In: Advanced Math
4) Laplace Transform and Solving second order Linear Differential Equations with Applications The Laplace transform of a function, transform of a derivative, transform of the second derivative, transform of an integral, table of Laplace transform for simple functions, the inverse Laplace transform, solving first order linear differential equations by the Laplace transform
Applications: a) Series RLC circuit with dc source b) Damped motion of an object in a fluid [mechanical, electromechanical] c) Forced Oscillations [mechanical, electromechanical]
You should build the theory portion of your report on what you have learned in the math courses including Mathematics 1, Applied Mathematics, Differential calculus and Integral Calculus. Any additional material you need in order to begin or complete your project must be included and discussed within the report. Special attention is paid to the consistency of the derivation of formulae and concepts in your report. Once the mathematical foundations are laid in a proper way, you need to introduce the topic you have been assigned from your program where the mathematical concepts you have explored are applied. It is important you support your derivations and conclusions by real world engineering applications