Origin of the “Power Rule”, and Visualizing Taylor polynomial approximations

This blog entry provides a helpful follow-up for a couple of calculus-related topics that we covered during the Mathematics Tutorial.

  1. See page 12 of the above-referenced lecture note. There, the equation for a parabola (y = {x^2}) appears, and the claim that dy/dx = 2x is corroborated by solving the following expression: \displaystyle\frac{{dy}}{{dx}} = \mathop {\lim }\limits_{\Delta x \to 0} \left[ {\frac{{{{(x + \Delta x)}^2} - {x^2}}}{{\Delta x}}} \right].In the 11-minute Khan Academy video at https://youtu.be/HEH_oKNLgUU, Sal Kahn takes on the solution of this problem in a very succinct and easy-to-comprehend fashion.
  2. On pp. 18-23 of the Mathematics Tutorial, I showed how y = ex can be approximated with a Taylor polynomial centered at x=0 for \delta x values ranging from -2 to +2.  In his video lesson entitled “Visualizing Taylor polynomial approximations”, Sal Kahn essentially replicates the work I did; the main difference between my example and Sal’s example is that Sal approximates y = ex with a Taylor polynomial centered at x=3 instead of x=0.  The important insight provided in both cases is that the accuracy of Taylor polynomial approximations increases as the order of the polynomial increases.

Lagrangian Multipliers

There is a section in the assigned “Optimization” reading due Thursday, January 20 on pp. 74-76 entitled “Lagrangian Multipliers” which (as noted in footnote 9 of that reading) may be skipped without loss of continuity. The primary purpose of this chapter is to re-acquaint students with basic calculus and how to use calculus to solve (unconstrained) optimization (i.e., maximization and minimization) problems. Since none of our work in Finance 4335 requires solving constrained optimization problems, there’s no need (in this course, anyway) for Lagrangian multipliers.

Besides reading the articles entitled “Optimization” and “How long does it take to double (triple/quadruple/n-tuple) your money?” in preparation for   Thursday’s meeting of Finance 4335, make sure you also (if you haven’t already done so) complete the Student information survey, sign up for your free WSJ student membership at https://wsj.com/ActivateBaylor, and subscribe via email to the course blog.

How to know whether you are on track with Finance 4335 assignments

At any point in time this semester, you can make sure that you are on track with Finance 4335 assignments by monitoring due dates on Canvas and on the course website. Links for future class meetings, quizzes, problem sets, and exams appear on the Canvas “To Do” list. Links for readings (along with their due dates) appear on http://fin4335.garven.com/readings/, and links for problem sets (along with their due dates) appear on http://fin4335.garven.com/problem-sets/. In the case of assigned readings, students are required to complete a short (10-minute) readings quiz prior to the start of class for each reading assignment due date; the window for completing this task begins 24 hours prior to the start of the class meeting for which the reading assignment is due.

Textbook for Finance 4335

The textbook for Finance 4335 is entitled “Integrated Risk Management: Techniques and Strategies for Managing Corporate Risk”, authored by my dissertation advisor Neil A. Doherty, who is an emeritus professor at the Wharton School, University of Pennsylvania. Here’s how the Baylor Bookstore lists this title:


Although the Finance 4335 textbook is “out of stock” at (i.e., not available from) the Baylor Bookstore, this book is available for purchase from Amazon.com as well as various other online booksellers. Alternatively, you may also download and print assigned chapters from the course website.

I supplement Doherty’s book with readings from various other sources, as well as readings that I have authored. See http://fin4335.garven.com/readings/ for a date-ordered list of reading assignments. Since the first reading assignment from the textbook isn’t due until Tuesday, February 1, y’all have plenty of time to order the book online, or if you prefer, source textbook readings from the course website.

Important notice concerning Section III.C.16 of Baylor’s Honor Code Policy and Procedures document

According to Section III.C.16 of Baylor’s Honor Code Policy and Procedures, using, uploading, downloading, or purchasing any online resource that has been derived from material pertaining to a Baylor course without the written permission of the professor constitutes dishonorable conduct; i.e., an act of academic dishonesty.  Section IV.A. of the same document obligates faculty members who suspect that a student has engaged in dishonorable conduct of this sort to either handle the matter directly with the student or refer it to the Honor Council.

While you may use course-related documents that I distribute in class and on the course website for strictly personal academic purposes, anything other than your personal use of these documents is in violation of Section III.C.16 of Baylor’s Honor Code Policy and Procedures and therefore, expressly forbidden.  Examples include sharing course-related documents with students who are not enrolled in Finance 4335 and uploading such documents to so-called course-sharing websites such as Quizlet, Coursehero, and Chegg, etc.  Furthermore, the use of course-related documents (e.g., old problem sets and exams) from any other source other than me also represents an honor code violation.

I close by citing the “Academic Honesty and Integrity” section of the Finance 4335 course syllabus:

Plagiarism, or any form of cheating, involves a breach of student-teacher trust. This means that work on quizzes, problem sets, and exams submitted under your name is expected to be your own, neither composed by anyone else as a whole or in part, nor handed over to another person for complete or partial revision. Instances of plagiarism, or any other act of academic dishonesty, will be reported to the Honor Council and may result in failure of the course or expulsion from the University.

Baylor’s honor code and the Finance 4335 honor code are important resources for understanding various types of academic dishonesty, and I expect my students to be intimately familiar with both of these documents. The standards set forth in both of these honor codes will be applied to all of your work in Finance 4335.

Course Requirement: Email subscription to the Risk Management Course Blog (instructions given here)

A course blog has been established for Finance 4335 at the address http://risk.garven.com; it is also linked from the “Course Blog” button located on the course website. This resource provides a convenient means for Dr. Garven to distribute important announcements outside of class. Topics covered on the course blog typically include things like changes in the course schedule, clarifications, and hints concerning problem sets, information about upcoming exams, announcements concerning extra credit opportunities, and short blurbs showing how current events relate to many of the topics covered in Finance 4335.

All students enrolled in Finance 4335 are required to subscribe to the course blog via email.

Email Subscription Instructions:

In order to subscribe to the course blog via email, go to http://risk.garven.com and enter your email address in the form provided on the right-hand side of that webpage:

After clicking “Subscribe”, the following information will appear on the screen:

Next, check for an email from “Risk Management Blog <donotreply@wordpress.com> ”:

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Next, simply click the “Confirm Follow” button. This will cause you to receive the following email:

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From that point forward, whenever I post to the course blog, you will immediately receive a nicely formatted version of the blog posting via email.

Calculus and Probability & Statistics recommendations…

Since many of the topics covered in Finance 4335 require a basic knowledge and comfort level with algebra, differential calculus, and probability & statistics, the second class meeting during the Spring 2022 semester will include a mathematics tutorial, and the third and fourth class meetings will cover probability & statistics. I know of no better online resource for brushing up on (or learning for the first time) these topics than the Khan Academy.

So here are my suggestions for Khan Academy videos that cover these topics (unless otherwise noted, all sections included in the links which follow are recommended):

Finally, if your algebra skills are generally a bit on the rusty side, I would also recommend checking out the Khan Academy’s review of algebra.