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Unformatted text preview: PHY 1321/1331 Principles of Physics I Fall 2009 Dr.Andrzej Czajkowski HOW TO DEAL WITH INTEGRALS IN PHYSICS? Only small part of the material presented here will be actually used in class. This material will be tested during your first midterm – but it will contribute only to part of your bonus grade! Also, the proper discussion of integrals will be done in your calculus class in this and the next semester. The basic idea as outlined here is very useful in understanding of many fine points outlined in the textbook. Finally: nobody ever failed physics due to a lack of full understanding of integrals. Also, nobody missed an A+ for the same reason! The key concept is that of the value of the linear integral of the function as the area under the curve! It is expected that everybody to be able to use geometry to find simple integrals this way! Anything beyond this that you might learn from me will be a nice extra! PHY 1321/1331 Principles of Physics I Fall 2009 Dr.Andrzej Czajkowski HOW TO DEAL WITH INTEGRALS IN PHYSICS? Calculus is integral part of Physics. Differential and Integral Calculus were invented by Sir. Isaac Newton and Gottfried Wilhelm Leibniz as a language of Mechanics. (XVII/XVIII century) In the XIXth century, calculus was put on a much more rigorous footing by mathematicians such as Gauss, Cauchy, Riemann, and Weierstrass. From its emergence in XVII century calculus continues to make various concepts in physics easier to comprehend. Trying to avoid calculus in physics typically leads to confusion. Fortunately, all students in this class already know basic differential calculus from high-school. It is somewhat different story when it comes to integral calculus. The proper introduction of the integrals with all necessary tricks and practicing, is left to your calculus Class. In this class we will need only the key ideas, and the simplest integrals. What follows is an attempt to deliver this content. PHY 1321/1331 Principles of Physics I Fall 2009 Dr.Andrzej Czajkowski Everything that you will ever need to know about integrals in first year Physics: 1 Indefinite Integrals as the anti-derivatives 2 Geometric Interpretation of the Definite Integral of a Function 3 Fundamental Theorem of Calculus 4 Examples 5 Integrals frequently encountered in Physics: Path, Work, Moment of Inertia, Change in Entropy, PHY 1321/1331 Principles of Physics I Fall 2009 Dr.Andrzej Czajkowski THE FIRST FUNDAMENTAL THEOREM OF CALCULUS Integrals as the anti-derivatives If we know how to find derivative of the fundamental function, we should be able to find the integral If: dt dF f = ∫ = fdt F We are looking for such function F (called fundamental function) that the function f is its derivative !...
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This note was uploaded on 01/17/2010 for the course PSY PSY1331 taught by Professor Czskowski during the Fall '09 term at University of Ottawa.
- Fall '09