MATHEMATICS UN1201, Fall 2018


Calculus III,  sections 6 and 7

 

Room:  TBA

Time:  Tuesday and Thursday, 1:10-2:25 PM (section 6), 2:40-3:55 PM (section 7)

Instructor:  Michael Harris

Office Hours:  Tuesday 4:30-5:30, Thursday, 11-12 and by appointment, room number 521

 

Teaching Assistants:             Monica Marinescu  (marinescu@math.columbia.edu)           Office hours T 10:00am - 1:00pm

                                                Robin Zhang  (rzhang@math.columbia.edu)                           Office hours MW 1:00pm -  2:30pm

                                                Lina Tian  (yt2511@columbia.edu)                                         Office hours W 4:00pm - 6:00pm

                                                Lekha Yesantharao      (lvy2002@columbia.edu)                    Office hours T 10:00am - 12:00pm

 

All office hours in the Help Room at 502 Milstein (Barnard)

 

 

 

A provisional schedule with homework assignments is indicated below; it will be updated regularly.  You can find a sample syllabus, with reading assignments, at this page.  More complete information about the course is on the department's Calculus III page. 

 

Textbook:  The course textbook is James Stewart, Calculus:  Early Transcendentals (8th edition)

 

WebAssign:  WebAssign will not be required for the course.  However, students who wish to take advantage of features of WebAssign can use the class key

 

columbia 8235 9880

 

 

Prerequisites:  The sole prerequisite for the course is Calculus I.  Familiarity with the material of Calculus II is helpful but not essential. 

 

 

Class and reading schedule

 

Date

Topics (chapters in Stewart)

Homework

Optional HW

9/4, 9/6

Vectors, coordinate systems (§12.1-2, 10.3, 15.7-8)

Due 9/12

12.1: 1, 4, 6, 15, 20, 35

12.2:  1, 4, 8, 21, 22

10.3:  3, 6

15.7:  2, 3, 6

12.1: 3, 5, 14, 19, 38

12.2:  5, 9-14

10.3:  4, 5

15.7:  7, 8

9/11, 9/13

Dot products, cross products (§12.3, 12.4)

Due 9/18

15.8: 2, 4, 7, 8

12.2: 24, 28, 44, 46

12.3: 1, 2, 5, 8, 17, 23, 31, 43, 54, 64

12.4: 4, 6, 13, 14, 25, 45, 53

12.3:  11, 13, 62, 63

12.4: 15, 29, 42, 46, 47, 54

For students comfortable with first-year physics: 

12.2: 30-40, 12.3: 49-53, 12.4: 9-12, 39-41

9/18, 9/20

Equations of lines and planes (§12.5) 

 

Due 9/26 

12.5: 1, 2, 4, 10, 14, 18, 19, 22, 26, 34, 40, 53, 55, 64, 65, 77

 

12.5: 5, 12, 13, 21, 33, 35, 37, 46, 62, 80

 

9/25, 9/27

Review of conic sections, cylinders and quadric surfaces in 3-space (§10.5, 12.6); parametric curves, vector-valued functions (§10.1, 13.1)

Due 10/3

12.5:  73, 74, 77, 78, 79

10.5: 2, 8, 14, 22, identify the conic sections in 25-30

12.6: 1, 4, 5, 10, 15, 16, 19, 21-28, 36, 47

10.5: All odd-numbered exercises.

12.6: Unassigned odd-numbered exercises 1-20, 31-38, 43-46, 49.

10/2, 10/4

Review for first midterm (through 12.6); first midterm

Due 10/9

10.1: 7, 8, 11, 14, 24, 28

Exercises 24 and 28 are designed to develop geometric intuition: using a graphic calculator defeats the purpose

13.1: 1, 4, 5; 9, 10 (for the last two find a one-word description for the graph); 16, 21-26.

10.1: 10, 19-22, 33; also 43, 44, 48, 52 (for fun)

13.1: 12, 13, 14, 28, 31

10/9, 10/11

Integrals of vector-valued functions, applications  (§13.2-3)

Due 10/16

13.2: 6, 7, 10-12, 16, 21, 26, 27, 34, 37, 42

13.3: 1, 4, 11, 13, 19, 20, 22, 32, 47

13.2: 1-5, 17-20, 28, 41

13.3: 2, 3, 5, 7-9, 16, 21, 25, 42-45

10/16, 10/18

Physical applications (§13.4, time permitting); functions of several variables (§14.1-2)

