# Engineering Mathematics 2 Solved Problems You can use the free Mathway calculator and problem solver below to practice Algebra or other math topics.Try the given examples, or type in your own problem and check your answer with the step-by-step explanations.We use cookies to offer you a better experience, personalize content, tailor advertising, provide social media features, and better understand the use of our services.

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 SCEE08009 Engineering Mathematics 2A Tutorial 2 (d) ( d 3 x dt 3 t d 2 x dt 2 x 2 t= sint, x(1) = 1,x ̇(1) = 0,x ̈(1) =− 2. 2 ,x ̇(1) = 1,x ̈(1) = 0, using forward Euler with a step size of ∆t= 0.025s.

Repeat the calculation with ∆t= 0.0125 and hence estimate the accuracy of your solution att= 2.

(a) dx dt −kx= 0 (b) d 3 x dt 3 t 2 dx dt =t d dt (xt) (d) d dt t d dt (t 2 x) =xt.

(3) Determine which members of the given sets are solutions of the differential equation.

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The topics are Chain rule, Partial Derivative, Taylor Polynomials, Critical points of functions, Lagrange multipliers, Vector Calculus, Line Integral, Double Integrals, Laplace Transform, Fourier series.Page 2 SCEE08009 Engineering Mathematics 2A Tutorial 2 h 0 2 sinωt.whereh 0 is the height of the waves acting on the float andωis the frequency of the waves.Hence write down the general solution of the differential equation (a) d 2 x dt 2 −p 2 x= 0 dx dt d 2 x dt 2 dx dt x= 0 dx dt (1) The temperature, T, (in Kelvin) of a reaction vessel during a particularly unstable chemical reaction is modelled by the linear differential equation, d 4 T dt 4 d 3 T dt 3 d 2 T dt 2 d T dt At the start of the experiment the reactor vessel is at 293K.Assuming, at the start of the reaction, the first derivative −20 Ks− 1 , the second derivative is−10 Ks− 2 and all other derivatives are zero, determine the temperature of the reaction vessel after 3 seconds.The analytical solution to this BVP is x=e 3 t 2 (28π 3 35π) sint 320 π 4 800π 2 3380 21 πcost 80 π 4 200π 2 845 (28π 2 −91) sinπt− 84 πcosπt 320 π 4 800π 2 3380 Calculate the predicted position,x 50 , which is found by performing 50 time steps with the forward Euler ODE solver with a uniform time step, ∆t= 0.1s.By comparing x 50 with the analytical solution,x(5), comment on the accuracy of your solution.In a particular experiment the float is excited by 700mm, 2s period, waves.The float is at rest at the start of the experiment sox(0) = 0.0 and ̇x(0) = 0.0.F 1 (s) = s 3 , ℜ(s) Remark:αandβare positive and real constants.(a)Calculate the Laplace transform - Use the Laplace transform properties  from Table 1 and the function transforms from Table 3 to calculate the Laplace transform of the following time domain function.

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