Math 110.211:  Honors Multivariable Calculus

Spring 2019 Course Page

Instructor:  Prof. Richard Brown

Sections: 

Text:

Vector Calculus, 4th Ed. by Susan Jane Colley

 

 

Course Syllabus and Homework Assignment Schedule

 

Welcome to the Spring 2019 version of AS.110.211 Honors Multivariable Calculus.  Most of the informational aspects of the course, as well as its logistics will be documented here and in the linked syllabus above.  As you know, this is an honors course.  The prerequisites for this course are a full year of single variable calculus AND a semester of university-level linear algebra.  Prior knowledge in linear algebra will be necessary as the study of the properties of functions of more than one independent variable (that are possibly vector-valued) relies critically on the linear structure of vector spaces.  We will use that knowledge (but not develop it) in this class.   The link above takes you to a page which details the basic structure of the course along with an idea of the week-by-week schedule.  As need be, this syllabus and schedule will be amended to reflect the current focus of the course.  Also, it will be updated regularly with the homework assignments and such.  For now, let's leave it at that. 

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 AS.110.108-109 Calculus I-II (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:

  • AS.110.108 Calculus I (Phys Sci & Eng)

  • AS.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: Just as in single variable calculus, where the entire idea of a function being differentiable at a point means that it locally can be well-modeled by a linear funciton, and its graph, as a curve, can be well-modeled by a line, differentiable functions of more than one variable can be modeled by linear spaces.  So a good foundational knowledge opf what is the structure of a linear subspace of real spoace will be vital to our understanding of teh properties of functions.  Hence ia solid foundation in linear algebra will be considereed prerequisite material for this course.  What that entails can be found in our version of linear algenbra, whose syllabus is here:

  • AS.110.201 Linear Algebra

• 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:  I will link to the final exam schedule for this course when it is available

  • The Hopkins Academic Calendar for academic year 2018-2019.

• Lecture Notes:

  • Monday, January 28:  Some Linear Algebra backstory:  As an introduction to the course, I thought to play with the structure of Euclidean space and linear algebra just to establish notation and begin the conversation.  As you are all well-versed in linear algebra, it should all be straightforward.  I also used a bit of Mathematica for visualization.

  • Wednesday, January 30:  Section 2.1.  Again, covering this section is mostly for notation and viewpoint.   Pay close attention to why and how we visualize functions, through parameterizations, graphs, slices and sections.  These will expose the visual clues to how we analyze functions. Some Mathematica to help in visualization:  Parameterized curves, surfaces, and sections and slices of graphs.

  Problem Sets:

  • Problem Set 1 (Due Wednesday, February 6):

    • Section 2.1:  2, 4, 6, 11, 12, 16, 18, 20, 36, 38, 40

  • Problem Set 2 (Due Wednesday, February 13):

  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.

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  Last updated:  01/19/2019