Your assignment submission should contain a few files. You should submit all of your Matlab code and it should be properly commented to explain what the code is doing. You can submit as separate m-files saved as HW#Q# OR you can submit a single word or text file with all of the code pasted in (specifying or delineating code for each problem). For additional written work and discussion of problems, this should be a single pdf that is well-organized and either typed or neatly written. (If hand-written, use an app to scan and save as a single pdf). This file should be saved as HW#. To receive full credit on a problem, the code must run with no errors and the written work/discussion of the problem must also be complete. Matlab output should be discussed in the write-up.
Circuits
In a circuit with impressed voltage ε(t) and inductance L, Kirchhoff’s first law gives the relationship
where R is the resistance in the circuit and i is the current. Suppose we measure the current i for several values of t and obtain:
t
1.00
1.01
1.02
1.03
1.04
i
3.01
3.12
3.14
3.18
3.24
where t is measured in seconds, i is in amperes, the inductance L is a constant 0.98 henries, and the resistance is 0.142 ohms.
Approximate the voltage ε(t) when t = 1.00,1.01,1.02,1.03, and 1.04 using the derivative approximations derived in class and/or 4.1 in Burden & Faires textbook.
Specify the order of accuracy of each approximation and whether it is a forward,backward, or centered approximation.
You can complete this by hand or with a Matlab code.
(10 points total) Approximating Derivatives(5 points) Derive a method for approximating f000(xo) whose error term is O(h2), by expanding the function f in a Taylor polynomial about xo using xo± h, xo, and xo± 2h.
(5 points) The partial derivative fx(x,y) of f(x,y) with respect to x is obtained by holding y fixed and differentiating with respect to x. Similar for fy when holding x Using a Taylor series expansion of a function of two variables, determine the O(h2) numerical approximation formulas and associated truncation error for fx and fy.
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