Differential Equations Differential Equations (Math 3301) Here are my online notes for my differential equations course that I teach here at Lamar University. Despite the fact that these are my “class notes”, they should be accessible to anyone wanting to learn how to solve differential equations or needing a refresher on differential equations. I’ve tried to make these notes as self contained as possible and so all the information needed to read through them is either from a Calculus or Algebra class or contained in other sections of the notes. A couple of warnings to my students who may be here to get a copy of what happened on a day that you missed. Because I wanted to make this a fairly complete set of notes for anyone wanting to learn differential equations I have included some material that I do not usually have time to cover in class and because this changes from semester to semester it is not noted here. Here is a listing and brief description of the material in this set of notes. Basic Concepts
HIGHLEVELMATHS.COM Three-Cornered Things | Weekly wanderings through higher math—from not so high a vantage point. THE MATHEMATICS OF LOVE: A Talk with John Gottman (JOHN GOTTMAN:) I look at relationships. What's different about what I do, compared with most psychologists, is that for me the relationship is the unit, rather than the person. What I focus on is a very ephemeral thing, which is what happens between people when they interact. It's not either person, it's something that happens when they're together. I've been working on a couple of puzzles right now. It's a very hard thing to look at. We've reconstructed it from what we have learned by talking to people about it, and it does seem that there are two very distinct forms of violence. Another kind of violence, which is very different, is where one person in the relationship is using violence to control and intimidate the other person and is very much not physiologically aroused, very much in control and trying to do something to the other person that alters their idea of reality. Another puzzle I'm working on is just what happens when a baby enters a relationship. Again.
Lee Lady: Calculus for the Intelligent Person Teaching students how to use the concepts of the derivative and the integral is different from teaching them to understand the concepts. Understanding is certainly nice, and to some extent it's something that students feel a need for, but my main goal is for students to be able to use calculus in applications. This means, among other things, being able to have confidence in setting up formulas using derivatives and integrals. Abstract (in HTML). These notes are an attempt to show how to express a given mathematical relationship in the form of an integral. However in practice, the evaluation of integrals has nothing to do with dividing areas into little vertical strips and taking Riemann sums. Further Notes on Applications of Integration (Click here for DVI version.) (Click here for postscript version.) This is a much more condensed version of the ideas in the preceding article. Outline Sketch for the Applications of Integration Method (Click here for DVI version.) Max-Min Problems. f(x)
I Love Maths Games Intuitive Understanding Of Euler’s Formula Euler's identity seems baffling: It emerges from a more general formula: Yowza -- we're relating an imaginary exponent to sine and cosine! Not according to 1800s mathematician Benjamin Peirce: It is absolutely paradoxical; we cannot understand it, and we don't know what it means, but we have proved it, and therefore we know it must be the truth. Argh, this attitude makes my blood boil! Euler's formula describes two equivalent ways to move in a circle. That's it? Starting at the number 1, see multiplication as a transformation that changes the number (1 * e^(i*pi))Regular exponential growth continuously increases 1 by some rate; imaginary exponential growth continuously rotates a numberGrowing for "pi" units of time means going pi radians around a circleTherefore, e^(i*pi) means starting at 1 and rotating pi (halfway around a circle) to get to -1 That's the high-level view -- let's dive into the details. It follows the post -- watch together, or at your leisure. The equals sign is overloaded.
Mysterious number 6174 March 2006 Anyone can uncover the mystery The number 6174 is a really mysterious number. At first glance, it might not seem so obvious. Kaprekar's operation In 1949 the mathematician D. It is a simple operation, but Kaprekar discovered it led to a surprising result. When we reach 6174 the operation repeats itself, returning 6174 every time. We reached 6174 again! A very mysterious number... When we started with 2005 the process reached 6174 in seven steps, and for 1789 in three steps. Only 6174? The digits of any four digit number can be arranged into a maximum number by putting the digits in descending order, and a minimum number by putting them in ascending order. 9 ≥ a ≥ b ≥ c ≥ d ≥ 0 and a, b, c, d are not all the same digit, the maximum number is abcd and the minimum is dcba. We can calculate the result of Kaprekar's operation using the standard method of subtraction applied to each column of this problem: which gives the relations for those numbers where a>b>c>d. How fast to 6174? and
Calculus Integrals Math Sheet Definition of an IntegralReturn to Top The integral is a mathematical analysis applied to a function that results in the area bounded by the graph of the function, x axis, and limits of the integral. Integrals can be referred to as anti-derivatives, because the derivative of the integral of a function is equal to the function. PropertiesReturn to Top Common IntegralsReturn to Top Integration by SubstitutionReturn to Top Integration by PartsReturn to Top Integration by Trigonometric SubstitutionReturn to Top Trigonometric identities can be use with integration substitution to simplify integrals. First Trigonometric SubstitutionReturn to Top To take advantage of the property Substitute After substitution Second Trigonometric SubstitutionReturn to Top After substitute Third Trigonometric SubstitutionReturn to Top
Mathematics resources - www.mathcentre.ac.uk or The Thirty Greatest Mathematicians Click for a discussion of certain omissions. Please send me e-mail if you believe there's a major flaw in my rankings (or an error in any of the biographies). Obviously the relative ranks of, say Fibonacci and Ramanujan, will never satisfy everyone since the reasons for their "greatness" are different. I'm sure I've overlooked great mathematicians who obviously belong on this list. Please e-mail and tell me! Following are the top mathematicians in chronological (birth-year) order. Earliest mathematicians Little is known of the earliest mathematics, but the famous Ishango Bone from Early Stone-Age Africa has tally marks suggesting arithmetic. Early Vedic mathematicians The greatest mathematics before the Golden Age of Greece was in India's early Vedic (Hindu) civilization. Top Thales of Miletus (ca 624 - 546 BC) Greek domain Apastambha (ca 630-560 BC) India Pythagoras of Samos (ca 578-505 BC) Greek domain Panini (of Shalatula) (ca 520-460 BC) Gandhara (India) Tiberius(?)
Have we caught your interest? June 2000 Introduction "Neither a borrower nor a lender be." Today, nobody heeds the advice of Polonius to his student son Laertes. Everybody borrows and lends all the time. Children put their pocket money into a bank account to save up to buy a bicycle.Students take out loans to finance their studies.Credit cards are widely used for short-term borrowing.Young couples buy houses on mortgages of 20 to 30 years, and save for their retirement. Understanding lending and borrowing means understanding compound interest. In this article we will not attempt a comprehensive coverage of all the intricate details of the subject, but will try to show that compound interest is an essential component of numeracy,involves some interesting maths,throws up some surprising, even paradoxical results from time to time. A slice of history Figure 1: The real purpose of the ziggurat? The application of mathematics to trade and financial affairs is as old as mathematics itself. Time is money Figure 3: Time is money? .