AS.110.211 Honors Multivariable Calculus

Spring 2019 Course Syllabus


Prof. Richard Brown

MW 1:30pm - 2:45pm: 316 Hodson Hall


403 Krieger Hall




Office Hours:



3:00-4:00 pm

by appt. other times


2:00-3:00 pm


Text: Vector Calculus, 4th Edition, Colley, Susan J., New Jersey: Pearson, September 15, 2011, ISBN-10: 0321780655, ISBN-13: 978-0321780652.


Recitation Section:






Friday 1:30pm

309 Maryland Hall


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 slightly 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 110.211 Honors Multivariable Calculus

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 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 110.109.  The link is here:

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

Linear algebra is also a required prerequisite fot this course, and this course will assume prerequisite knowledge of the content from our version of linear algebra AS.110.201 Linear Algebra. If you have teken a linear algebra course outside of Hopkins, please use the content syllabus given here as a guide to the topics we cover:

Content Syllabus for AS.110.201 Linear Algebra

Grade Policy:  There will be weekly homework sets (10%), 2 in-lecture exams (50%) 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 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 Wednesday (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, however, 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 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 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 ( ).


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.


Spring 2019 Tentative Schedule

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





Support Documents

January 28

January 30

Course Orientation

2.1 Fncs of Several Variables

Problem Set 1 (Feb 6)





February 4 (Hack B-17)

February 6

2.2 Limits

2.3 The Derivative

Problem Set 2 (Feb 13)



February 11

February 13

2.3 The Derivative

2.4 Properties: Higher-order Partials

2.5 The Chain Rule

Problem Set 3 (Feb 20)


February 18

February 20   (Notes)

2.5 The Chain Rule

2.6 Directional Derivatives & Gradient

2.6 Implicit and Inverse Fnc Thms



February 25

February 27

3.1 Parameterized Curves

3.2 Arc Length

3.3 Vector Fields

3.4 Divergence, Curl, & Del Operator



March 4

4.1 Differentials/Taylor's Thm

4.2 Extrema of Functions



March 6

Exam 1 (Sections covered to 3.4)

March 11

March 13

4.3 Lagrange Multipliers

5.1 Multiple Integration

5.2 Double Integrals



March 18-20

Spring Break (No classes)

March 25

March 27

5.2 Double Integrals

5.3 Order of Integration

5.4 Triple Integrals

5.5 Changing Variables



April 1

April 3

6.1 Line Integrals

6.2 Green's Theorem

6.3 Conservative Vector Fields



April 8

April 10

6.3 Conservative Vector Fields

7.1 Parameterized Surfaces

7.2 Surface Integrals



April 15

April 17

7.2 Surface Integrals

7.3 Gauss' and Stokes Theorems



April 22

8.1 Differential Forms



April 24

Exam 2 (Sections covered to 7.3)

April 29

May 1

8.1 Differential Forms

8.2 Manifolds/Integrals of k-forms

8.3 Generalized Stokes Theorem






> May 8

Final Exam