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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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 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 Water: H2O Carbon dioxide: CO2 The chemical equation states that ethanol (C2H6O)
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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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ME 381 Mechanical and Aerospace Control Systems Dr. Robert G. Landers State Equation Solution State Equation Solution Dr. Robert G. Landers Unforced Response 2 The state equation for an unforced dynamic system is Assume the solution is x ( t ) = e At x ( 0 ) The derivative of eAt with respect to time is d ( e At ) dt Checking the solution x ( t ) = Ax ( t ) = Ae At x ( t ) = Ax ( t ) ⇒ Ae At x ( 0 ) = Ae At x ( 0 ) Letting Φ(t) = eAt‚ the solution
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Maxwell’s EquationsMaxwell’s equations represent one of the most elegant and concise ways to state the fundamentals of electricity and magnetism. From them one can develop most of the working relationships in the field. Because of their concise statement‚ they embody a high level of mathematical sophistication and are therefore not generally introduced in an introductory treatment of the subject‚ except perhaps as summary relationships. These basic equations of electricity and magnetism can be used
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The Drake Equation * The Drake Equation was created by Frank Drake in 1960. * estimate the number of extraterrestrial civilizations in the Milky Way. * It is used in the field of Search for ExtraTerrestrial Intelligence (SETI). * National Academy of Sciences asked Drake to organize a meeting on detecting extraterrestrial intelligence. Reason drake equation created * Drake equation is closely related to the Fermi paradox * The Drake Equation is: N = R * fp * ne * fl * fi
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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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Upstream: 60 = 6(b-c) Downstream: 60 = 3(b+c) There are now two separate equations: 60 = 6b - 6c and 60 = 3b + 3c Solve both equations for b: b = 10 + c b = 10 - c Now make both equations equal each other and solve for c: 10 + c = 10 - c 2c = 0 c = 0 The speed of the current was 0 mph Now‚ plug the numbers into one of either the original equations to find the speed of the boat in still water. I chose the first equation: b = 10 + c or b = 10 + 0 b = 10 The speed of the boat in still water must
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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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