332: 305 Numerical Modeling in Biomedical Systems Fall 2010 Homework Solutions #3
1) Prob. 2.4.3
Hwk Soln #3 Fall, 2010 Dr. Shoane
R
+ _
eS
C vC
+ _
L
RC
d2 d R d v + vC + vC = eS 2C dt dt L dt
Dividing the differential equation of the circuit by RC and c

125:305 Numerical Modeling in Biomedical Systems Homework Assignment #4 Due Tuesday, 10/5/2010 1) Prob. 2.6.4 a-e (pg. 68) Provide all answers in terms of k1, k2, and . For Part c, ignore Comment on the result. Selected Answer: Part e,
Fall, 2010 Dr. Shoa

125:305 Numerical Modeling in Biomedical Systems Minimum Things to Know for the Exam
Fall, 2010 Dr. Shoane
1) Know how to find the damping ratio and undamped natural frequency given a 2nd-order differential equation. 2) Know the exact form of the equation

332: 305 Numerical Modeling in Biomedical Systems Homework Solutions #2
Fall 2010 Dr. Shoane
1) Prob. 2.2.3
c1 , F1
dQ = c1 F1 cF0 dt
c,Q
a)
dQ = c1 F1 cF0 , dt dQ Q + F0 = c1 F1 dt V
Q c= , V
Q(0) = 0
c, F0
V dQ V + Q = c1 F1 F0 dt F0 V dQ + Q = Vc1 , F

Notes on Newton-Raphson A root-solving technique
1. Introduction to Newton-Raphson
(Updated 11/3/2010) (Dr. Shoane)
Based on geometric interpretation or Taylor series expansion of the function, f(x) at xi.
From the geometry of the situation seen in the gr

Chapter 2 Lecture Notes for Students * Section 1 * Notes on Conversion of Two First Order Equations to a Second Order Model A linear second order system is sometimes represented as a system of two first order differential equations like those in Eqs and b

Cramer's Rule - Derivation and Examples
Derivation of Cramer's Rule Given a system of equations:
Dr. Shoane
In matrix form:
This can be written in the general form
To solve for x, we multiply both sides of the equation by A-1
A-1 can be computed by dividi