Mathematics 103X Honors Intermediate Calculus Fall 2006Section 02 MWF 11:55am–12:45pm Physics building 299Professor: Lenny Ng Office: Physics 231E-mail: ng AT math.duke.edu Office phone: 919-660-6972Course web site: Assignments, announcements, and other course material will be postedat http://www.math.duke.edu/~ng/math103x/ . Grades will be posted on Blackboard,http://blackboard.duke.edu/ .Textbook: Vector Calculus, third edition, by S. J. Colley.Office hours: Tentatively 3:00-4:00pm on Tuesdays and Wednesdays, and by appoint-ment. To set up an appointment, e-mail me, but please keep in mind that I can’t usuallyanswer e-mail immediately; on occasion it may take a day for me to respond.Course information: This is a more theoretical version of Mathematics 103 but coversmuch of the same material: vector calculus, curves and surfaces in 2D and 3D, multivari-able differentiation, max/min problems, multivariable integration, and Green’s, Stokes’,and divergence theorems.Structure: The course will be loosely divided into four sections. Here is a tentative out-line:I. Vector geometry and curves and planes in 2D and 3DVector algebra Sections 1.1, 1.3, 1.4Lines, planes, distances Sections 1.2, 1.5Curves in 3D Sections 3.1, 3.2II. Multivariable differential calculusFunctions of several variables, limits, partial derivatives Sections 2.1, 2.2, 2.3, 2.4Chain rule, directional derivatives, gradient Sections 2.5, 2.6Linear approximation, max/min problems, Lagrange multipliers Chapter 4III. Multivariable integral calculusDouble and triple integrals Chapter 5, Section 1.7Vector fields and line integrals Sections 3.3, 3.4, 6.1Surface integrals Sections 7.1, 7.2IV. Fundamental theorems of vector calculusGreen’s Theorem, conservative vector fields Sections 6.2, 6.3Stokes’ Theorem and the divergence theorem Section 7.31Grading: Your grade will consist of a weighted average of in-class tests (60%), the finalexam (30%), and homework (10%).• Homework: I will assign weekly homework, mainly out of the book. Not all prob-lems will be graded. The primary purpose of the homework is to help you learn theclass material, and you must write up solutions to all problems. Always show work—this helps you find mistakes in your solutions, and it helps with the assignment ofpartial credit. You may not receive full credit if steps are missing in your solution.You are encouraged to work with other students in the class on the homework, butyou must write up the homework by yourself (no copying!), and acknowledge anycollaborators. No unexcused late homework will be accepted. Your two lowest home-work scores will be dropped.• Tests: There will be four in-class tests, roughly covering each section of the course.No calculators are allowed. The first two tests are tentatively set for September20 and October 6. You will only be excused from a test if you have prior writtenauthorization from your dean or you have a serious short-term illness; in the lattercase, you need to fill out the Short-Term Illness Notification form (linked from thefirst-year information web page, see below).• Final examination: The final exam will be given on Thursday, December 14 from7:00-10:00pm. Note that this is in the math block exam time slot and not the usualslot for the class time.Computing: Calculators and computing programs such as Maple, Mathematica, Matlab,etc., will not be necessary in this course.Other information: http://www.math.duke.edu/first_year/f_y_info.html is a usefulweb site with general information about first-year math courses, the Help Room, what todo in case of illness, etc.Under construction: This syllabus is subject to change; I will inform you of any changes.The latest syllabus can always be found at the course web