Mathematical Methods 1: e-Gear

Below is a growing list of on-line course materials an links. Links marked with an asterisk (*) point to PDF files; to view them, you may need to obtain the proper plug-in and Reader software from Adobe.

As much as it used to be a practice to test the students in their knowledge of functional analysis and calculus within the homework and test questions, modern technology has made that very moot: with sites such as [WolframAlpha], which are even accessible from internet-capable mobile telephones, it is practically impossible to prevent students from using such services. On the other hand, I find it unfair to expect students to use such services, as affording an internet-capable mobile phone should not be a prerequisite for learning. I will therefore try and assign (at least in the tests) problems that the AI^† behind sites such as [WolframAlpha] cannot (as yet) solve. In turn, please visit the web-page “Wolfram Technology at Howard University” for information about installing a licensed copy of Mathematica on your computer, and also on using “Wolfram Alpha Pro” under the University’s campus license; for any questions and supprt, please refer to the iLab.

Study material

• A handout on motivating the use of non-convergent series* in solving differential equations
• A handout on vector calculus* & its updated version*
• A vector calculus* reference table
• A handout on orthogonal coordinate systems*
• A handout on potential theory*
• A handout on Dirac’s delta-“function”*
• A handout on tensor calculus*
• A 38-page introduction to tensor calculus* (completely general n-dimensional coordinate systems!)
• A (dated) handout on integration and ordinary differential equations*
• Two handouts, first* and second*, on evaluating integrals using contour integration and the residue theorem
• A handout on Lauent power series*
• A handout on Euler's Gamma function*
• The Clebsch-Gordan coefficients*

Past exams

• Some sample quizzes*
• A pretest* and a sample double quiz*, for self-testing
• The 1997: first mid-term exam* (and its solution*)
• The 1997: second mid-term exam* (and its solution*)

Both mid-term exams had an in-class and a take-home component. After having done as much as possible in-class (in 1 hour), the students completed and corrected their work over the next couple of days, at 2/3 of credit. That is, a proposed take-home solution (or part thereof) superseded the in-class attempt. However, as take-home effort only carried 2/3 of the credit, students should have reworked only those (parts of) problems where they could successfully solve at least 1.5 times more than they did in-class.

• The final exam*, take-home and comprehensive.

From Fall 2014, the order in which the topics are covered has changed, partly owing to the reordering of the material in the 7th edition of Arfken-Webber-Harris's text, partly so as to provide a better running co-requisite for the courses Electromagnetic Theory and Classical Mechanics. For this reason, I am listing a full complement of the mid-term and final exams from 2010; they cover the same types of problems, but grouped and ordered differently than they are covered since Fall 2014.

2010, MM1: Midterm-1 (sol'n), Midterm-2 (sol'n), Final
2010, MM2: Midterm-1, Midterm-2, Final
MM1: 2019 Midterm-1 sol'n, 2014 Midterm-2 sol'n

^†AI = authentic idiocy, in some folks’ opinion