This free online textbook is a one semester course in basic analysis. …
This free online textbook is a one semester course in basic analysis. These were my lecture notes for teaching Math 444 at the University of Illinois at Urbana-Champaign (UIUC) in fall 2009. The course is a first course in mathematical analysis aimed at students who do not necessarily wish to continue a graduate study in mathematics. A Sample Darboux sums prerequisite for the course is a basic proof course. The course does not cover topics such as metric spaces, which a more advanced course would. It should be possible to use these notes for a beginning of a more advanced course, but further material should be added.
The laws of physics are generally written down as differential equations. Therefore, …
The laws of physics are generally written down as differential equations. Therefore, all of science and engineering use differential equations to some degree. Understanding differential equations is essential to understanding almost anything you will study in your science and engineering classes. You can think of mathematics as the language of science, and differential equations are one of the most important parts of this language as far as science and engineering are concerned. As an analogy, suppose all your classes from now on were given in Swahili. It would be important to first learn Swahili, or you would have a very tough time getting a good grade in your classes.
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