Problem 19. Double numerical integration is the application twice of a numerical integration method for single integration, once for the y direc- tion and another for the r direction. Any numerical integration method for single integration can be applied to double integration. Write a C++ program that applies Simpson's 1/3 rule to find the double integral rb%3D3 rv3+exp(z/5) I = a=1 sin(x + y)dy ) dr. y=In(z)
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- 2. C++ Implement a function for integrating a function by means of Riemann sums. Use the formula Write a function that returns the numerical derivative of a given function fat a given point x. using a given tolerance h. Use the formula Yx+h) -f(x-h) f(x) = %3D 2hUse the C++ language to solve the following A)Write a computer program for Gauss elimination method using C programming language. Decide the number of significant figures yourselves. While writing your program, consider the effects of the number of significant figures, pivoting, scaling and do not forget to check if the system is ill conditioned. B)Repeat the same procedures for Gauss-Jordan method. C)Solve an example system using your Gauss elimination and Gauss-Jordan method. Measure the time your computer solves the system for both programs. D)Write a report in which you discuss and compare your Gauss elimination and Gauss-Jordan programs. Upload you report and two code files to the DYS system2. Write a program that implements the first order (linear) interpolations. 3. Use the program to apply first order (linear) interpolation to the function f(x)=sin(x²) initially calculated in 10 uniform points in the interval [0.0, 5.0]. G
- SOLVE IN PYTHON PYTHON NOT MATLAAAB PLEASEWrite a function that finds the period of the fundamental mode of oscillation for a shear building where the masses of each floor and the stiffnesses of each story are all the same . For example, for a 8-story shear building where each floor is 1200 kg and the stiffness between each floor is 10 5 N/m, the period of the fundamental mode would be 3.73 s. def sb(m, k, n): '''Find the period of fundamental mode of oscillation for an n-story shear building model with all masses equal to m and all stiffnesses equal to k. Example: if m = 1000, k = 10000, n = 3, then fm = 4.46'''F(x.y,z)=x'y'z+x'yz+xy'z'+xy'z can you simplify this and draw the diagram of the simplified functionWrite a C++ fraction calculator program that adds, subtracts, multiplies, and divides fractions. Your program should check for the division by 0, have and use the following functions: (a) abs - returns the absolute value of a given integer.(b) min - returns the smallest of two positive integers.(c) gcd - returns the greatest common divisor of two positive integers.(d) reduce - reduces a given fraction.(e) flip - reduces a given fraction and flips the sign if the denominator is negative.(f) add - finds the reduced sum of a pair of given fractions.(g) subtract - finds the reduced difference of a pair of given fractions, by makingthe second fraction negative then using the add function.(h) multiply - finds the reduced product of a pair of given fractions.(i) divide - finds the reduced quotient of a pair of given fractions by inverting the second fraction then using the multiply function. Sample Runs:Fraction Calculator 1.0Enter an arithmetic expression of the form a/b operator c/d,replace…
- )Write a computer program for Gauss elimination method using C programming language. Decide the number of significant figures yourselves. While writing your program, consider the effects of the number of significant figures, pivoting, scaling and do not forget to check if the system is ill conditioned.2)Repeat the same procedures for Gauss-Jordan method.3)Solve an example system using your Gauss elimination and Gauss-Jordan method. Measure the time your computer solves the system for both programs.4)Write a report in which you discuss and compare your Gauss elimination and Gauss-Jordan programs.ما 2. Write a program that implements the first order (linear) interpolations.. 3. Use the program to apply first order (linear) interpolation to the function f(x)=sin(x²) initially calculated in 10 uniform points in the interval [0.0, 5.0]. (1) 4. Write a program that implements n-point Lagrange interpolation. Treat n as an input parameter. 5. Use third and fifth order polynomial interpolation to interpolate the function f(x) Equation (1) above.1. For the function a). f (x) = x³ + 2a2 - rewrite it as x = g(x) and write a program that uses the Fixed point method to iterate to the solution starting at xo = 1.5. Use the following for g(x) (c) g(x) = x+ f/3 (d) g(a) = (x³ – f)/x? (e) g(x) = (2x? - f)/(2x) %3D %3D -
- C+ Programming Question: You are given a sequence of integers A1, A2,..., AN and an integer M. For any valid integers p, q, let's define F(p, q) as the dot product of the subsequences Ap, Ap+1, ..., Ap+M–1 and Aq, Aq+1, ·.., Aq+M–1, İ.e. F(p, q) = Eo Ap+i · Aqti- M-1 You should process Q queries. In each query: • You are given two integers pos and val. Change the value of Apos to val. • Then, find the sum S = 5N-M+1¬N-M+1 F(i, j). Since this sum could Lj-1 be very large, compute it modulo 998, 244, 353. Test Case Result 1 340 521 32415 24Write a C++ function that evaluates polynomials an an x" + an-1 X -1, .. . , a2 x²,a1 x', ao x°. It should take following inputs: • Value of x. • Highest power n. Coefficients in descending order an, an-1 , ... , a2 , a1 n+1) ao (coefficients will ne For instonge fficionts ore (2 2 121 thon outnut chould be 182 which1. Given the following data set: X: 0 2 4 6 9 11 12 15 17 19 22 25 Y: 5 6 7 6 9 8 7 10 12 12 15 10 (a) Write a Python program to fit a curve using: Polynomial function of order 4 Cubic spline fit Plot both the data set and the approximating curve for the polynomial and spline functions. (b) In the Python program, add labels along the x and y axes, and put a title of your choice for each plot.