Math 20C Fall 2009

Instructor: James Lin Office: 7157 APM email address: jimlin@math.ucsd.edu, Office hours Monday at 10, Friday at 11. 

Course times: MWF 9-9:50am, Place: Center Hall 101

Sections  Tuesdays, 3,4,5,6,7,8 WLH 2208 8,9am in WLH 2115

TAs- Moe Ebrahimi, 5768 APM  maebrahi@math.ucsd.edu  Moe has sections 8-10 and 3-5.  Office hours Tuesdays 10-12 in the Calculus Lab, 12-2 in 5768 APM

Michael White, 6446  APM, mrwhite@math.ucsd.edu  Office Hours Monday 2-4 pm in 6446 apm, in Calculus Lab Monday 10-11, 12-1. 

Text: Rogawski, Jon,  Multivariable Calculus, Early Transcendentals, Freeman and Company 

Recommended: Students Solutions Manual and  Shenk’s interactive examples  http://math.ucsd.edu/~ashenk/cgi-bin/tutorials.cgi

Recommended Calculator Texas Instruments 85 (TI85)

Prerequisites: Math 20B with passing grade, or AP calculus BC grade of 4 or 5

 Announcements-1.   The curve for Midterm 1 out of 75 points is 69+ A (99), 60+ B (70), 37+ C (95), 30+ D (9), 30- F (12).   It is worth noting that 34 students got a perfect score. Solutions to the midterm appear on Web CT. 

  1. Midterm 2 will be on Wednesday, December 2, 2009 from 7-8:50 pm in York 2722.  The midterm will be worth 135 points and covers all the material since the first midterm.  Students need to bring blue books, student ID, pencil and know their section time.  You can also have one side of an 8 ˝ x 11” sheet of handwritten notes. 
  2. There is a practice midterm 2 that has been handed out in class and will appear on Web CT beginning on Friday. 

Course Description: This course focuses on problems involving several variables and its applications to max, min problems, computing areas, volumes, arc lengths, and regions that are described in polar coordinates. Engineers will use some of these concepts to describe physical phenomena like velocity, acceleration, and forces in 3 dimensional space, Maxwell’s equations, or to do computer aided design.    In 20E, these concepts are used to describe fluid flow, curl, flux and divergence. Economics majors should pay special attention to the section on Lagrange multipliers.  This course requires that the student visualize objects in the plane and also objects in three dimensions.  Sometimes the geometric picture is more important than the algebraic equation.  This will be the first time the student is expected to be able to sketch volumes in three space and interpret the geometric meanings of partial derivatives and the gradient.  Besides visualization, we will learn about vectors, the use of gradients and directional derivatives to analyze functions of several variables.  During the second half of the course we will develop methods to integrate functions of several variables.  These techniques are used in the sciences to study centers of mass, moments of inertia, and probability.

Goals of the Course: I am assuming that most of you will use vector calculus in applications in engineering, physics, biology, chemistry and the social sciences.  To be ready to apply these methods, we want the student to have a grasp of the concepts and also to have done a significant number of problems so that the concepts are tied to concrete problems.  Mathematics is a participatory activity. The student should actively join in the lectures for maximum understanding. This means students will ask questions, talk with other students, and debate the solutions and meanings of various problems as well as present solutions on the board. By the end of the course, students should be able to communicate to a stranger the significance of vector calculus and how the student might find it useful to him or her personally.  We will move at a rapid pace, so that you will definitely make mistakes now and then, but this will enhance your learning.  Students are expected to attend both lectures and sections.  After a few weeks, the instructor will lecture about one week ahead of the syllabus.  This will permit us to review a bit before the midterms.  Although the instructor will try to summarize the content of the course as clearly as possible, the student should not totally rely on lectures as the sole source of information. Students should develop enough confidence so that they can read the book on their own. It is very important that you read the assigned material in advance of the lecture. This exercise will train you to eventually be able to read math books on your own. 

Other Resources-    You may want to purchase the Student’s solutions manual.  I am told that all the odd problems have solutions in the Student’s solutions manual.    Also after the second week, there usually is a calculus lab(B411 APM) which is open M-F from around 10am to 8 pm.  Finally OASIS may run a workshop for students who sign up for the whole quarter.  This entire syllabus will be posted online at http://www.math.ucsd.edu/  click on the title course websites and look for 20C.  The instructor assumes no responsibility for updating the syllabus in a timely manner.  Efforts will be made, but occasionally I may be too busy to get everything online immediately.  Occasionally, I will email you about various announcements.  You are expected to read your email. 

