Mechanical Engineering | Proveiff Study

real and imaginary part of e^(sin(x+iy))

By SK Math Expert August 19, 2021Advanced Math, Complex Analysis, Computer science, Mathematics, Mechanical Engineering, Multivariable Calculus

Question : Find the real and imaginary part of e^(sin(x+iy)) Solution: Let \[z = e^(sin(x+iy))\] We shall write it as \[z = e^{Sin\left(x+iy\right)}=e^{Sin\left(x\right)Cos\left(iy\right)+\cos{\left(x\right)}\sin{\left(iy\right)}}\] Since \[Cos\left(iy\right)=\cosh{\left(y\right)}\ ,\ \ \sin{\left(iy\right)}=isinh\left(y\right)\] we shall…

How to plot direction field and solution curves of the logistic model dP/dt =(1/3)(P-2)(3-P) with initial conditions P(0)=1, P(0)=2,P(0)=5

By SK Math Expert February 24, 2021Mechanical Engineering, ODEspopulation model solution

Introduction: In this article , we present the solution of the question How to plot direction field and solution curves of the logistic model dP/dt =(1/3)(P-2)(3-P) with initial conditions P(0)=1,…

How to write function method in matlab

By SK Math Expert February 13, 2021MATLAB, Mechanical EngineeringNewton's method in Matlab

Introduction : In this solution, we answer a question how to write function method in matlab. We will write function method in matlab to solve the following problem. Question :…

Identify the smooth function whose graph given below and evaluate area under curve for x=-infinity to infinity

By SK Math Expert February 13, 2021Advanced Math, Mathematics, Mechanical Engineeringarea under the curves

Introduction : In this question, we will Identify the smooth function whose graph given below and evaluate area under curve for x=-infinity to infinity Question : Identify the smooth function…

Use Euler method in Excel sheet to solve Initial value problem dy/dt=-y/3+t

By SK Math Expert February 12, 2021Excel, Mechanical EngineeringMath using Excel

Introduction : In this question, we will use Euler method in Excel sheet to solve Initial value problem dy/dt=-y/3+t. Question : Using Excel sheet to solve Initial value problem \[\frac{dy}{dt}=-\frac{y}{3}+t,…

Draw direction field of the differential equation dy/dx=2x+y and plot solution curves for (0,0),(0,1),(0,-1)

By SK Math Expert February 12, 2021Mechanical Engineeringdirection field examples

Introduction :Draw direction field of the differential equation dy/dx=2x+y and plot solution curves for (0,0),(0,1),(0,-1) Question : Draw direction field of the differential equation \[\frac{dy}{dx}=2x+y\] and plot solution curves for…

For what values of initial guess x0 does the fixed point iteration sequence converges to the root?

By SK Math Expert February 12, 2021Advanced Math, Mechanical Engineering, Real Analysisfixed point iteration sequences examples

Introduction : In the following question, we apply fixed point theory to determine for what values of initial guess does the fixed point iteration sequence converges to the root as…

Apply Master theorem to show T(n)=2T(n/2)+n^2 is theta(n^2)

By SK Math Expert February 11, 2021Computer science, Mechanical Engineeringcomplexity of recurrence relation

Introduction : In this question, we will apply master theorem to show T(n)=2T(n/2)+n^2 is theta(n^2). Master theorem finds an upper bound for some recurrence relations if some conditions on parameters…

Modified Euler Method to solve initial value problem y'(t)=1/(1+2*t^2),y(0)=1

By SK Math Expert February 11, 2021Mechanical EngineeringModified Euler Method examples

Introduction: In this question, we apply modified Euler Method to solve initial value problem y'(t)=1/(1+2*t^2),y(0)=1 Question : Apply modified Euler Method to solve initial value problem \[y'\left(t\right)=\frac{1}{(1+2*t^{2})}, y(0)=1\] for \(0\le…

Bisection method example to solve 1/sqrt(x)+2(log(10^(-4))+2*10^(-4)/sqrt(x))

By SK Math Expert February 10, 2021Mechanical EngineeringBisection method examples

Introduction : Bisection method example to solve Question : Bisection method example to solve \[\frac{1}{\sqrt{x}}+2\cdot\log_{e}\left(10^{-4}+2\cdot\frac{10^{-4}}{\sqrt{x}}\right)\] Solution: \[\frac{1}{\sqrt{x}}+2\cdot\log_{e}\left(10^{-4}+2\cdot\frac{10^{-4}}{\sqrt{x}}\right)\] Bisection method fr=(fl+fu)/2 % error=|(f_r-f_exact)/f_exact |*100% iflF(fl)fuF(fu)frF(fr)% error00.02-5.9146503390.03-7.588210.025-6.86878259.195410.02-5.9146503390.025-6.868780.0225-6.42884223.2759