Due 10/23

13.4: 5, 8, 10, 11, 16, 18(a), 19

14.1: 3, 12, 13, 22, 25, 28, 29, 32, 46, 48, 61-66, 67, 70

13.4: 3, 4, 7, 15, 17, 22, 28, 35, 44, 45

14.1: 5, 8, 10, 16, 20, 33, 36, 49, 52, 71

10/23, 10/25

Partial derivatives and tangent planes (§14.3-4)

Due 10/30

14.2: 6, 10, 11, 14, 17, 18, 25, 32, 33, 37, 41

14.3: 5-8, 10, 18, 20, 21, 29, 36, 47

14.2: 2, 5-20 (those not assigned), 29,38

14.3: 25, 27, 31, 33, 35, 37, 43, 48

10/30, 11/1

Chain rule (§14.5);  Review for second midterm (through 14.4)

Due 11/13 (note the date!)

14.3: 64, 65, 72, 78, 88, 94

14.4: 2, 4, 12, 18, 21, 25, 28, 32

14.5: 2, 3, 6, 7, 12, 13

314.3: 75, 76, 86, 95

14.4: 1, 3, 5, 26, 27, 29

14.5: 1, 4, 5, 8, 9, 11, 19

11/8

Second midterm

Second midterm (no HW)

 

11/13, 11/15

Directional derivatives and the gradient (§14.6), Maximum/minimum problems (§14.7, beginning)

Due 11/20

14.5: 22, 23, 27, 30, 31, 42, 49

14.6: 5, 7, 13, 21, 22, 29

14.5: 28, 29, 32, 44, 50

14.6: 6, 11, 27

11/20

Complex numbers (Appendix)

Due 11/29 (note the date!)

14.7:  1, 2, 3, 6, 9, 11, 16 (graphing not necessary),  21, 32, 35, 36, 39 (graphing not necessary)

Appendix H:  4, 8, 9, 12, 16, 39

 

14.7:  13, 19, 31, 33, 37

Appendix H: 24, 34, 44, 45

11/27,  11/29

The gradient (§14.6),  Maximum/minimum problems and Lagrange multipliers (§14.7-8)

Due 12/4

14.6:  9, 15, 41, 43, 52, 55, 60, 64(a)

14.7: 41, 43, 44, 46, 54, 57

14.8: 4, 6, 7, 8, 12, 22, 31, 33, 34, 36

14.6: 10, 16, 24, 56, 63

14.7: 42, 47, 49, 50, 55, 56, 59

14.8: All odd problems 1-23, 31-43

12/4, 12/6

Maximum/minimum problems and Lagrange multipliers, continued; Review for final exam

 

 

 

 

           

Midterms:  October 4,  November 8 (in class)

 

Final:  date to be announced by the registrar

 

If you have a conflict with any of the exams, you must inform the instructor as soon as possible and at least one month before the exam.  Make-up exams will not be given unless the student has two other exams scheduled the same day.  Students with three exams scheduled on the same day should visit the Student Service Center in 205 Kent Hall to fill out a form which can then be submitted to each instructor or department.  An attempt will then be made to arrange for one of the instructors to schedule a make-up exam on a different day.  Students can only be excused from the exams because of serious illness or family emergency;  documentation from your doctor or dean must be provided. 

 

No electronic devices (laptops, calculators, telephones) are allowed during exams.

 

 

Practice exams and notes

 

Homework will be graded and will count for 20% of the final grade.  Homework is due on Tuesday the week after it is assigned, except where otherwise indicated.  Late homework will not be accepted.    

 

The two lowest grades (of 12 assignments) will be dropped.

 

Grades will be computed as follows:

 

            Homework (and occasional quizzes):  20%

            Final exam:  40%

            Midterms:  20% each

 

 

Academic integrity:   Students are encouraged to work together on homework but any assignments handed in should be the work of the person whose name appears at the top of the page.  Collaboration during exams is considered cheating and is taken very seriously.  Cheating during a midterm or final entails failing the course.  Students are advised to consult the Columbia University Undergraduate Guide to Academic Integrity.  

 

Disability services:    In order to ensure their rights to reasonable accommodations, it is the responsibility of students to report any learning-related disabilities, to do so in a timely fashion, and to do so through the Office of Disability Services. Students who have documented conditions and are determined by DS to need individualized services will be provided an DS-certified ‘Accommodation Letter’. It is students’ responsibility to provide this letter to all their instructors and in so doing request the stated accommodations. 

More information on the DS registration process is available online at https://health.columbia.edu/content/disability-services.

 

 

 

            Solution sheets

1st week           

2nd week          

3rd week

4th week

5th week

6th week           

7th week

8th week

9th week

10th week

11th week

12th week         

           

 

 

 

 

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