Math 109:  Calculus II (Physical Sciences & Engineering)

Spring 2012 Course Page

Instructor:  Dr. Richard Brown

Sections: 

Text:

Single Variable Calculus:  Early Transcendentals, 7th Ed. James Stewart, ISBN-10: 0-495-01169-X  ISBN-13: 978-0-495-01169-9

 

 

Course Syllabus and Homework Assignment Schedule

 

• There is now a Facebook page for this course: 

• 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:  This is the second semester of our course series 110.108-9 Calculus for the Physical Sciences and Engineering.  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 here at Hopkins, you will need to 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 the syllabus for 110.108 (the text is the same) 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.

• 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.  Here is a brief idea of what I think makes for a well-constructed homework solution.  And here are a set of selected homework solutions from the course 110.108 Calculus I last fall.  Note the style of the presentation of solutions.  You should strive to emulate a style like this.

  • Problem 2.3.9

  • Problem 2.3.28

  • Problem 2.3.40

  • Problem 2.4.22

  • Problem 2.4.30

  • Problem 2.5.36

  • Problem 3.4.42

  • Problem 3.4.54

  • Problem 3.9.16

  • Problem 3.9.22

  • Problem 3.9.46

  • Problem 4.2.18

  • Problem 9.5.15

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

  • The Final Exam Schedule:  The link currently goes to last spring's schedule.  However, the structure will be the same.  The final exam schedule for this course, along with all of the other 'service' courses, will be scheduled for the morning of the first day of the finals period: Wednesday, May 9, 2012 at 9am.

  • The Academic Calendar.

  • Deadlines Dates for Adds, Drops and Withdrawals (Currently, this link will fail.  It has not been posted yet.)

• Lecture Notes:

  • Week 3

  • Week 4

  • Week 5

  • Week 6

  • Week 7

• Exam Solutions: 

  • Midterm 1

• Extra Material you may find useful:

  • Section 2.1:  Geogebra Module: The Tangent Line Problem

  • Section 2.4:  Geogebra Module: The Limit Idea

  • Section 2.6:  Geogebra Module: The Limit at Infinity: An Exponential Function

  • Section 2.6:  Proof of the theorem on the continuity of a differentiable function.

  • Section 3.3:  Geogebra Module: The Derivative of the Sine Function.

  • Section 3.3:  Proof of the derivative of the sine function.

  • Section 3.6:  An example of Implicit Differentiation as an analytical tool.

  • Section 4.1:  Proof of the Extreme Value Theorem.

  • Section 4.4:  Simple proof of a special case of L'Hospital's Rule.

  • Section 7.1:  Two examples of the Integration by Parts and how it can be used are here and here.

  • Section 7.2:  Integrating a product of powers of sine and cosine functions where both powers are even.

  • Section 7.3:  Slightly weirder problems where inverse trigonometric substitutions are useful.

  • Section 7.4:  A Partial Fraction Decomposition problem.

  • Section 9.5:  A Linear IVP.

  • Section 10.3:  Polar Plots from Mathematica.

  • Section 11.1: Sequences from Mathematica.

• JODE Differential Equations Slope Field Calculator.

• In case you are interested, I ran across a YouTube video about infinite series that is cute.  Just thought I would post it here...

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:  03/13/2012