to reduce any first-order linear PDE to an ODE‚ which can be subsequently solved using ODE techniques. We will see in later lectures that a subclass of second order PDEs second order hyperbolic equations can be also treated with a similar characteristic method. We derived the wave and heat equations from physical principles‚ identifying the unknown function with the amplitude of a vibrating string in the first case and the temperature in a rod in the second case. Understanding the physical
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trigonometric and exponential functions in the polar coordinate system for annular sector plates subjected to uniform loading. The salient feature of the solution development includes the derivation of a closed-form solution for the fourth-order partial differential equation governing plate deflections in the polar coordinate system. The series solution developed in this study is not only very stable but also exhibits rapid convergence. To demonstrate the convergence and accuracy of the present method‚ several
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U.P. TECHNICAL UNIVERSITY LUCKNOW Syllabus [Effective from the Session : 2008-09] B.TECH. COURSES [Common to all Branches of B.Tech. 1st Year except B.Tech. Agricultural Engg. ] 1 S. No. Course Code SUBJECT Evaluation Scheme SESSIONAL EXAM. PERIODS L 1. 2. 3. 4. 5. 6. EAS-103 EAS-101 EAS-102/ EME-102 EEE-101/ ECS-101 EEC-101/ EAS-104 EME-101/ EAS-105 7. EAS-109 8. EAS-152/ EME-152 EEE-151/ ECS-151 Mathematics-I Engg. Physics-I
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fendpaper.qxd 11/4/10 12:05 PM Page 2 Systems of Units. Some Important Conversion Factors The most important systems of units are shown in the table below. The mks system is also known as the International System of Units (abbreviated SI )‚ and the abbreviations sec (instead of s)‚ gm (instead of g)‚ and nt (instead of N) are also used. System of units Length Mass Time Force cgs system centimeter (cm) gram (g) second (s) dyne mks system meter (m) kilogram (kg) second (s) newton
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author explains the basic points and a few key results of the most important undergraduate topics in mathematics‚ emphasizing the intuitions behind the subject. The topics include linear algebra‚ vector calculus‚ differential geometry‚ real analysis‚ point-set topology‚ differential equations‚ probability theory‚ complex analysis‚ abstract algebra‚ and more. An annotated bibliography offers a guide to further reading and more rigorous foundations. This book will be an essential resource for advanced
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Euler’s Method for Ordinary Differential Equations After reading this chapter‚ you should be able to: develop Euler’s Method for solving ordinary differential equations‚ determine how the step size affects the accuracy of a solution‚ derive Euler’s formula from Taylor series‚ and use Euler’s method to find approximate values of integrals. 1. 2. 3. 4. What is Euler’s method? Euler’s method is a numerical technique to solve ordinary differential equations of the form dy (1) = f (x
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DIFFERENTIAL EQUATIONS A differential equation is amathematicalequationfor an unknownfunctionof one or severalvariablesthat relates the values of the function itself and itsderivativesof variousorders. Differential equations play a prominent role inengineering‚ physics‚economics and other disciplines.Differential equations arise in many areas of science and technology: whenever adeterministicrelationship involving some continuously varying quantities (modelled byfunctions) and their rates of change
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EI y dx M x dx C1 x C2 Solved Problem SOLUTION: • Develop an expression for M(x) and derive differential equation for elastic curve. W 14 68 I 723 in 4 P 50 kips L 15 ft E 29 106 psi a 4 ft For portion AB of the overhanging beam‚ (a) derive the equation for the elastic curve‚ (b) determine the maximum deflection‚ (c) evaluate ymax. • Integrate differential equation twice and apply boundary conditions to obtain elastic curve. • Locate point of zero slope or point of maximum
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Model A The very first differential equation that one typically encounters is the equation that models the change of a population as being proportional to the number of individuals in the population. In symbols‚ if P(t) represents the number of individuals in a population at time ‚ then the so called called exponential growth model is: Recall that the general solution of this differential equation is . Recall also that in order
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7 questions will have to be set. All questions will carry equal marks‚ except where stated otherwise. First Semester Compulsory Papers Paper I : Groups and Canonical Forms Paper II : Topology-I Paper III : Differential and Integral Equations Paper IV : Riemannian Geometry Paper V : Hydrodynamics Optional Papers Any one of the following papers will have to be opted. Paper VI (a) : Spherical Astronomy-I Paper VI (b) : Operations Research-1
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