Homogeneous Differential Equation

A first order equation $ \frac{dy}{dx} = f(x,y) $ is said to be a homogenous equation if $ f(x,y) = f(tx,ty) $. Steps to solve: Substitute $ y = vx $ into f(x,y) to get $ \frac{dy}{dx} = f(x,vx) $ Differentiate $ y = vx$ to get $ \frac{dy}{dx} = x\frac{dv}{dx} + v $ Substitute the equation you got in …

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Variable Separable Differential Equation

A first order equation $\frac{dy}{dx} = f(x,y) $ is said to be variable separable if f(x,y) is of the form:$$ g(x)h(y) $$ Steps to solve $\frac{dy}{dx} = g(x)h(y) $: Swap the variables around: $\frac{1}{h(y)}dy = g(x) dx$ Evaluate: $\int \frac{1}{h(y)} \, dy = \int g(x) \, dx$ You’re done! (Note: you might want to attempt to solve for y explicitly)   Back …

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Effective resistance of resistors

In many situations, several electrical devices are connected to the same power supply. There are two basic methods of connecting resistors or other devices together. They are called series and parallel connections. The derivation of the formula for effective resistance for series and parallel resistors can be found at the end of this post. Effective Resistance Of Resistors Resistors In …

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Resistivity

Besides temperature, experimental results shows that the resistance (R of a given conductor) also depends on the composition and size. Resistance, R is found to be: directly proportional to its length, L inversely proportional to its cross-sectional area dependent on the type of material From experimental results, we can show that: $R = \rho \frac{L}{A} $ ,where R = resistance …

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Undergraduate Year 1 Physics Notes

The topics available are tailored towards first year undergraduate. The topics are intended to provide a firm foundation to the undergraduates so that they have the pre-requisite knowledge to tackle the four pillars of Physics – Quantum Mechanics, Classical Mechanics, Statistical Mechanics and Classical Electromagnetism. Topics: (% Completed) Mechanics (50%) Thermodynamics (80%) Optics Electromagnetism (Completed) Quantum Physics Special Relativity For Undergrads (10%) …

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H3 Physics (Junior College)

The topics are meant for H3 Physics (MOE Syllabus). These notes are mainly meant for revision purposes. H3 Physics notes are at a level slightly higher than A level Physics notes. They are meant to give a preview of what Physics will be like in the University. There will be more maths involved – e.g. differentiation and integration. Topics: Special …

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