Math 2210 - 4 Calculus III April 15, 2019 Credit Hours: Three Meeting Time: MWF 11:50 - 12:40 AM in CSC 208 Homepage: http://www.math.utah.edu/~treiberg/M2210.html Instructor: Prof. A. Treibergs, JWB 224, 581 - ­8350. Office Hours: MWF 12:45 - 1:45 (tent.) & by appt. E-mail: treiberg@math.utah.edu Prerequisites: ”C” or better in (MATH 1220 OR MATH 1250 OR MATH 1320) OR AP Calculus BC score of at least 4. Text: Calculus with Differential Equations, by Varberg, Purcell, and Rigdon (9th edition) For information on purchasing the textbook, go to http://www.math.utah.edu/schedule/bookInfo/ Course Description: Vectors in the plane and in 3-space, differential calculus in several variables, integration and its applications in several variables, vector fields and line, surface, and volume integrals. Green’s and Stokes’ theorems. Topics: We cover chapters 11-14, with a brief review of parametric equations from chapter 10. Chapter 10 - Parametric Representation of Curves. 10.4 (1-2 classes) Chapter 11 - Geometry in Space and Vectors. 11.1-11.6, 11.7, 11.8, 11.9 (10-12 classes) Chapter 12 - Derivatives for Functions of Two or More Variables. 12.1-12.9 (8-10 classes) Chapter 13 - Multiple Integrals. 13.1-13.4, 13.5∗, 13.6-13.9 (9-11 classes) Chapter 14 - Vector Calculus. 14.1-14.7 (8-10 classes) Expected Learning Outcomes: Upon successful completion of this course, a student should be able to: 1. Perform basic vector computations, as well as dot and cross products of two vectors and projection of one vector onto another vector. 2. Convert between cylindrical, rectangular and spherical coordinates. Understand when it’s prudent to switch to one coordinate system over another in computing an integral. 3. Determine the equation of a plane in 3-d, including a tangent plane to a surface in 3d. 4. Find the parametric equations of a line in 3d. 5. Perform calculus operations on functions of several variables, including limits, partial derivatives, directional derivatives, and gradients; understand what the gradient means geometrically. 6. Find maxima and minima of a function of two variables; use Lagrange Multipliers for constrained optimization problems. 7. Understand divergence and curl of a vector field. 8. Compute double and triple integrals in rectangular, spherical and cylindrical coordinates; proper use of double or triple integrals for finding surface area or volume of a 3d region. 9. Compute line and surface integrals. 10. Determine if a vector field is conservative and if so, find the corresponding potential function. 11. Use and understand when to apply Green’s Theorem, Gauss’ Divergence Theorem and Stokes Theorem. Evaluation Methods and Grading Homework: To be assigned weekly. Written homework will be due Fridays and will be collected in class. Papers turned into my mailbox in the math mail room (JWB 228) by 3 PM Fridays will be regarded as being turned in on time. Homework that is late but not more than one week late will receive half credit. Homework that is more than one week late will receive no credit at all. Webwork: Students will do weekly on-line homework using Webwork which focuses on routine calculation and short answer problems. Exams: Exams will be closed book. Your calculators, text, notes, homework papers, other books, laptops, tablets, phones and text messaging devices will not be allowed. Midterms: There will be two in-class one-hour midterm exams on Feb. 6 and Mar. 20. Final Exam: Fri., Apr. 26, 10:30 am - 12:30 pm. Half of the final will be devoted to material covered after the second midterm exam. The other half will be comprehensive. Students must take the final to pass the course. Course grade: Two midterms 40% + HW 25% + Webwork 5% + final 30%. Grades will be assigned "on the curve." Withdrawals: Last day to register is Jan.11. Last day to drop class is Jan 18. Until Mar. 8 you can withdraw from class with no approval at all. After that date you must petition your dean's office to be allowed to withdraw. Additional Resources • Tutoring Center & Computer Lab- There is free tutoring in the T. Benny Rushing Mathematics Student Center (room 155, the lower level between JWB and LCB), as well as a computer lab. For more information see http://www.math.utah.edu/undergrad/mathcenter.php • Private Tutoring- University Tutoring Services, 330 SSB. There is also a list of tutors at the math department office JWB 233. • Departmental Videos- The math department has a full set of lecture videos which you are welcome to use to supplement our course material. These can be found at http://www.math.utah.edu/lectures/ Student Responsibilities All students are expected to maintain professional behavior in the classroom setting, according to the Student Code, spelled out in the Student Handbook. Students have specific rights in the classroom as detailed in Article III of the Code. The Code also specifies proscribed conduct (Article XI) that involves cheating on tests, plagiarism, and/or collusion, as well as fraud, theft, etc. Students should read the Code carefully and know they are responsible for the content. According to Faculty Rules and Regulations, it is the faculty responsibility to enforce responsible classroom behaviors, and I will do so, beginning with verbal warnings and progressing to dismissal from and class and a failing grade. 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