Question

PART 1 : CURVE FITTING 1. Use the Method of Least Squares to fit a straight line y = c1x + c2 to x | 0 | 2 | 4 | 6 | 9 | 11 | 12 | 15 | 17 | 19 y | 5 | 6 | 7 | 6 | 9 | 8 | 7 | 10 | 12 | 12 2. Fit the following data to a parabolic model y = c1x^2 + c2x using least squares x | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 y | 2.5 | 7 | 38 | 55 | 61 | 77 | 83 | 145 3. Fit an exponential model y = ae^bx to the following data set using Least Squared Method. x | 0.4 | 0.8 | 1.2 | 1.6 | 2 | 2.3 y | 800 | 975 | 1500 | 1950 | 2900 | 3600 4. It is known that the data tabulated below can be modeled by the following equation y = ((a + sqrt(x))/(b*sqrt(x)))^2 . Use a transformation to linearize this equation and then employ linear regression to determine the parameters a and b. Based on your analysis predict y at x = 1.6. x | 0.5 | 1 | 2 | 3 | 4 y | 10.4 | 5.8 | 3.3 | 2.4 | 2 PART 2 : EULER'S METHOD 1. Using Euler' Method, solve for y(1) given the differential equation y' - y = -1/2 e^(x/2) sin(5x) + 5e^(x/2) cos(5x); y(0) = 0; h = 0.1 In your table, add an additional column for % relative true error for each step given that the analytical solution to the DE is y(x) = e^(x/2) sin(5x) . 2. Using Euler's Method, solve for y(3) given dy/dx = yx^3 - 1.5y; y(0) = 1 using a step size of a. h=0.5 b. h=0.25

          PART 1 : CURVE FITTING

1. Use the Method of Least Squares to fit a straight line y = c1x + c2 to

x | 0 | 2 | 4 | 6 | 9 | 11 | 12 | 15 | 17 | 19
y | 5 | 6 | 7 | 6 | 9 | 8 | 7 | 10 | 12 | 12

2. Fit the following data to a parabolic model y = c1x^2 + c2x using least squares

x | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8
y | 2.5 | 7 | 38 | 55 | 61 | 77 | 83 | 145

3. Fit an exponential model y = ae^bx to the following data set using Least Squared Method.

x | 0.4 | 0.8 | 1.2 | 1.6 | 2 | 2.3
y | 800 | 975 | 1500 | 1950 | 2900 | 3600

4. It is known that the data tabulated below can be modeled by the following equation
y = ((a + sqrt(x))/(b*sqrt(x)))^2 . Use a transformation to linearize this equation and then employ linear regression to determine the parameters a and b. Based on your analysis predict y at x = 1.6.

x | 0.5 | 1 | 2 | 3 | 4
y | 10.4 | 5.8 | 3.3 | 2.4 | 2

PART 2 : EULER'S METHOD

1. Using Euler' Method, solve for y(1) given the differential equation
y' - y = -1/2 e^(x/2) sin(5x) + 5e^(x/2) cos(5x); y(0) = 0; h = 0.1
In your table, add an additional column for % relative true error for each step given that the analytical solution to the DE is y(x) = e^(x/2) sin(5x) .

2. Using Euler's Method, solve for y(3) given dy/dx = yx^3 - 1.5y; y(0) = 1 using a step size of
a. h=0.5
b. h=0.25

PART 1 : CURVE FITTING

1. Use the Method of Least Squares to fit a straight line y = c1x + c2 to

x | 0 | 2 | 4 | 6 | 9 | 11 | 12 | 15 | 17 | 19
y | 5 | 6 | 7 | 6 | 9 | 8 | 7 | 10 | 12 | 12

2. Fit the following data to a parabolic model y = c1x^2 + c2x using least squares

x | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8
y | 2.5 | 7 | 38 | 55 | 61 | 77 | 83 | 145

3. Fit an exponential model y = ae^bx to the following data set using Least Squared Method.

x | 0.4 | 0.8 | 1.2 | 1.6 | 2 | 2.3
y | 800 | 975 | 1500 | 1950 | 2900 | 3600

4. It is known that the data tabulated below can be modeled by the following equation
y = ((a + sqrt(x))/(b*sqrt(x)))^2 . Use a transformation to linearize this equation and then employ linear regression to determine the parameters a and b. Based on your analysis predict y at x = 1.6.

x | 0.5 | 1 | 2 | 3 | 4
y | 10.4 | 5.8 | 3.3 | 2.4 | 2

PART 2 : EULER'S METHOD

1. Using Euler' Method, solve for y(1) given the differential equation
y' - y = -1/2 e^(x/2) sin(5x) + 5e^(x/2) cos(5x); y(0) = 0; h = 0.1
In your table, add an additional column for % relative true error for each step given that the analytical solution to the DE is y(x) = e^(x/2) sin(5x) .

2. Using Euler's Method, solve for y(3) given dy/dx = yx^3 - 1.5y; y(0) = 1 using a step size of
a. h=0.5
b. h=0.25

Added by Amber A.

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