Grades:.Grades for the course will be determined in the following way

Homework                                                        80 points

Class Participation                                           10 pts

Midterm I      October 28                               75 pts

Midterm II     December 2                      135 pts

Total                                                                 300 points

Final exam (replaces the two midterms

if  turned in.)                                                   210 points

 To obtain a C grade without taking the final, students will have to score on their midterms at least 5 points below the lowest C grade determined by the curve on the two midterms.  To obtain a B without taking the final, students will have to average a B on the two midterms.  To implement this grading system, we should note that this course will have to move faster than other courses because we will want to complete all the material of the course by Monday of the 10th week to give a midterm on Wednesday of the 10th week.  . 

Class Participation: We will also ask students to present various problems on the board. In addition, students who come to office hours and ask informed questions will earn some class participation points (2 points per problem). No points for simply attending class or section.  Questions should address specific issues that are not understood and should be phrased to describe where you got stuck. So for example, asking me to do problem 9 without any remarks about what you tried will not earn class participation points. Students can also earn points by coming to office hours and asking questions(2 points per office hour). 

Midterms and Final: Midterm 1 will be Wednesday, October 28, 7-8:50 pm in York 2722 and Midterm 2 will be Wednesday, December 2, 7-8:50 pm in York 2722. Note these dates and times appeared on the schedule of classes at the time of enrollment.  Note that Midterm 1 is given after the 4th week so students must decide on their own by the 4th week if they need to drop the course. The Final is scheduled for Wednesday December 9, 8-11 am in Center Hall 101. All exams will be taken using blue books which can be purchased at the student store.

Homework: There will be weekly homework assignments. Students will be required to work in groups of 3. All 3 students in the group must belong to the same section.  A group of 3 students will turn in one homework assignment for each group. Students will work on homework by themselves, then get together for at least one hour each week to discuss the solutions with other members of their group.  Homework will count for one fifth of your grade.  Doing the homework is crucial to succeeding in this class.   The instructor will do a fair amount (about 25%) of the homework problems in class, so if the student takes reasonable notes, he/she can use these solutions as samples of how to do the rest. To learn this material, it is crucial that you make mistakes in the homework so that you can examine these mistakes and learn from them.  Quite often, you will learn by talking with other members of your homework group. Selected problems from the homework will be graded depending on the resources we are provided for graders. Homework will correlate strongly with the exams, so students who do not do the work on their own will definitely pay a heavy price on the midterms and final.    Homework is due at the beginning of section.  Homework must be turned in with 3 names appearing at the top of the homework. No individual homework will be accepted. Full solutions should be written out with answers boxed. Many of the assigned problems may already have numerical answers given in the back of the book. The answer in the back of the book will generally not be an acceptable answer on your homework. The homework must show how one arrives at the numerical answer to obtain any credit. Solutions to the homework will be available in Soft Reserves the day after it is turned in. In the past, a 90% correct grade on the homework was a B grade on the curve.  Students should feel free to check their homework by going to office hours with the TAs or the professor. 

 

 

 

SYLLABUS This will be the first time I have used this text so we may end up moving faster or slower depending on the difficulty of the text. 

Week 1 Sept 25  Sections 11.1-3,  12.1-2.  Parameterized curves, polar coordinates, arc length.  Vectors in 2 and 3 dimensions.  (CAUTION) Vectors behave in different ways from numbers. The rules we outline for addition and scalar multiplication must be followed. Do not invent your own rules.  In writing up your homework, you will be required to put an arrow over your vectors.  In the book, vectors are in bold print, but when writing them in hw the convention is to use arrows on top of the letter.    Otherwise we will assume your variables are numbers.  Points will be deducted for improper notation. 

Week 2 October 2 Section 12.3-5  Dot product and Cross product,. Equations of lines and planes, quadric surfaces

Week 3 Oct 9   Section 12.1 More equations of planes 13.1-3,, Vector valued functions,  arclength, speed,  .  Pictures of functions from their level curves. 

