The Maxwell equations Introduction:- One of Newton’s great achievements was to show that all of the phenomena of classical mechanics can be deduced as consequences of three basic‚ fundamental laws‚ namely Newton’s laws of motion. It was likewise one of Maxwell’s great achievements to show that all of the phenomena of classical electricity and magnetism – all of the phenomena discovered by Oersted‚ Ampère‚ Henry‚ Faraday and others whose names are commemorated in several electrical
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UNIT -I Chapter-1 One Dimensional Wave Equation Introduction Wave equation in one dimension Chapter-2 Three Dimensional Wave Equation Total energy of a vibrating particle Superposition of two waves acting along the same line Graphical methods of adding disturbances of the same frequency Chapter – 1 Introduction: The branch of Physics based on the wave concept of light is called ‘Wave Optics’ or ‘Physical Optics’. Mathematical representation of a wave:
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Application of linear algebraic equation for chemical engineering problem The chemical engineering system models often outcome of set of linear algebraic equations. These problems may range in complexity from a set of two simultaneous linear algebraic equations to a set involving 1000 or even 10‚000 equations. The solution of a set two or three linear algebraic equations can be obtained easily by the algebraic elimination of variables or by the application of cramer’s rule. However for systems involving
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around 250A.D. started some kind of research on some equations involving more than one variables which would take only integer values.These equations are famously known as “DIOPHANTINE EQUATION”‚named due to Diophantus.The simplest type of Diophantine equations that we shall consider is the Linear Diophantine equations in two variables: ax+by=c‚ where a‚b‚c are integers and a‚b are not both zero. We also have many kinds of Diophantine equations where our main goal is to find out its solutions
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6 Systems Represented by Differential and Difference Equations Recommended Problems P6.1 Suppose that y 1(t) and y 2(t) both satisfy the homogeneous linear constant-coeffi cient differential equation (LCCDE) dy(t) + ay(t) = 0 dt Show that y 3 (t) = ayi(t) + 3y2 (t)‚ where a and # are any two constants‚ is also a solution to the homogeneous LCCDE. P6.2 In this problem‚ we consider the homogeneous LCCDE d 2yt + 3 dy(t) + 2y(t) = 0 dt 2 dt (P6.2-1) (a) Assume that a solution to
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QUADRATIC EQUATIONS Quadratic equations Any equation of the form ax2 + bx + c=0‚ where a‚b‚c are real numbers‚ a 0 is a quadratic equation. For example‚ 2x2 -3x+1=0 is quadratic equation in variable x. SOLVING A QUADRATIC EQUATION 1.Factorisation A real number a is said to be a root of the quadratic equation ax2 + bx + c=0‚ if aa2+ba+c=0. If we can factorise ax2 + bx + c=0‚ a 0‚ into a product of linear factors‚ then the roots of the quadratic equation ax2 + bx + c=0 can be found
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Kinematic Derivation of the Wave Equation http://prism.texarkanacollege.edu/physicsjournal/wave-e... KINEMATIC DERIVATION OF THE HARMONIC WAVE EQUATION AND RELATED TOPICS An extremely important type of wave in physics is the harmonic wave. This is a wave consisting of propagating simple harmonic oscillations or linear combinations thereof. Attach a weight to a spring and hang the spring so the weight is free to move. Then lift the weight straight up and release it; it will oscillate up and down
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To solve a system of equations by addition or subtraction (or elimination)‚ you must eliminate one of the variables so that you could solve for one of the variables. First‚ in this equation‚ you must look for a way to eliminate a variable (line the equations up vertically and look to see if there are any numbers that are equal to each other). If there is lets say a –2y on the top equation and a –2y on the bottom equation you could subtract them and they would eliminate themselves by equaling zero
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On Mathieu Equations by Nikola Mišković‚ dipl. ing. Postgraduate course Differential equations and dynamic systems Professor: prof. dr. sc. Vesna Županović The Mathieu Equation An interesting class of linear differential equations is the class with time variant parameters. One of the most common ones‚ due to its simplicity and straightforward analysis is the Mathieu equation. The Mathieu function is useful for treating a variety of interesting problems in applied
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DIFFERENTIAL EQUATIONS 2.1 Separable Variables 2.2 Exact Equations 2.2.1 Equations Reducible to Exact Form. 2.3 Linear Equations 4. Solutions by Substitutions 2.4.1 Homogenous Equations 2.4.2 Bernoulli’s Equation 2.5 Exercises In this chapter we describe procedures for solving 4 types of differential equations of first order‚ namely‚ the class of differential equations of first order where variables x and y can be separated‚ the class of exact equations (equation
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