Math 20C – Calculus and Analytic Geometry for Science and Engineering

Instructor:
Emre Mengi
APM 5763 (Click here to see a map of the APM building)
emengi@math.ucsd.edu
534-2126

Teaching Assistants:
Bill Alto – Sections C01, C02
APM 6311
walto@math.ucsd.edu

Ruben Arenas – Section C03
APM 6444
rjarenas@math.ucsd.edu

Chris Chang – Sections C04, C05, C06
APM 6436
chc007@math.ucsd.edu

Lecture Hours and Location:
MWF 8am-8:50am at WLH 2005

Discussion Sections:
Tuesdays

  • C01(8am), C02(9am), C03(10am) at SOLIS 111
  • C04(5pm), C05(6pm), CO6(7pm) at SEQUO 148

Office Hours:
Tue-Thr: 2pm-3:30pm (E. Mengi, APM 5763)
Tue: 12noon-2pm (C. Chang, APM 6436)
Thr: 9am-11am (R. Arenas, APM 6444)
Tue: 10am-12noon (B. Alto, APM 6311)

Announcements:

  • Please have a look at the solutions for the final and homework 5. There were two versions of the final. The solutions are provided for only one version.
  • We should be completely done with grading by next Monday. Enjoy your winter breaks.

Plane g(x,y)=-2x-2y+5 is tangent to f(x,y)=3-x^2-y^2 at (x,y)=(1,1). The tangent plane is a flat surface and intersects the graph of the function only at (x,y)=(1,1) and nowhere else. 

Calendar

Monday Wednesday Friday
Week 0 Sep 28
Organization
and Review
Week 1 Oct 1
12.1		 Oct 3
12.2		 Oct 5
12.3
Week 2 Oct 8
12.4		 Oct 10
12.5		 Oct 12
10.1 – 13.1
#hw1 is due
Week 3 Oct 15
10.2		 Oct 17
13.2 – 13.3		 Oct 19
13.3 – 13.4
Week 4 Oct 22
Canceled		 Oct 24
Canceled		 Oct 26
Canceled
Week 5 Oct 29
14.1		 Oct 31
14.2		 Nov 2
Midterm 1
#Chap 10,12,
13 included
Week 6
Nov 5

14.3
#hw2 is due

 Nov 7
14.4		 Nov 9
14.5
Week 7 Nov 12
Veteran’s day		 Nov 14
14.6		 Nov 16
14.7
#hw3 is due
Week 8 Nov 19
14.7		 Nov 21
14.8		 Nov 23
Thanksgiving
Week 9 Nov 26
15.1		 Nov 28
Midterm 2
#Chap 14 is
included
#hw4 is due		 Nov 30
15.2
Week 10 Dec 3
15.3		 Dec 5
15.4		 Dec 7
15.6 – 15.7
Finals Week Dec 10
8am-11am
Final
#hw5 is due

Important Enrollment Dates

  • October 12  ; Last day to add classes
  • November 2  ; Last day to drop without W on transcript
  • November 30 ; Last day to withdraw

Homework

Please return the homeworks to the drop-off box reserved for our class on the 6th floor in the APM building.

Suggested Questions
Your solutions to the suggested questions from the textbook are not going to be collected or graded. Some of these questions will be solved during the discussion sections. Some of the homework questions will be extensions of the suggested questions.

  • Chapter 12
    12.1 – 4,6,13,17,22,29,32,38,41
    12.2 – 1,6,11,17,25,29,30,43
    12.3 – 1,7,9,11,19,24,39,41,43,47,51,57,58
    12.4 – 1,5,9,11,12,15,24,35,41
    12.5 – 1,3,5,9,19,21,25,30,35,41,51,65,67,71
  • Chapter 10
    10.1 – 3,9,13,21,24,33,39,42,43
    10.2 – 5,13,17,25,31,34,39,45,51,61
  • Chapter 13
    13.1 – 2,6,14,25,34,40
    13.2 – 1,7,15,21,27,31,37,45,46,49
    13.3 – 3,11,13,15,26,27,29,41,49,55
    13.4 – 2,7,13,20,21,25,33,40
  • Chapter 14
    14.1 – 5,15,16,18,25,30,32,34,38,47,63,64,69
    14.2 – 2,5,7,11,12,14,25,27,31,35
    14.3 – 3,6,9,13,17,21,35,41,48,53,66,71,76,77,85
    14.4 – 3,5,15,20,23,29,35
    14.5 – 2,3,9,11,13,15,19,25,33,37,40,41,47
    14.6 – 1,3,5,8,13,18,23,29,31,36,47,61,62
    14.7 – 4,9,11,13,17,21,27,30,32,39,45,53,54
    14.8 – 1,2,6,19,21,27,33,40,43
  • Chapter 15
    15.1 – 3,5,7,9,13,17
    15.2 – 3,5,7,8,11,15,20,25,29,33,36
    15.3 – 5,9,11,13,16,22,23,25,27,31,37,41,44,45,55,57
    15.4 – 3,6,7,11,15,16,19,23,25,31,33
    15.6 – 5,7,11,15,23
    15.7 – 2,3,7,9,11,13,15,18,27,32,37,48

