HIGHER ORDER ORDINARY DIFFERENTIAL EQUATIONS.pptx

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DEPARTMENT OF MATHEMATICS MGC ARMORI

Graduation level theory of higher order linear differential equations

Department of Mathematics
Mahatma Gandhi College, Armori
HIGHER ORDER ORDINARY
DIFFERENTIAL
EQUATIONS
topics:
1) Linear differential equations of higher
orders with constant coefficients
2) Complementory function
3) Particular integral
4) Simultaneous differential equations

HIGHER ORDER ORDINARY DIFFERENTIAL EQUATIONS.pptx

HIGHER ORDER ORDINARY DIFFERENTIAL EQUATIONS.pptx

HIGHER ORDER ORDINARY DIFFERENTIAL EQUATIONS.pptx

HIGHER ORDER ORDINARY DIFFERENTIAL EQUATIONS.pptx

HIGHER ORDER ORDINARY DIFFERENTIAL EQUATIONS.pptx

HIGHER ORDER ORDINARY DIFFERENTIAL EQUATIONS.pptx

HIGHER ORDER ORDINARY DIFFERENTIAL EQUATIONS.pptx

HIGHER ORDER ORDINARY DIFFERENTIAL EQUATIONS.pptx

HIGHER ORDER ORDINARY DIFFERENTIAL EQUATIONS.pptx

HIGHER ORDER ORDINARY DIFFERENTIAL EQUATIONS.pptx

HIGHER ORDER ORDINARY DIFFERENTIAL EQUATIONS.pptx

HIGHER ORDER ORDINARY DIFFERENTIAL EQUATIONS.pptx

HIGHER ORDER ORDINARY DIFFERENTIAL EQUATIONS.pptx

HIGHER ORDER ORDINARY DIFFERENTIAL EQUATIONS.pptx

HIGHER ORDER ORDINARY DIFFERENTIAL EQUATIONS.pptx

HIGHER ORDER ORDINARY DIFFERENTIAL EQUATIONS.pptx

HIGHER ORDER ORDINARY DIFFERENTIAL EQUATIONS.pptx

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HotJupiters are amongthebest-studied exoplanets, but it is still poorly understood how their chemical composition and cloud properties vary with longitude. Theoretical models predict that clouds may condense on the nightside and that molecular abundances can be driven out of equilibrium by zonal winds. Here we report a phase-resolved emission spectrum of the hot Jupiter WASP-43b measured from 5–12µ 5–12µ 5–12µm with JWST’s Mid-Infrared Instrument (MIRI). 1524 ±35 1524 ±35 and 863±23 The spectra reveal a large day–night temperature contrast (with average brightness temperatures of 1524 ± 35 863 ±23 863 ±23Kelvin, respectively) and evidence for water absorption at all orbital phases. Comparisons with three-dimensional atmospheric models show that both the phase curve shape and emission spectra strongly suggest the presence of nightside clouds which become optically thick to thermal emission at pressures greater than ∼100mbar. The dayside is consistent with a cloudless atmosphere above the mid-infrared photosphere. Con3trary to expectations from equilibrium chemistry but consistent with disequilibrium kinetics models, methane is not detected on the nightside (2σ upper limit of 1–6 parts per million, depending on model assumptions).

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The six step guide to practical project management If you think managing projects is too difficult, think again. We’ve stripped back project management processes to the basics – to make it quicker and easier, without sacrificing the vital ingredients for success. “If you’re looking for some real-world guidance, then The Six Step Guide to Practical Project Management will help.” Dr Andrew Makar, Tactical Project Management

The six step guide to practical project management

The six step guide to practical project management

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Time Management & Productivity - Best Practices

Time Management & Productivity - Best Practices

Time Management & Productivity - Best Practices

The six step guide to practical project management

The six step guide to practical project management

The six step guide to practical project management

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