AS.110.202 Calculus III

Fall 2019 Course Syllabus


 

Prof. Richard Brown

MWF 11:00am - 11:50am: Shaffer Hall 3

brown@math.jhu.edu

MWF 12:00pm - 12:50pm: Shaffer Hall 3

403 Krieger Hall

 

410-516-8179

 

Office Hours:

M

3 - 4pm, Maryland 201

by appt. other times

Th

2 - 3pm, Krieger 300

 

Text: Vector Calculus, 6th Edition, Marsden, Jerrold E., and Tromba, Anthony, New York: WH Freeman, 2012, ISBN-10: 1-4292-1508-9, ISBN-13: 978-1-4292-1508-4.

 

Recitation Section:

 

Recitation Section:

 

TA Office Hours:

Section

Time

Place

Instructor

 

Section

Time

Place

Instructor

 

Instructor

Time

Place

1

T 1:30pm

218 Ames

Clingman (H)

 

7

T 4:30pm

119 Gilman

Sherwood

 

Tslil Clingman (H)

Th 4:00pm - 5:00pm

200 Krieger

2

T 3:00pm

216 Hodson

Koh

 

8

Th 1:30pm

176 Bloomberg

Kansal

 

Julia Costcurta

W 5:00pm - 7:00pm

207 Krieger

3

T 4:30pm

211 Hodson

Koh

 

9

Th 3:00pm

216 Hodson

Kansal

 

Yang He

M 4:00pm - 5:00pm

211 Krieger

4

Th 3:00pm

301 Hodson

Y He

 

10

T 1:30pm

176 Bloomberg

Costacurta

 

Kalyani Kansal

T 5:00pm - 6:00pm

202 Krieger

5

Th 1:30pm

B32 Croft

Je Zhang

 

11

T 3:00pm

211 Hodson

Costacurta

 

Hanveen Koh

M 3:00pm - 4:00pm

201 Krieger

6

T 1:30pm

B32 Croft

Sherwood

 

12

T 4:30pm

G02 Croft

VanBlargan

 

Jim Sherwood

T 2:55pm - 3:55pm

306 Krieger

 

 

 

 

 

13

Th 4:30pm

G02 Croft

Y He

 

Caroline VanBlargan

W 3:00pm - 4:00pm

202 Krieger

 

 

 

 

 

 

 

 

 

 

Jeffrey Zhang

T 4:30pm - 5:30pm

207 Krieger

 

Course Material: The core of the course will center on the text material, and will basically cover the material detailed in the syllabus link below. I may add and/or alter this material depending on how the semester plays out. But the core set of material that I will cover will be what is on the syllabus:

Content Syllabus for AS.110.202 Calculus III

In addition to this, you should be aware that the prerequisite for this is a full year of single variable calculus. With an Advanced Placement BC exam score of 5, or the equivalent credits of the course AS.110.109 Calculus II (Phys Sci & Eng), you are considered prepared for this course. If there is a question, please come see me. For now, what we consider prerequisite content is everything on the syllabus for both AS.110.108 and AS.110.109. The links are here:

Content Syllabus for AS.110.108 Calculus I (Phys Sci & Eng)

Content Syllabus for AS.110.109 Calculus II (Phys Sci & Eng)

Linear algebra is NOT a required prerequisite for this course. However, a good working pre-knowledge of vectors and matrices will be extremely helpful, as I will only quickly go over the content in Chapter 1 of the text, on the geometry of Euclidean space. Please review this material prior to the start of term.

 

Another resource: Here are written versions of the set of lectures I gave last yeear to the course AS.110.211 Honors Multivariable Calculus. It is my plan to eventually make this a textbook. For the most part, the topics are similar. The focus, however, is a bit different. But there is much here that is completely relevant to our current course. Use this as an additional resource, if you like.