Lecture Notes

The lecture notes for each week will normally be available here on Friday at the end of the week. However, if the level of attendance to the class drops drastically, I may no longer post them here and instead distribute them in the class. I am sorry that the quality of my hand-writing may not be so good in some of the notes. But they should be readable and comprehendable.

  • Lecture 1 12.1 – 3D Coordinate System
  • Lecture 2 12.2 – Vectors
  • Lecture 3 12.3 – The Dot Product
  • Lecture 4 12.4 – The Cross Product
  • Lecture 5 12.5 – Lines and Planes in 3D
  • Lecture 6 10.1-13.1 – Parametric curves in 2D and 3D
  • Lecture 7 10.2 – Calculus with parametric curves
  • Lecture 8 13.1-2-3 – Calculus with vector-valued functions
  • Lecture 9 13.3-4 – Normal, Binormal Vectors, Motion in Space
  • Lecture 10 14.1 – Functions of Two Variables
  • Lecture 11 14.2 – Limits and Continuity
  • Lecture 12 14.3 – Partial Derivatives
  • Lecture 13 14.4 – Tangent Planes, Differentiability, Linear Approximations
  • Lecture 14 14.5 – The Chain Rule
  • Lecture 15 14.6 – Directional Derivatives and Gradient Vector
  • Lecture 16 14.7 – Basics of Optimization
  • Lecture 17 14.7-8 – Unconstrained and Constrained Optimization
  • Lecture 18 15.1 – Double Integrals over Rectangular Domains
  • Lecture 19 15.2 – Iterated Integrals over Rectangular Domains
  • Lecture 20 15.3 – Double Integrals over General Domains
  • Lecture 21 15.4 – Double Integrals in Polar Coordinates

Past Exam

  • Math 20C – Spring 2007 (taught by Andrew Linshaw)  : See the exams and their solutions.

Resources

  • Calculus web-sites:
    • Calculus.org Offers tips on how to prepare for exams, some supplemental notes about multi-variable calculus. Some web-based programs (called applets) are also provided.
    • The Math Forum  Especially math tools under the “resources and tools” menu can be useful.
    • Calculus by Gilbert Strang This is a free book available online (thanks to Gilbert Strang). The book is not completely compatible with our syllabus. But some of the most essential topics are common. Chapter 13 in Strang’s book closely matches Chapter 14 in our textbook. Chapter 14 in Strang’s book and Chapter 15 in our textbook are along the same lines, though what we will cover is more comprehensive. Chapter 11 in Strang’s book is a more general version of what are going to see about vectors, lines and planes in 3D (sections 12.1-5 in our textbook).
    • Al Shenk’s Website Prof. Shenk taught Calculus classes for many years at UCSD. On his website there are exercises with step-by-step solutions.
  •  Visualization Software: It is a good idea to use computers to plot graphs in 3D space, whether the graph is a surface or a curve. Calculators may not do as good of a job as computers when you need to visualize in 3D. If you cannot figure out the usage of any software below, please let me know.
      • Grapher If you have access to an Apple computer, the software grapher comes for free to plot surfaces, curves; even the parametric ones.
      • Surface Explorer 3D If you have access to a PC, surface explorer 3D is a free software running under Windows to plot surfaces and curves. (also parametric curves and surfaces)
      • Plot3D This is another free software for Windows to plot graphs in 3D. Surface explorer 3D is a more general purpose tool, but Plot3D may be easier to use.
      • FooPlot This is a web-based software to plot 2D and 3D graphs that seems to work fine with Windows. Its capabilities are limited. Its advantage is it does not require installation.
      • Virtual Math Museum On this site some of the common curves and surfaces are illustrated. Most of them are advanced shapes, which we are not going to see in our class. But our famous friend sphere and the cycloid from section 10.1-example 7 in our textbook (though I am not sure how much time we will have for cycloids) occupy spots in this museum. This site is listed here to have some fun. We all need a break after working so hard.

