Ordinary Differential Equations [FDM 1023] Chapter 1 Introduction to Ordinary Differential Equations Chapter 1: Introduction to Differential Equations Overview 1.1. Definitions 1.2. Classification of Solutions 1.3. Initial and Boundary Value Problems 1.1. Definitions Learning Outcomes At the end of the section‚ you should be able to: 1) Define a differential equation 2) Classify differential equations by type‚ order and linearity Recall Dependent and Independent
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The reason why the Drake Equation is not a successful science is because it would be impossible to calculate some of the elements in the equation. The elements would take too long to get an accurate sample to give a scientifically sound explanation. For instance how would you calculate fi (the fraction of intelligent life forms)‚ how do you define intelligent? Is intelligent like you and I‚ is it like a bird or a rat‚ could it be a plant? There is no way to truly determine what counts and doesn’t
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Absorption to Activation Energy Calculating the rate constants‚ half-lives‚ and activation of a reaction by monitoring the change in absorption Department of Chemistry Dusten Dussex Lab partner: John Drury Lab date: February 7th‚ 2013 Due date: February 21st‚ 2013 Introduction In this experiment we are analyzing the relationship between reaction rates at different concentrations and temperatures to determine the true rate constant‚ activation energy‚ reaction orders‚ and half-life
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_________________ Teacher: _______________ Reviewer: Quadratic Equations I. Multiple Choice: Choose the letter of the correct answer. Show your solution. 1. What are the values of x that satisfy the equation 3 – 27x2 = 0? A. x = [pic]3 B. x = [pic] C. x = [pic] D. x = [pic] 2. What are the solutions of the equation 6x2 + 9x – 15 = 0? A. 1‚ - 15 B. 1‚ [pic] C. – 1‚ - 5 D. 3‚ [pic] 3. For which equation is – 3 NOT a solution? A. x2 – 2x – 15 = 0 C. 2x2
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behave differently. The general reaction equation is a A + b B → c C +d D in this equation A and B are the reactants forming the products C and D. However‚ unlike the common thought that the reaction ends when it runs out of A and B it actually does not. In most reactions C and D start to react to form A and B at a certain point as you can see in the equation c C + d D → a A + b B. These two reactions occur until the rate of reaction in both equations become equal (meaning the speed of the production
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Reaction Order and Rate Law Name Data‚ Calculations‚ and Questions A. Calculate the initial and final concentrations as needed to complete Tables 1 and 2. Data Table 1: Varying the Concentration of 1.0 M HCl | | | | |Concentrations | | |# Drops |# Drops |# Drops |Initial
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RESULTS AND DISCUSSION REPORT—EXPERIMENT 3 (CHEMICAL KINETICS) CALCULATIONS Effect of Concentration on Reaction Rate [S2O32-]initand [H+]init for each run‚ knowing the original concentrations and volumes of [S2O32-]‚ [H+]‚ and water used. [S2O32-]init= __(M[S2O32-])(V[S2O32-])__ [H+]init= _____(M[H+])(V[H+])____ V[S2O32-]+V[H+]+V[water] V[H+]+V[S2O32-]+V[water] Run 1 [S2O32-]init= (0.15 M)(10 mL) (10+3+2)mL = 0.1 M [H+]init= (3 M)(2
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Heat Equation from Partial Differential Equations An Introduction (Strauss) These notes were written based on a number of courses I taught over the years in the U.S.‚ Greece and the U.K. They form the core material for an undergraduate course on Markov chains in discrete time. There are‚ of course‚ dozens of good books on the topic. The only new thing here is that I give emphasis to probabilistic methods as soon as possible. Also‚ I introduce stationarity before even talking about state classification
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mathematics at a deeper level. Review of homogeneous equations The homogeneous constant coefficient linear equation an y (n) +· · ·+a1 y +a0 y = 0 has the characteristic polynomial an rn +· · ·+a1 r+a0 = 0. From the roots r1 ‚ . . . ‚ rn of the polynomial we can construct the solutions y1 ‚ . . . ‚ yn ‚ such as y1 = er1 x . We can also rewrite the equation in a weird-looking but useful way‚ using the symbol d D = dx . Examples: equation: y − 5y + 6y = 0. polynomial: r2 − 5r + 6 = 0. (factored):
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7 Ordinary Differential Equations Matlab has several different functions for the numerical solution of ordinary differential equations. This chapter describes the simplest of these functions and then compares all of the functions for efficiency‚ accuracy‚ and special features. Stiffness is a subtle concept that plays an important role in these comparisons. 7.1 Integrating Differential Equations The initial value problem for an ordinary differential equation involves finding a function
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