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Numerical Analysis: a) The basic form of the Gaussian quadrature formula is The integration formula using two points can be made exact when a polynomial of order 3 is integrated. i) Determine the...
Problem 1 (max 10 Points): The function Ca)2 x-3Vx +10 can be integrated analytically x - 3Vx +10...
Problem 1 (max 10 Points): The function Ca)2 x-3Vx +10 can be integrated analytically x - 3Vx +10 7 (a) Plot the function f(x) within the interval [20, 100] using 101 samples (b) Calculate the area under the curve of f(x) within the interval [20, 100] using the analytical solution of the integral. (c) Calculate the area under the curve of f(x) within the interval [20, 100] using trapezoidal numerical integration (hint: "trapz") (d) Calculate the area under the curve...
Question 1 (Quadrature) [50 pts I. Recall the formula for a (composite) trapezoidal rule T, (u) for 1 = u(a)dr whic...
Question 1 (Quadrature) [50 pts I. Recall the formula for a (composite) trapezoidal rule T, (u) for 1 = u(a)dr which requires n function evaluations at equidistant quadrature points and where the first and the last quadrature points coincide with the integration bounds a and b, respectively. 10pts 2. For a given v(r) with r E [0,1] do a variable transformation g() af + β such that g(-1)-0 and g(1)-1. Use this to transform the integral に1, u(z)dz to an...
Problem 1: Consider a 2nd order homogeneous differential equation of the form aa2y"(x)bay(x) + cy =...
Problem 1: Consider a 2nd order homogeneous differential equation of the form aa2y"(x)bay(x) + cy = 0 (1) where a, b, c are constants satisfy so that y(x) = x (a) Find and justify what conditions should a constant m to (1) is a solution (b) Using your solution to (1) Write these three different cases as an equation that a, b,c satisfy. Hint: Use the quadratic formula we should get three different cases for the values that m can...
Hi can you please show how you get the answers using the long way just so I can see how you worke...
Hi can you please show how you get the answers using the long
way just so I can see how you worked it out even if you can label
which properties you've used Thank you
1. (a) (i) A student claims that if p and q are odd integers then the evaluation of the expression (p 1)(g2 - 1) will always be a multiple of 8. Give 3 numerical examples you would 2 marks) 3 marks) use to check this...
MATLAB Create a function that provides a definite integration using Simpson's Rule Problem Summar This example demo...
MATLAB Create a function that provides a definite integration
using Simpson's Rule
Problem Summar This example demonstrates using instructor-provided and randomized inputs to assess a function problem. Custom numerical tolerances are used to assess the output. Simpson's Rule approximates the definite integral of a function f(x) on the interval a,a according to the following formula + f (ati) This approximation is in general more accurate than the trapezoidal rule, which itself is more accurate than the leftright-hand rules. The increased...
If you’re using Visual Studio Community 2015, as requested, the instructions below should be exact but...
If you’re using Visual Studio Community 2015, as requested, the instructions below should be exact but minor discrepancies may require you to adjust. If you are attempting this assignment using another version of Visual Studio, you can expect differences in the look, feel, and/or step-by-step instructions below and you’ll have to determine the equivalent actions or operations for your version on your own. INTRODUCTION: In this assignment, you will develop some of the logic for, and then work with, the...
Numerical Methods 125% 4 16 (i) [1 mark] Given the data points {(ak,Uk))3-{(-1,03), (2.-01), (0.0.1)), the ai. Which of least-squares regression line can be written in the form y - do the following 2...
Numerical Methods
125% 4 16 (i) [1 mark] Given the data points {(ak,Uk))3-{(-1,03), (2.-01), (0.0.1)), the ai. Which of least-squares regression line can be written in the form y - do the following 2 x 2 linear systms of equations are the normal equations that determine the unknown coefficients do and ai? 0.5 0.6 0.6 A. 1 3 a1 B. 0.5 C. 0.5 0.5 0.6 0.26 [ao D.13 0.6」[al -0.5 0.6 3 1 o E. 5 La G) [I mark]...
Midterm Examination CSCI 3321 Summer, 2015 &n
Midterm Examination CSCI 3321 Summer, 2015 ___________ Your Name … .. Please answer each question by entering the most nearly correct answer (a, b, c, d) in the blank on the left. ____1. When approximating ex by a truncated Taylor series (expanded about x=0), how many terms would be required to keep the absolute value of the error below 10-3 over the interval [-1,1] ? a. 1 b. 2 c. 3 d. 4 ____2. The polynomial that...