SYLLABUS

Catalog Name :
Math 20C, Calculus & Analytic Geometry for Science and Engineering

Credits :
4 credits (unless you have  already taken Math 10C in which case this course is considered 2 credits)

Prerequisites :
Math 20B with a grade of C- or better, or AP Calculus BC Score of 3,4 or 5

Description :
The following topics will be covered:

  • Vectors and Basic Operations on them
  • 3D Coordinate System, Lines and Planes in 3D
  • Parametric Representations of Curves
  • Vector Valued Functions
  • Functions of Two Variables, their Differentiation and Optimization
  • Cylindrical and Spherical Coordinates – will be omitted due to loss of one week because of the wildfires.
  • Multiple Integrals

Course Webpage:
http://www.math.ucsd.edu/~emengi/teaching/math20c/math20c.html
(It is your responsibility to check the webpage regularly.)

Textbook :
Calculus, Early Transcendentals by James Stewart – 5th Edition
The thicker version including single variable calculus is recommended. If you are confident about single variable calculus, the thinner multivariable calculus should also be fine. But keep in mind that we will generalize concepts from single variable calculus. You may need to review some of the key concepts from single variable calculus.

We will cover parts of Chapters 10,12,13,14,15 from the textbook. For the exams you are responsible from all of the sections on the course calendar.

Grading Policy :
Your grade will be based on your performance in five homeworks, two midterms and the final. We will use one of the following two schemes (whichever yields the higher score) to calculate your overall score out of 100.

  • %25xMidterm 1  +  %25xMidterm 2  +  %20x(Average of best 4 homeworks)  +  %30xFinal
  • %25x(Best of Midterm 1 and Midterm 2)  +  %20x(Average of best 4 homeworks)  +  %55xFinal

Remember always that this is a curved-class . We will use curve in favor of you. This means that if the class average is high, then we will use the standard scale below.

D C B A
60<= score <70 70<= score <80 80<= score <90 90<= score <=100

But more likely we will have to use a different scale so that you can get better grades than the above scale suggests.  For instance if your overall score is 80 but if you are in the upper %10 of the class, you should normally receive an A. Unless the class-average is high, what matters in the end will be your rank in the class and your average as compared to the class-average. Please don’t get discouraged if you find an exam difficult; possibly it was a tough exam for the majority of the class.

Midterms :
Midterms will be held during the lecture hours on the indicated dates on the course calendar. Typically there will be four or five questions in each of the midterms. Midterm 1 will cover Sections 12.1-5, 10.1-2, 13.1-4. Midterm 2 will cover Sections 14.1-8. Both of the midterms will be open-book exams meaning you can bring any book and notes to the midterms.  There will be no make-up midterms; if you have to miss a midterm, you still have the opportunity to make it up by performing well in the final.

Final :
Final is scheduled on December 10th, 2007 from 8am to 11am. Please make sure that you have no other final scheduled at this time. (neither you would like to have multiple finals, especially three or more, on this date.) There will be no make-up final under no circumstances.

Homeworks :
Homeworks are due at 3pm on the dates indicated on the course calendar. You will have to drop them off to the homework box reserved for our class on the 6th floor of the APM building. Homework boxes are on the right on the 6th floor as soon as you leave the elevator. One of the boxes will be labeled as Math20C (Lecture C). Late homeworks will not be accepted. Additionally there will be suggested questions from the textbook, which will be solved during the discussion sections. These questions are not going to be collected or graded.  Their sole purpose is to get you prepared for the exams. Please check the homework page to access the latest homeworks and suggested questions posted.

Calculators :
Use of a graphic calculator such as TI-85 or TI-86 when solving the homeworks or suggested questions is recommended. Calculators are not allowed during the exams.

Lectures :
Attendance to the class is not required. However, I believe that the most efficient way to learn is sitting in the class. Because this gives you the opportunity to interact in case something is not clear. Besides we will be spending our time on the most essential concepts and skipping some of the less important ones in your book that are likely to be forgotten quickly. The aim of the lectures is to teach you memorable concepts and techniques that you can apply in your careers.

Discussion Sections :
Discussion sections meet every Tuesday and last 50 minutes. Your TAs will be solving some of the homework and suggested questions. Here you will find more time to raise individual questions. This provides a good opportunity to practice with your friends and knowledgable TAs.

Academic Dishonesty :
I wish this does not have to be mentioned in the syllabus. Unfortunately in the past I had incidents of academic dishonesty in my class when I thought it was humiliating to mention at the beginning of the quarter. I apologize for this remark here, because it is not a civilized message and it does not concern most of you. Please realize that you are in one of the most respected colleges in California and we expect you to behave accordingly during the lectures and exams. In the case of any unethical act during the lectures or exams, necessary steps will be taken. Do you know that in one of the colleges in California there is no proctoring during the exams? Here is an interesting pbs article on academic dishonesty.