Notes from AS.110.211 Honors Multivariable Calculus

 

And one last resource: Describing the properties of functions (which is what calculus essentially is) usually requires describing the properties of sets. Set notation is an extremely valuable language for this endeavor. It is also something that is not fully developed in single variable calculus. In the case that you are not fully versed in the notation and concepts of set theory, here is a quick primer, pulled off the internet from Clemson University:

A primer on Set Theory (notation)

 

Grade Policy: There will be weekly homework sets (10%), 2 in-lecture exams (50% total) and a final (40%). The schedule of these exams is given with the homework problems below. There will be no make-ups on homework or exams. If you will not be present when homework is to be submitted, please submit the assignment early. If you miss a homework or project deadline, you can talk to the TA for late acceptance, but I have instructed them to not accept late submissions. If you miss an exam, you will have to be cleared by me to be excused from the exam, a process that will include documentation and a valid excuse. In this case the ultimate grade for that exam will be calculated based on your performance on future exams and the final.

 

Homework: Homework, based on the week’s lectures, will be posted as official on the course web site sometime on Friday (Homework may be posted earlier, but may change as the lectures evolve for the week). That assignment will be due in lecture at the end of the following week. See below for the due dates. Homework is an absolutely essential educational part of the course. You will be graded mostly on your ability to work problems on exams. You cannot work problems on exams if you have not practiced the techniques and become comfortable applying the concepts within the homework problems. If you misuse homework by not doing it yourself, or not checking that you can solve a problem on your own after having been shown how to do it, then your exam scores and corresponding grade will reflect this. Trust me on this last point. Talk to the Teaching Assistant about how to turn in a homework if you cannot go to class. Some additional points:

  • You are strongly encouraged to collaborate in the analysis and study stage of homework preparation. However, you are required to submit completely original work, and must write up your homework for final submission alone.

  • You will be graded on your PROCESS in homework construction rather than simply your ability to calculate. You must present your homework solutions (keeping the reader in mind) and not simply answer questions.

  • Here is a brief idea of how one should construct homework problems for submission:

How to construct homework problem solutions: Example 1: Calculus I Bio , Example 2: Linear Algebra

Also, here is an excellent quick article on good mathematics writing . It is worth the read....

Course Policy: You are responsible for lecture notes, any course material handed out, and attendance in class. While I will not formally record your attendance, I will get to know you and your rate of presence over time. The lectures will be conducted as if you have already read the material and attempted some homework problems. In this manner, you can focus mainly on those parts of the lectures that cover the areas of your reading you found difficult to understand. My teaching style is that of interactive discussion and I will rely on your input in developing the material. Active participation in the classroom is a great way to generate the discussion necessary to fully grasp the material.

 

Help Room:   213 Kreiger Hall.  The hours are 9am - 9pm on Monday through Thursday, and 9am - 5pm on Friday. This free service is a very valuable way to get one-on-one help on the current material of a class from other students outside the course.  It is staffed by mathematics graduate students and advanced undergraduates.

 

Ethics Statement: The strength of the university depends on academic and personal integrity. In this course, you must be honest and truthful. Cheating is wrong. Cheating hurts our community by undermining academic integrity, creating mistrust, and fostering unfair competition. The university will punish cheaters with failure on an assignment, failure in a course, permanent transcript notation, suspension, and/or expulsion. Offenses may be reported to medical, law, or other professional or graduate schools when a cheater applies.

Violations can include cheating on exams, plagiarism, reuse of assignments without permission, improper use of the Internet and electronic devices unauthorized collaboration, alteration of graded assignments, forgery and falsification, lying, facilitating academic dishonesty, and unfair competition. Ignorance of these rules is not an excuse.

In this course, as in many math courses, working in groups to study particular problems and discuss theory is strongly encouraged. Your ability to talk mathematics is of particular importance to your general understanding of mathematics.

You should collaborate with other students in this course on the general construction of homework assignment problems. However, you must write up the solutions to these homework problems individually and separately. If there is any question as to what this statement means, please see the professor or the grader.

For more information, see the guide on "Academic Ethics for Undergraduates" and the Ethics Board web site ( https://studentaffairs.jhu.edu/policies-guidelines/undergrad-ethics/ ).