I need to enter everything in formula form. Thanks! Maple Moving Company has provided you their...
I need to enter everything in formula form. Thanks!
Maple Moving Company has provided you their unadjusted account balances to before year-end adjustments. The Controller has asked you to prepare the Adjusted Trial Balance and has provided you with further year end information. Use the information included in the Excel Simulation and the Excel functions described below to complete the task. • Cell Reference: Allows you to refer to data from another cell in the worksheet. From the Excel Simulation...
Titration: Acids and Bases 2. How can you determine which acid is diprotic? 3. using the...
Titration: Acids and Bases
2. How can you determine which acid is diprotic?
3. using the answers to questions one and two, which acid is
diprotic?
4. Which base has more hydroxide ions per molecule?
Acid Volume Base Base Initial Volume (mL) Base Final Volume (mL) Volume of Base Used (mL) Acid: Base Ratio Acid 1 20 mL Base 1 50 mL 34.5 15.5 4:3 Acid 2 20 mL Base 1 Acid 1 20 mL Base 2 Acid 2 20...
Problem 1 (max 10 Points): The function Ca)2 x-3Vx +10 can be integrated analytically x - 3Vx +10 7 (a) Plot the function f(x) within the interval [20, 100] using 101 samples (b) Calculate the area under the curve of f(x) within the interval [20, 100] using the analytical solution of the integral. (c) Calculate the area under the curve of f(x) within the interval [20, 100] using trapezoidal numerical integration (hint: "trapz") (d) Calculate the area under the curve...
Question 1 (Quadrature) [50 pts I. Recall the formula for a (composite) trapezoidal rule T, (u) for 1 = u(a)dr which requires n function evaluations at equidistant quadrature points and where the first and the last quadrature points coincide with the integration bounds a and b, respectively. 10pts 2. For a given v(r) with r E [0,1] do a variable transformation g() af + β such that g(-1)-0 and g(1)-1. Use this to transform the integral に1, u(z)dz to an...
Problem 1: Consider a 2nd order homogeneous differential equation of the form aa2y"(x)bay(x) + cy = 0 (1) where a, b, c are constants satisfy so that y(x) = x (a) Find and justify what conditions should a constant m to (1) is a solution (b) Using your solution to (1) Write these three different cases as an equation that a, b,c satisfy. Hint: Use the quadratic formula we should get three different cases for the values that m can...
Hi can you please show how you get the answers using the long
way just so I can see how you worked it out even if you can label
which properties you've used Thank you
1. (a) (i) A student claims that if p and q are odd integers then the evaluation of the expression (p 1)(g2 - 1) will always be a multiple of 8. Give 3 numerical examples you would 2 marks) 3 marks) use to check this...
MATLAB Create a function that provides a definite integration
using Simpson's Rule
Problem Summar This example demonstrates using instructor-provided and randomized inputs to assess a function problem. Custom numerical tolerances are used to assess the output. Simpson's Rule approximates the definite integral of a function f(x) on the interval a,a according to the following formula + f (ati) This approximation is in general more accurate than the trapezoidal rule, which itself is more accurate than the leftright-hand rules. The increased...
Numerical Methods
125% 4 16 (i) [1 mark] Given the data points {(ak,Uk))3-{(-1,03), (2.-01), (0.0.1)), the ai. Which of least-squares regression line can be written in the form y - do the following 2 x 2 linear systms of equations are the normal equations that determine the unknown coefficients do and ai? 0.5 0.6 0.6 A. 1 3 a1 B. 0.5 C. 0.5 0.5 0.6 0.26 [ao D.13 0.6」[al -0.5 0.6 3 1 o E. 5 La G) [I mark]...
I need to enter everything in formula form. Thanks!
Maple Moving Company has provided you their unadjusted account balances to before year-end adjustments. The Controller has asked you to prepare the Adjusted Trial Balance and has provided you with further year end information. Use the information included in the Excel Simulation and the Excel functions described below to complete the task. • Cell Reference: Allows you to refer to data from another cell in the worksheet. From the Excel Simulation...
Titration: Acids and Bases
2. How can you determine which acid is diprotic?
3. using the answers to questions one and two, which acid is
diprotic?
4. Which base has more hydroxide ions per molecule?
Acid Volume Base Base Initial Volume (mL) Base Final Volume (mL) Volume of Base Used (mL) Acid: Base Ratio Acid 1 20 mL Base 1 50 mL 34.5 15.5 4:3 Acid 2 20 mL Base 1 Acid 1 20 mL Base 2 Acid 2 20...
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