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What are non linear differential equations? How do you solve them? Watch this presentation to find out. Here, we learn what are non linear differential equations and how to split a non linear differential equation into linear factors and solve it. We also learn that when when y is a function of x and p, we solve for y, that is, we differentiate w.r.t x. This is useful for engineering mathematics and graduate mathematics. For more videos, consider subscribing to my channel or visit my page https://www.mathmadeeasy.co/about-4 You can also visit my playlist on engineering maths.
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ppt on applications of first order non linear partial differential equation in subject of Advanced engineering maths useful for GTU students
applications of first order non linear partial differential equation
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Dhananjaysinh Jhala
What are non linear differential equations? How do you solve them? Watch this presentation to find out. Here, we learn what are non linear differential equations and how to split a non linear differential equation into linear factors and solve it. We also learn that when when y is a function of x and p, we solve for y, that is, we differentiate w.r.t x. This is useful for engineering mathematics and graduate mathematics. For more videos, consider subscribing to my channel or visit my page https://www.mathmadeeasy.co/about-4 You can also visit my playlist on engineering maths.
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• Equations which are composed of an unknown function and its derivatives are called differential equations. • Differential equations play a fundamental role in engineering because many physical phenomena are best formulated mathematically in terms of their rate of change. • When a function involves one dependent variable, the equation is called an ordinary differential equation (ODE). • A partial differential equation (PDE) involves two or more independent variables. Figure 1: CHARACTERIZATION OF DIFFERENTIAL EQUATION FIRST ORDER DIFFERENTIAL EQUATION: FIRST ORDER LINEAR AND NON LINEAR EQUATION: A first order equation includes a first derivative as its highest derivative. - Linear 1st order ODE: Where P and Q are functions of x. TYPES OF LINEAR DIFFERENTIAL EQUATION: 1. Separable Variable 2. Homogeneous Equation 3. Exact Equation 4. Linear Equation i. SEPARABLE VARIABLE: The first-order differential equation: Is called separable provided that f(x,y) can be written as the product of a function of x and a function of y. Suppose we can write the above equation as We then say we have “separated” the variables. By taking h(y) to the LHS, the equation becomes: Integrating, we get the solution as: Where c is an arbitrary constant. EXAMPLE 1. Consider the DE : Separating the variables, we get Integrating we get the solution as:
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Feature-aligned N-BEATS with Sinkhorn divergence (ICLR '24)
Joonhun Lee
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biology HL practice questions IB BIOLOGY
biology HL practice questions IB BIOLOGY
1301aanya
Context. WASP-76 b has been a recurrent subject of study since the detection of a signature in high-resolution transit spectroscopy data indicating an asymmetry between the two limbs of the planet. The existence of this asymmetric signature has been confirmed by multiple studies, but its physical origin is still under debate. In addition, it contrasts with the absence of asymmetry reported in the infrared (IR) phase curve. Aims. We provide a more comprehensive dataset of WASP-76 b with the goal of drawing a complete view of the physical processes at work in this atmosphere. In particular, we attempt to reconcile visible high-resolution transit spectroscopy data and IR broadband phase curves. Methods. We gathered 3 phase curves, 20 occultations, and 6 transits for WASP-76 b in the visible with the CHEOPS space telescope. We also report the analysis of three unpublished sectors observed by the TESS space telescope (also in the visible), which represents 34 phase curves. Results. WASP-76 b displays an occultation of 260±11 and 152±10 ppm in TESS and CHEOPS bandpasses respectively. Depending on the composition assumed for the atmosphere and the data reduction used for the IR data, we derived geometric albedo estimates that range from 0.05 ± 0.023 to 0.146 ± 0.013 and from <0.13 to 0.189 ± 0.017 in the CHEOPS and TESS bandpasses, respectively. As expected from the IR phase curves, a low-order model of the phase curves does not yield any detectable asymmetry in the visible either. However, an empirical model allowing for sharper phase curve variations offers a hint of a flux excess before the occultation, with an amplitude of ∼40 ppm, an orbital offset of ∼−30◦ , and a width of ∼20◦ . We also constrained the orbital eccentricity of WASP-76 b to a value lower than 0.0067, with a 99.7% confidence level. This result contradicts earlier proposed scenarios aimed at explaining the asymmetry observed in high-resolution transit spectroscopy. Conclusions. In light of these findings, we hypothesise that WASP-76 b could have night-side clouds that extend predominantly towards its eastern limb. At this limb, the clouds would be associated with spherical droplets or spherically shaped aerosols of an unknown species, which would be responsible for a glory effect in the visible phase curves.
Asymmetry in the atmosphere of the ultra-hot Jupiter WASP-76 b
Asymmetry in the atmosphere of the ultra-hot Jupiter WASP-76 b
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Feature-aligned N-BEATS with Sinkhorn divergence (ICLR '24)
Feature-aligned N-BEATS with Sinkhorn divergence (ICLR '24)
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biology HL practice questions IB BIOLOGY
biology HL practice questions IB BIOLOGY
Asymmetry in the atmosphere of the ultra-hot Jupiter WASP-76 b
Asymmetry in the atmosphere of the ultra-hot Jupiter WASP-76 b
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