 

Students with Disabilities: Students with documented disabilities or other special needs that require accommodation must register with the Office of Academic Advising. After that, remind me of your needs at least 5 days prior to each exam; we will need to have received confirmation from Academic Advising.

 

Midterm 1 Room Assignments: The following rooms are assigned for the first midterm, scheduled for Monday, October 7, 2019. You must report to the proper room assigned to your section number for this exam, as we will not have extra exam copies for students who are not assigned to the room in which they appear. Good luck, all!!

  • 11am, Shaffer Hall Room 3: Sections 1, 4, 5, and 13.

  • 11am, Olin Hall Room 305: Sections 2, and 3.

  • 11am, Krieger Hall Room 170: Section 6.

  • 12pm, Shaffer Hall Room 3: Sections 7, 8, 10, and 11.

  • 12pm, Shaffer Hall Room 2: Section 9.

  • 12pm, Bloomberg Hall Room 170: Section 12.

 

Midterm 2 Room Assignments: The following rooms are assigned for the second midterm, scheduled for Wednesday, November 20, 2019. You must report to the proper room assigned to your section number for this exam, as we will not have extra exam copies for students who are not assigned to the room in which they appear. Good luck, all!!

  • 11am, Shaffer Hall Room 3: Sections 1, 2, 3, and 4.

  • 11am, Olin Hall Room 305: Sections 6, and 13.

  • 11am, Krieger Hall Room 170: Section 5.

  • 12pm, Shaffer Hall Room 3: Sections 7, 8, 9, and 10.

  • 12pm, Shaffer Hall Room 2: Section 11.

  • 12pm, Shaffer Hall Room 202: Section 12.

 

Final Exam Information: The final exam will occur on Monday, December 16, 2019, from 9am to 12pm in Hodson Hall Room 110. The following rooms are assigned for review sessions. For TAs that run review sessions, the sessions are primarily for their own students. But anyone in the course is invited to attend, at least up to the capacity of the room. I will add more here as they become part of the schedule. Good luck, all!!

  • Tuesday, December 10, 2019, 4:30pm - 6:00pm, Remsen Hall Room 1: Kalyani Kansal.

  • Friday, December 13, 2019, 5:00pm - 7:00pm, Hodson Hall Room 201: Julia Costacurta, Jim Sherwood, and Jeff Zhang.

 

Fall 2019 Tentative Schedule

The details of this material will be updated and reformed as the semester progresses. 

2019-2020 JHU KSAS Academic Calendar

 

Week

Sections

Homework

Support Documents

Other Suggested Exercises

August 29

August 30

Course Orientation

1.1 Vectors in 2 and 3-Dim. Space

1.2 Inner Prod., Length & Dist.

1.3 Matrices and the Cross Product

Problem Set 1 (Sept 6)

VectorsDefineAPlane.nb

1.1: 5,10,13,15,18,23

1.2: 2,8,13,20,26

1.3: 1,4,6,13,15b,16a,17,20,33,34

September 4

September 6

1.5 n-dim. Euclidean Space

2.1 Geometry of Real-Valued Fncs

Problem Set 2 (Sept 13)

IntersectionOf2Planes.nb

VisualizingFunctions.nb

LevelSets.pdf

Problem 2.3a Solution.pdf

1.5: 1,3,7,9,12,24

2.1: 3,5a,12,14,17,19,22,29

September 9

September 11

September 13

2.2 Limits and Continuity

Problem Set 3 (Sept 20)

PlottingSurfaces.nb

Problem 3.2 Solution

2.2: 3b,5,8ab,12ab,18

September 16

September 18

September 20

2.3 Differentiation

2.4 Paths and Curves

2.5 Properties of the Derivative

Problem Set 4 (Sept 27)

