Index for Differential Equations

MAP 2302

Differential Equations

Revised 1/9/12

Course Handouts

Ø Syllabus<= /b>: This document will give you a good idea of what the course will be like.<= /p>

Ø Schedule: This document gives a tentative schedule for the entire term.

Ø Practice Problems: This document contains a list of homework problems to help students prepare for tests.

Ø Course Objectives: This is the list of course of obje= ctives established by the HCC mathematics cluster.

Ø Blackboard: Handouts, reviews, practice tests, and the gradebook can be found here.

Links

Online Learning Tools

Ø Wol= framAlpha: According to the website this is an “online computation knowledge engine.”   This is a remarkable website= !

Ø Visual Cal= culus: Contains lots of example problems = solved step-by-step.   Good cove= rage of techniques of integration (a Calculus II topic) especially integration by parts, partial fractions, and substitution problems. These techniques are useful for so= lving differential equations.

Ø Calculus: A free calculus textbook courtesy = of Wikibooks! Unfortunately its explanations are= brief and the exercises are very limited. &= nbsp; Perhaps in the future it will be as good as a commercial text. An improved book, in the public do= main like this one, would save students a pretty penny! Use it to review Calculus topics i= f you do not have easy access to a Calculus book.

Ø MathWo= rld: An online encyclopedia of mathemat= ics.

Ø MIT OpenCourseWare for Differential Equations: An online course on Differential Equations designed at MIT.   The video lectures and lecture notes cover many of the same topics we will be learning in this course.

Ø Paul’s Onl= ine Math Notes – Differential Equations: Nice notes for a Differential Equa= tions course created by Paul Dawkins of Lamar University.

History Topics

Ø Gottfried Leibniz: A short biograph= y of one of the creators of the Calculus.

Ø Sir Isaac Newton: A short bio= graphy of one of the creators of the Calculus.

Ø Leonard= Euler: A short biography of the most prol= ific mathematician of all time. He= was one of the most prolific mathematicians of all time. We will study Euler’s Method= —a procedure for numerically solving a first order differential equation.

Ø Willard Libby: He won the Nobel P= rize in chemistry in 1960 for his method of dating organic material by measuring= the radioactive decay of carbon-14. His method uses an exponential model for radioactive decay as he mentions in his presentation speech: <= /span>

The disintegration [of Carbon-14] is such a slow procedure, however, that 5,600 years are required to convert half of these atoms into nitrogen. After anot= her 5,600 years, there is still one quarter left, and after an equally long per= iod of time one eighth, etc. Carbon-14 is thus said to have a half-life of 5,600 years.

The presentation speech found at the link giv= es a good explanation of his work. Libby’s very readable Nobel speech is also available on this w= eb page.

Ø Thomas Malthu= s: In his An Essay on t= he Principle of Population Malthus proposed an exponential model for the growth of human populations and discusses the negative effect of such a mod= el on human happiness. His paper= helped Charles Darwin and Alfred Wallace, independently, to develop the theory of natural selection.

Ø Jules Verne’= s From the Earth to the Moon: An etext version of Jules Verne= 217;s novel. In the novel, the Gun = Club sends a manned projectile to the moon.&nbs= p; We will compute the earth’s escape velocity by doing the “incontrovertible calculations” that Barbicane, president of the Gun Club, alludes to at the end of Chapter 2.   At the end of Chapter 11<= /a>, Barbicane chooses Tampa Town for the firing of the Gun Club’s moon shot! A historical marker at = the spot of the fictional launch can be found at Ballast Point in Tampa.

Ambri= oso Fall 2011