Hi everyone. I have a homework on numerical differentiation and I just want to know if my answers are correct.
1.) The partial derivative, of with respect to x is obtained by holding y fixed and differentiating with respect to x. Similarly, is found by holding x fixed and differentiating with respect to y. The equation below is adapted to partial derivatives:
[The two equations above are denoted as equation (i)]
(a). Let . Calculate the approximations to and using the formulas in (i) with h = 0.1, 0.01, and 0.001. Compare with the values obtained by differentiating
MY ANSWERS:
First, I solved for the derivative of with respect to x. I got:
Solving for using equation (i)
h_____ _ _____2h______
0.1_____1.23529____1.16327____0.20000___0.36014
0.01____1.20359____1.19639____0.20000___0.36000
0.001___1.20036____1.19964____0.20000___0.36000
Solving for
Derivative with respect to y:
Solving for using equation (i)
h_____ _ _____2h______
0.1_____1.21569____1.18367____0.20000___0.16006
0.01____1.20160____1.19840____0.20000___0.16000
0.001___1.20016____1.19984____0.20000___0.16000
Am I doing this right??
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2.) The distance traveled by an object is given in the table below:
_t_____D(t)
8.0___17.453
9.0___21.460
10.0__25.752
11.0__30.301
12.0__35.084
(a) Find the velocity by numerical differentiation
(b) Compare your answer with .
My Answers:
(a). Is it okay if I use central-difference to solve for the velocity? Or should I use forward of backward difference? If so, should I assume different step values (h)? Using central-difference, my answer is:
(b). .