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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.
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.
Definition of an Integral Return 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.
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?
George Cain & James Herod © Copyright 1996, 1997 by George Cain and James Herod. All rights reserved. This is a textbook for a course in multivariable calculus.