Week 4 Oct 16 Section 13.4  Curvature Sections 14.1-14.2 Limits, Continuity

Week 5 Oct 23, section 14.3-5  Partial derivatives, linear approximation, gradient, directional derivative  Midterm 1

Week 6 Oct 30 Section 14.6-7 Chain rule, Maximum, minimum of functions of two variables

Week 7 Nov 6 Section 14.8  Lagrange multipliers  Sections 15.1-3,  Multiple integrals. Riemann Sums

Week 8 Nov 13 Sections 15.3  .  Multiple integrals, over rectangles and other regions Triple integrals

Week 9 Nov 20 Sections 15.4 Multiple integrals using polar coordinates, spherical coordinates,  triple integrals

Week 10 Nov 30 Review, Midterm 2

 

 

HOMEWORK – Here is a list of assigned problems.  To prepare for exams, students should do more problems than just the homework.  All homework must be turned in in groups of 3 at the beginning of section. It must be neatly written with answers boxed. Pages should be stapled or clipped together. No late homework will be accepted.  Students must attend section on Tuesday, Sept 29 to get into a homework group.  Students who are not in a homework group cannot get any credit for their homework.  Homework #1 and 2 will be turned in together on Tuesday, October 6. 

Week 1 Section 11.1 #3, 5,7 16, 19,31 Section 11.2 #4, 8, 21, 22 Section 11.3 #1,2,3,7, 8, 18,20, 22,25 Section 12.1 #1,3, 4, 6, 12, 15, 16, 17, 20, 24, 34, 38, 43, 46, 58 , 60

Week 2  Section 12.2 #2,4, 8, 9, 12, 17, 20, 28, 36,52 Section 12.3 #6,10,14,20,26,32,36,38,42,50,58 Section 12.4 #6, 11, 18, 23, 27, 28, 39,

Week 3 Section 12.5 #  2, 12, 16, 22, 27, 30, 44 Section 13.1 #1,6,7,29 Section 13.2 #4,11, 17, 21,23,28,33 Section 13.3 # 3,6,9

Week 4 Section 13.4 #1,10,11, 15,19,22,26 Section 13.5 #2, 5 Section 14.1 #20, 22, 31, 32, 44 Section 14.2: 2, 5, 11, 16, 17, 31, 32, 34

Week 5 Section 14.3: 1, 4, 9, 14, 23, 37, 42, 58, 67. Section 14.4: 2, 6, 9, 17 Section 14.5 #1,2, 4, 10, 21,31, 35

Week 6  Section 14.6 #1,6,7,9,20,27 Section 14.7 #1,3,4,5,7,10, 14

Week 7  Section 14.8 #1,3,4,6,8,12,18,19  Section 15.1 #2,3,6,8, 9, 15, 18, 22, 26, 31, 36, 42 

Week 8 Section 15.2  #3, 4,6,8, 10,14, 15, 18 ,26, 29, 37,38, 42 Section 15.3 #3,4, 5,8,11, 14,17, 18(x limit is from 0 to 3) ,20( just reduce it to a double integral in the xy plane),  32

Week 9 Section 15.4 #1, 2, 3, 4,5,6,9, 10,15,19,23,29, 31 , 51,52

 

 

The following contract is a list of minimal requirements to be successful in the course.  Please think this over before signing the contract because the instructor will regard your signature as your word.  Students will sign this contract and give it to the TA of their section on Tuesday, September 29. 

 

 

20C CONTRACT WITH STUDENT

As a 20C student, I agree to the following requirements of the course:

    1. This course is labor intensive.  To get any value out of the course, I must attend lectures and work on problems for on average 6 hours or more per week. 
    2. I agree to work on my homework individually, to do it all to the best of my ability.  After I have written up a full solution set on my own, I will then meet at least once a week in a group of three students for a minimum of one hour to discuss our solutions. From this meeting, we will compile a common homework solution set to be turned in with 3 names on it. I will not turn in individual homework. To succeed in this course, I will have to commit to at least 5 hours of individual study outside of class.  I realize that to write up the weekly assignments, I will have to commit at least this amount of time.
    3. I have checked the dates and times of the midterms and final and have determined that I will be able to take the exams at the prescribed times.  I understand that due to the large number of students, there will be no makeup exams or homework.
    4.  I agree to ask questions about concepts that I do not understand. I will do                               the work to be able to verbalize exactly what I do not understand.  I will not wait for the instructor to guess what I do not understand.  I agree to verbalize any complaints in a timely manner  to someone (such as the instructor or the TA)  who can be of assistance with my complaint.

 

 Here are the names of the people in my homework group along with their student IDs and a common time when we will meet

 

 

 

 

 

 

 

 

 

 

 

               Meeting Time:  

 

 

 

________________________________ ______________________

signature                                                    date