PartialDerivatives.nb

CurvesInSpace.nb

ChainRuleEx.pdf

Problem 4.2a Solution.pdf

2.3: 3acde,5,9,13,14,19,21,26

2.4: 2,4,6,12,13,15,18,21,24,25

2.5: 3a,5,6,8,9,10,11,18,32,35,36

September 23

September 25

September 27

2.6 Gradient and Directional Ders.

3.1 Iterated Partial Derivatives

Problem Set 5 (Oct 4)

Extrema.nb

LectureQuestions0925.pdf

TangentSpaces.pdf

Problem 5.1 Solution.pdf

2.6: 2ac,3a,4,6,8a,9a,10a,13,17,18

3.1: 1,3,6,9,11,16

September 30

October 2

October 4

3.2 Taylor's Theorem

3.3 Extrema of Real-Valued Fncs

Problem Set 6 (Oct 11)

TaylorPolynomials.nb

Problem 6.1 Solution.pdf

3.2: 1,2,3,4,9,10

3.3: 4,12,13,20,21,28,37

October 7

Exam 1 (Sections covered thru 3.2) Q1 Solution

Problem Set 7 (Oct 21)

MoreExtrema.nb

LagrangeMult.nb

ImplicitFunctionTheoremExample.nb

IFTproof.pdf

Problem 7.2ad Solution.pdf

3.4: 4,6,9,12,17,22

4.1: 3,8,9,12,23,25

October 9

October 11

3.4 Lagrange Multipliers

4.1 Curve Acceleration

October 14

October 16

4.2 Arc Length

4.3 Vector Fields

Problem Set 8 (Oct 25)

ParameterizationIndependence.pdf

LectureQuestions1016.pdf

Problem 8.1a Solution.pdf

4.2: 5,8,10,14

4.3: 9,10,13,16,19,21,22

October 18

Fall Break (No classes)

October 21

October 23

October 25

4.4 Divergence and Curl

5.1 Multiple Integral Introduction

5.2 Double Integrals on a Rectangle

5.3 Double Integration over a Region

Problem Set 9 (Nov 1)

Problem 9.3 Solution.pdf

4.4: 4,8,12,16,19,25,27,32,37

5.1: 3cd,4d,6,9,11,13

5.2: 4,10,12

5.3: 3,4f,7,8,12,13,15

October 28

October 30

November 1

5.4 Changing the Order of Integration

5.5 Triple Integrals

6.1 Geometry of Plane to Plane Maps

6.2 Change of Variables Theorem

Problem Set 10 (Nov 8)

SphereVolume.pdf

5.4: 1,2,5

5.5: 1,5,16,18

6.1: 2,3,7,10,11

6.2: 3,5a,8,10,15,23,35

November 4

November 6

November 8

7.1 The Path Integral

7.2 Line Integrals

Problem Set 11 (Nov 15)

LineIntegralOfScalarField.gif LineIntegralOfVectorField.gif

7.1: 4,6,9,11a,20,24

7.2: 1,4d,5,8,11,14,20

November 11

November 13

November 15

7.3 Parameterized Surfaces

7.4 Area of a Surface

7.5 Integrals of Fncs over Surfaces

7.6 Surface Integrals of Vector Fields

Problem Set 12 (Nov 22)

ParameterizedSurfaces.nb

7.3: 2,5,8,14,18,23

7.4: 3,5,25

7.5: 3,5,12,20

7.6: 2,4,6,13

November 18

8.1 Green's Theorem

Problem Set 13 (Not due)

GreensThmLemma.pdf

8.1: 8,11a,15,22

8.2: 1,5,8,15,18

November 20

Exam 2 (Sections covered thru 7.2)

November 22

8.2 Stokes' Theorem

November 25-29

Thanksgiving Break (No classes)

December 2

December 4

December 6

8.3 Conservative Vector Fields

8.4 Gauss' Theorem

Course Review

LectureQuestions1204.pdf

8.3: 2,3,8,9,11,17,19

8.4: 1,3,9a,11,12,14

 

 

 

December 16

Final Exam

9am -- 12pm:  Hodson Hall Room 110