Calculus. 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. Math21b, Fall 2003, Linear Algebra and Differential Equations. Stuff You MUST Know Cold for AP Calc. 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). Article in PDF (Adobe Acrobat) format.DVI version of the article.Postscript version of the article.Slides for a brief talk on this article. 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.) (Click here for DVI version.) Max-Min Problems. f(x) Calculus Mega Cheat Sheet.
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. Differential Calculus Introduction: Simple Polynomial Equations Polynomial Calculations: Image by blumik The Main Question in Differential Calculus “Differential calculus” is a big phrase but a very useful part of mathematics. Several previous articles have built a foundation, and now the first floor will be erected. The question that differential calculus asks is: What is the slope of a function at a given point?
What Do “Slope” and “Function” Mean? To Define a Function: For this article, a function relates one variable to another; it is often written as “y = f(x)”. Again, for this article, the best way to think of a function is that it prescribes a line or curve graphed on a Cartesian plane. Three other necessary features of a function for calculus are “smooth” and “continuous” and “well defined”. A function: “y = x unless ‘x’ is negative; in that case y = -x” is not smooth. To Define Two Types of Slopes The “average slope” between two points is the vertical change divided by the horizontal change. The slope then is (y – y)/(x – x). Pages: 1 2. Calculus Online Book.
An approach to calculus. TheMathPage. Mathematics reference: Rules for differentiation. IntegralCALC.com - StumbleUpon. Multivariable Calculus. The OnLine Math Tests Home Page - Department of Mathematics - University of Missouri-Columbia. Fourier Series Tutorial.