*Engineering Mathematics is an essential tool for describing and analyzing engineering processes and systems.*

Every chapter has easy to follow explanations of the theory and numerous step-by-step solved problems and examples.

The questions have been hand-picked from the previous years’ question papers and are suitable to the current pattern of questions asked.

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.

[20] 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.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.We also have free math calculators and tools to help you understand the steps and check your answers.Lagrange multipliers Extreme values of a function subject to a constraint Lagrange multiplier example: Minimizing a function subject to a constraint Multivariable Calculus: Directional derivative of $f(x,y)$ Lagrange multipliers example Path integral (scalar line integral) from vector calculus Line integral example in 3D-space Line integral from vector calculus over a closed curve Line integral from vector calculus over a closed curve Line integral example from Vector Calculus Homogeneous first order ordinary differential equation Solution to a 2nd order, linear homogeneous ODE with repeated roots 2nd order ODE with constant coefficients: simple method of solution 2nd order ODE with constant coefficients: non-standard method of solution Calculus Calculator with step by step solutions Functions, Operations on Functions, Polynomial and Rational Functions, Exponential and Logarithmic Functions, Sequences and Series, Evaluating Limits, Derivatives, Applications of Differentiation, Integrals, Applications of Integration, Techniques of Integration, Parametric Equations and Polar Coordinates Rotate to landscape screen format on a mobile phone or small tablet to use the Mathway widget, a free math problem solver that answers your questions with step-by-step explanations.f(t) = (αt) 5 e−βt H(t) (t−β) sinh(t−β)H(t−β) (b)Calculate the inverse Laplace transform- Use the Laplace transform prop- [10] erties from Table 1 and the function transforms from Table 3 to invert the fol- lowing frequency domain function.F(s) = e−αs 3 (s 7) 2 (s−1) Page 3 of 5 Continued SCEE08009 Engineering Mathematics 2A Tutorial 3 Table 3: Function transforms Name f(t), t≥ 0 F(s) Convergence region Unit impulse δ(t) 1 alls Ideal delay δ(t−α) exp(−αs) ℜ(s)≥α Unit step H(t) 1 s ℜ(s)−α Page 5 of 5 END SCEE08009 Engineering Mathematics 2A Tutorial 4 Questions (1) and (2) are taken from or similar to Exercise 5.3.5 and question (3) from 5.5.7 in Advanced Modern Engineering Mathematics (questions (1)-(2) are also in 11.3.4, 11.3.6 and 11.4.3 in Modern Engineering Mathematics).F 1 (s) = s 3 , ℜ(s) Remark:αandβare positive and real constants.(a)Calculate the Laplace transform - Use the Laplace transform properties [10] from Table 1 and the function transforms from Table 3 to calculate the Laplace transform of the following time domain function.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.

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