Try WriteLatex’s online collaborative LaTeX editor to create and submit content straight to Flooved. Introduction: The solution of problems in most parts of applied mathematics and some areas of pure can more often than not be reduced to the problem solving some diﬀerential equations. Furthermore, many parts of pure maths were originally motivated by issues arising from diﬀerential equations, including large parts of algebra and much of analysis. From Mods, and even from school, you now know how to solve some diﬀerential equations. In this course, we shall learn to solve a much larger variety both explicitly and qualitatively, and we also develop some general theory. Deﬁnition of Laplace Transform: The Laplace transform of a function f(t) of a real variable t is another function depending on a new variables, which is in general complex. We will denote the Laplace transform of f by L f. Roughly speaking, a differential equation is an equation involving the derivatives of one or more unknown functions. In calculus (differential, integral and vector), you’ve studied ways of analyzing functions. You might even have been convinced that functions you meet in applications arise naturally from physical principles. As we shall see, differential equations arise naturally from general physical principles. In many cases, the functions you met in calculus in applications to physics were actually solutions to a “natural” differential equation. This is a one semester first course on differential equations, aimed at engineering students. 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. The Beatles. Natalie Portman. Dancing on tables with my blonde and not-so-blonde friends. Trying to make my accent in English sound more British. Stealing books from my father’s huge collection. Watching ten episodes of Friends in a row and laughin Source.