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Mathematics 2210 Syllabus Calculus III, Section 1, Fall Semester, 2014 Time & Place: M, W, F 9:40 AM - 10:30 AM in JTB 130 Instructor: Andrew Basinski, LCB 315, [email protected] Webpage: http://www.math.utah.edu/∼basinski Office Hours: Fridays, 10:45am - noon in LCB 315 or by appointment Text: Calculus with Differential Equations, 9th edition, by Varberg, Purcell and Rigdon Course: 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. Prerequisites: “C” or better in (MATH 1220 OR MATH 1250 OR MATH 1320) OR AP Calculus BC score of at least 4. Tests: We will have 3 exams and a final, all of which will be cumulative. More details on content will be provided as the first test-date nears. Homework: Homework will be assigned on a weekly basis. Assignments will be posted on the website, under the “Math 2210” link. Grading: A (93-100), A- (90-92), B+ (87-89), B (83-86), B- (80-82), C+ (77-79), C (73-76), C- (70-72), D+ (67-69), D (63-66), D- (60-62), E (0-59). 3 exams, homework, and a final exam will determine your grade. I will drop your lowest exam score (but not the final). The remaining 2 exam scores, homework score, and final exam score will each count toward 25% of your grade. Missed exams cannot be made up - see me if you need to reschedule an exam. Discussion Section: Wednesdays, 5-6 pm in LCB 222 Free tutoring: Available at the T. Benny Rushing Mathematics Student Center (adjacent to JWB and LCB), Room 155. M - Th 8am - 8pm; F 8am - 6pm. http://www.math.utah.edu/ugrad/tutoring.html Learner Outcomes: Upon successful completion of this course, a student should be able to: • • • • Compute dot and cross products of two vectors, projection of one vector onto another vector. Convert between cylindrical, rectangular, and spherical coordinates. Determine the equation of a plane in 3-d, including a tangent plane to a surface in 3-d. Find the parametric equations of a line in 3-d. 1 • Perform calculus operations on functions of several variables, including limits, partial derivatives, directional derivatives, and gradients; understand what the gradient means geometrically. • Find maxima and minima of a function of two variables; use Lagrange Multipliers for constrained optimization problems. • 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 3-d region. • Compute line and surface integrals. Tenative Outline: August September October November December 25 - 29 1-5 8 - 12 15 - 19 22 - 26 29 - 3 6 - 10 13 - 17 20 - 24 27 - 31 3-7 10 - 14 17 - 21 24 - 26 1-5 8 - 12 15 - 19 11.1 11.4 11.8 12.1 12.5 12.7 13.1 - 11.3 11.7 11.9 12.4 12.6 12.9 13.3 13.4 13.7 13.9 14.1 14.3 14.5 14.7 - 13.6 - 13.8 - 14.2 - 14.4 - 14.6 Three-space, vectors, dot product Cross-product, motion, acceleration, curvature Surfaces, coordinate systems Multivariable functions, derivatives Directional derivatives, the chain rule Tangent planes, Maxima and minima Double integrals *FALL BREAK* Polar coordinates, surface areas Triple integrals Changing variables in multiple integrals Vector fields, line integrals Path independence, Green’s theorem Surface integrals, Gauss’s theorem Stokes’s theorem Partial differential equations ? Catchup, mystery topic EXAM I (9/26) EXAM II (10/24) EXAM III (11/21) FINAL EXAM (12/18: 8 - 10am) ADA Statement: The University of Utah seeks to provide equal access to its programs, services and activities for people with disabilities. If you will need accommodations in the class, reasonable prior notice needs to be given to the Center for Disability Services (CDS), 162 Olpin Union Building, 581- 5020 (V/TDD). CDS will work with you and me to make arrangements for accommodations. All information in this course can be made available in alternative format with prior notification to CDS. 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. You 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, collusion, fraud, theft, etc. Students should read the Code carefully and know you are responsible for the content. According to Faculty Rules and Regulations, it is the faculty responsibility to enforce responsible classroom behaviors, beginning with verbal warnings and progressing to dismissal from class and a failing grade. Students have the right to appeal such action to the Student Behavior Committee. http://regulations.utah.edu/academics/6-400.php 2