Math 110.211:  Honors Multivariable Calculus

Spring 2012 Course Page

Instructor:  Dr. Richard Brown

Sections: 

Text:

Vector Calculus, 4th Ed. by Susan Jane Colley

 

 

Course Syllabus and Homework Assignment Schedule

 

Welcome to the Spring 2012 version of 110.211 Honors Multivariable Calculus course.  As you know, this course is now to be considered a shortened version of the standard course.  On the Schedule link directly above, you will find a tentative schedule for the remainder of the semester.  Due to the brevity of the time remaining in the semester, the approach to this course will be the following:  We will cover MOST of the material that is usual for this course, and ALL of the material necessary to use this course as a prerequisite for any course requiring vector calculus as prior knowledge.  We will have to do so with an understanding that we may have to sacrifice a depth of coverage of certain topics for an adequate treatment of all topics.  Part of the burden of this situation will be placed on your backs;  there will be more assumptions made and work expected on the part of the student.  The pace of the course will be quicker, requiring more background and follow up on the student's part to acquire the skills necessary to keep this pace.  I, as the instructor, will provide more office time and possible a few extra class periods to help make up for the lost time.  The TA, Peng Shao, will also be readily available to provide the extra support needed to make this course a success.  We will continue this conversation on Monday, March 26.  For now, welcome to the course.

Some extra stuff:

• So do you want to start thinking like a mathematician?  Here is a good place to start:

  • 10 Ways to Think Like a Mathematician

• Prerequisite material for this course: 

  Calculus:  This is to be considered the third semester of our course series 110.108-9 Calculus for the Physical Sciences and Engineering.  The techniques you will see and the theory we will develop all stem from appropriate generalizations of what we consider to be Single Variable Calculus.  Should you need, the official department syllabi for this series can be found here:

  • 110.108 Calculus I (Phys Sci & Eng)

  • 110.109 Calculus II (Phys Sci & Eng)

  If you did not take 110.108 and/or 110.109 here at Hopkins, you should acquaint yourself with the material that I will assume you already know.  Unfortunately, this will have to be done on your own.  Take some time to review these syllabi and make sure you have covered ALL of this material.  Feel free to consult with me and/or your Section TA about this prerequisite material.

  Linear Algbra:  Linear Algebra is considered a co-requisite for this course.  Hence I will make the assumption that any material up to and including the 7th week of our standard 110.201 Linear Algebra course is known.  We can certainly make adjustments in class.  But this will help alot.

• How to write up Homework Solutions:  Constructing homework solutions is a vital way to explore and strengthen your understanding of the theoretical underpinnings and practical applications of the material in this course.  There is no better way to fully comprehend the mathematical content of this course than to attempt to explain in full detail just how a mathematical problem is posed, presented and solved via the conceptual and practical application of technique and theory.  Besides developing a great tool for continued study, both in this course and in future courses, constructing comprehensive and detailed solutions to mathematical problems develops your ability to communicate mathematical ideas effectively, rather than simply to calculate.  The construction of your solutions, in effect the story you tell that convinces the reader that your solution is indeed correct, will be an important part of all grading criteria regarding homework assignments. 

• Some relevant deadlines, calendars and schedules to keep in mind:

  • The Final Exam Schedule:  The final exam schedule for this course is currently scheduled for the afternoon of the last day of the finals period: Thursday, May 17, 2012 at 2pm.

  • The Academic Calendar.

  • Deadlines Dates for Adds, Drops and Withdrawals

• Some Extra stuff:

  • An example of the level sets of a scalar-valued function on three variables, as subsets of three-space.

  • Some Mathematica plots of the graphs and limits we are looking at in class.

  • A Product Rule for limits of vector-valued functions.

  • A 110.108 lecture on the definition of a limit in single variable calculus.

  • Some information about the differential of a function.

  • Why the length of a path is independent of its parameterization.

  • Proof of the Implicit Function Theorem in three space.

  • Midterm Exam Solutions

  • Proof of one of the lemmas behind the proof of Green's Theorem.

  • Lecture Notes from Monday, April 30, on Green's Theorem.

  • Lecture Notes from Wednesday, May 2, on Parameterized Surfaces.

  • Lecture Notes from Friday, May 4, on Stokes' and Gauss' Theorems.

This page will be updated regularly when new information about the course arises.  General information about course structure, requirements, as well as specific information related to your lecture or section, will be posted here and updated as needed. 

For those of you who would like help outside of that of the professor or TAs, there is a free service offered by the Mathematics Help Room.  Click for more details.

Last updated:  03/29/2012