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Newton’s laws, chemical kinetics



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Chapter 1 Newton s laws chemical kinetics Last updated September 11 2008 When you look around you you see many things changing in time Our most powerful tools for describing such dynamics are based on differential equations This mathematical approach to the description of nature started with mechanics and grew to encompass other phenomena In this section of the course we ll introduce you to these ideas using what we think are the simplest examples Following the historical path we ll begin with mechanics but we ll quickly see how similar equations arise in chemical kinetics electric circuits and population growth Sometimes the simple equations have simple solutions but even these have profound consequences such as understanding that most of the chemical elements in our solar system were created at some definite moment several billion years ago In other cases simple equations have strikingly complex solutions even generating seemingly random patterns This is just a first look at this whole range of phenomena 1 1 Starting with F ma By the time you arrive at the University you have heard many things about elementary mechanics In fact much of what we cover in these first lectures are things you already know We hope to emphasize several points 1 Many of the things which you have may have remembered as isolated facts about the trajectories of objects really all follow from Newton s laws by direct calculation 2 You need to take seriously the fact that Netwon s 21 22 CHAPTER 1 NEWTON S LAWS CHEMICAL KINETICS F ma is a differential equation 3 Hidden inside some elementary facts that you learned in high school are some remarkably profound truths about the natural world We won t have a chance to discuss their consequences but we d like to give you some flavor for these advanced but fundamental ideas Let us begin with Newton s famous equation F ma 1 1 At the risk of being pedantic let s be sure we know what all the symbols mean We all have an intuitive feeling for the mass m



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