1. Define functions of two, three, or more variables and describe the domain of definition of such functions. 2. Define locate level curves and surfaces of such functions. 3. Define the concept of limit for functions of two or more variable; find limits of such functions; be able to show whether the limit exists. 4. Define and investigate the continuity of functions of two or more variables. 5. Define and calculate partial derivatives including first order partial derivatives, higher order derivatives, and mixed partial derivatives. Describe properties and physical meaning and applications of such derivatives. 6. Describe and use the chain rule for partial derivatives. 7. Define and calculate the directional derivatives and the gradient of a function. Describe the physical meaning and applications of the gradient. 8. Define the total differential. 9. Solve problems involving the tangent plane approximation. 10. Find relative minima, relative maxima, and saddle points. 11. Solve problems involving Lagrange Multipliers. 12. Define the concept of multiple integrals. 13. Set up multiple integrals, supply the limits of integration, and carry out the integration in a variety of situations including: A. Functions in two variables in 1. Rectangular coordinates 2. Polar coordinates B. Functions in three variables in 1. Rectangular coordinates 2. Cylindrical coordinates 3. Spherical coordinates 14. Apply multiple integrals to problems involving area, volume, moments, centers of mass, and other applications. 15. Use the Jacobian to change variables in integrals. Transform from one coordinate system to another. 16. Define the concept of a vector field. 17. Define the concepts of gradient, divergence, and curl of a vector field. Calculate example of these quantities. Find a function with a given gradient. 18. Describe conditions under which a vector field can be expressed as the gradient of a scalar function 19. Calculate the line integrals in various circumstances. 20. Describe conditions under which the line integral is independent of path. 21. Evaluate surface integrals over various flat, curved, open, and closed surfaces. 22. Describe and make use of various theorems involving vector fields including: A. Green’s theorem B. Stoke’s theorem C. The Divergence theorem 23. Apply vector field concepts to selected applications chosen from problems involving force, energy, flux, electric and magnetic fields, Gauss’s law, and/or Maxwell’s Equations.

GRADING: A point system is used. It will be based on 6 take-home exams worth 75 - 150 points each. I will try to make them 100 points each. NO LATE TAKE-HOME EXAMS WILL BE ACCEPTED. EACH TAKE HOME EXAM WILL BE DUE BY 2:30 p.m. OF THE DATE STATED. ATTENDANCE: Attendance is mandatory for the following reasons: 1. Corrections, additions, and deletions to the textbook material are announced in the lecture. 2. Although test problems are similar to those in the textbook, it is often the case that an exam contains problems posed and completely solved in class. 3. Changes in the syllabus, schedule, exam dates, etc. are announced in lecture and thus become official without further notice. If you must miss class for an “appropriate” reason and let me know before hand, (talking to me or via a written or phone message), then the absence will be excused.

EXAMPLE GRADING SCALE: 6 TAKE-HOME EXAMS 600 POINTS A plus/minus grading system will be used.

100 – 90% A 89 – 80% B 79 – 70% C 69 – 60% D 59% and below F

TAKE-HOME EXAM FORMAT: 1. All homework must be done on loose- leaf notebook paper. 2. If the homework is more than one page, please staple or paper-clip them together in the upper left hand corner. 3. Writing must by legible. If I cannot read it, then I will not grade it. 4. Make sure your name is on the assignment. ACADEMIC DISHONESTY Cheating on exams or copying of homework will not be tolerated and will result in a grade of zero for the assignment. Cheating on an exam will not be tolerated, and if caught, the student will be turned into the appropriate college official for disciplinary actions.

This course is going to move at a fast pace. If possible, try to keep up in the homework. When possible, I may cover more than the assigned sections; hence attending every day is strongly suggested. Each take home exam will be due by 2:30 p.m. of the data stated. DATE SECTION NOTES May 27 12.1/12.2 12.3/12.4 28 12.4/12.5 Exam 1 given (Chapter 12) 29 12.5/12.6 30 13.1 June 2 13.2/13.3 3 13.3/13.4 Exam 1 due 4 13.4/13.5 Exam 2 given (Chapter 13) 5 13.5 6 14.1 9 14.2 10 14.3 Exam 2 due 11 14.4 Exam 3 given (14.1 – 14.9) 12 14.9 13 14.5 16 14.6 Exam 3 due 17 14.7 Exam 4 given (14.5 – 14.8) 18 14.8 19 15.1 20 15.1 23 15.3 Exam 4 due 24 15.1/15.2 25 15.2/15.3 Exam 5 given (15.1 – 15.5 ) 26 15.3/15.4 27 15.4/15.5 30 15.5/15.6 July 1 15.6/15.7 2 16.1/16.2 3 16.3/16.4 Exam 5 due 7 16.5 Exam 6 given (15.6 – 15.7, Chapter 16) 8 16.7/16.8 9 Workday 10 Workday 11 Workday 14 Workday No class 15 Workday No class July 16 Workday Exam 6 due