Description
- 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.
- Approximating Derivatives
-  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.
- Â 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.
