Alexandria 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
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MATHEMATICAL METHODS PARTIAL DIFFERENTIAL EQUATIONS I YEAR B.Tech By Mr. Y. Prabhaker Reddy Asst. Professor of Mathematics Guru Nanak Engineering College Ibrahimpatnam‚ Hyderabad. SYLLABUS OF MATHEMATICAL METHODS (as per JNTU Hyderabad) Name of the Unit Unit-I Solution of Linear systems Unit-II Eigen values and Eigen vectors Name of the Topic Matrices and Linear system of equations: Elementary row transformations – Rank – Echelon form‚ Normal form – Solution of Linear Systems
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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 by
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Physical Optics 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
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Accounting is founded on the basic equation that states a company’s Assets equal their total Liabilities plus their total Owner’s Equity . This equation is summarized as ALOE . This isthe basis of the Balance Sheet.Assets are the company’s furniture‚ fixtures and equipment‚ physical property‚ intellectual property and other resources. These properties include the physical land as well as the equipmentand building improvements on the property.A company’s liabilities
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Quadratic Equation: Quadratic equations have many applications in the arts and sciences‚ business‚ economics‚ medicine and engineering. Quadratic Equation is a second-order polynomial equation in a single variable x. A general quadratic equation is: ax2 + bx + c = 0‚ Where‚ x is an unknown variable a‚ b‚ and c are constants (Not equal to zero) Special Forms: * x² = n if n < 0‚ then x has no real value * x² = n if n > 0‚ then x = ± n * ax² + bx = 0 x = 0‚ x = -b/a
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vessel in which the pressure of the gaseous products can increase to a point that the gases break violently out of the container. In this chemistry and physics science fair project‚ you will use the combustion of ethanol to provide energy for a small explosion. The chemical equation that describes the combustion of ethanol is shown below. (Note: Hover over the equations in this Introduction with your cursor to view enlarged formulas.) Equation 1: C2H6O+3O2→3H2O+2CO2+heat Ethanol: C2H6O Oxygen: 3O2
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Equations of State (EoS) Equations of State • From molecular considerations‚ identify which intermolecular interactions are significant (including estimating relative strengths of dipole moments‚ polarizability‚ etc.) • Apply simple rules for calculating P‚ v‚ or T ◦ Calculate P‚ v‚ or T from non-ideal equations of state (cubic equations‚ the virial equation‚ compressibility charts‚ and ThermoSolver) ◦ Apply the Rackett equation‚ the thermal expansion coefficient‚ and the isothermal compressibility
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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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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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