M 427L Section 2/1/11
TA: Davi Maximo
A problem I dint nish in class
Problem 32, Section 1.3. Given vectors a and b, do the equations (yes, both of
them, and at the same time) x a = b and x a = |a| determine a unique vector
x? Argue both geometrically and
Inductors & Capacitors
Store energy
Introduce derivatives d/dt
Capacitance
Capacitor = charge bucket
Voltage V
pressure p
Current i
flow rate Q
Charge q
fluid volume v
Units: Farads (F) = Coulomb/Volt (C/V)
Conservation of charge:
dq
=i
dt
d
i=C
dt
q = C
Signal Conditioning and A/D Conversion*
1. Measurement Concepts and Sensors
2. Circuit Loading and Measurement Errors
3. Single Input and Differential Amplifiers
4. Analog-to-Digital Conversion, Quantizing, and
Digital-to-Analog Conversion
*Hambley Chapte
Transistors
3terminal semiconductor devices, for
Amplica8on
Amplier magnies signal (current/voltage across 2 input terminals),
external power boosts copy of signal (current/voltage)
Input controls output: transistors nonl
Chapter 16 Overview
Motor type for various applica7ons
How motor torque varies with speed
Equivalent circuit for DC motors
Use motor nameplate informa7on
Understand opera7on & characteris7cs
shuntconnected DC mot
Magne&c Circuits & Transformers
Magne&c eld around a long straight wire
Flux density in a toroidal core
Flux and ux linkages for a toroidal core
The toroidal coil as a magne&c circuit
A magne&c circuit with an air
PN Junc(ons & Diodes
Semiconductors
Basic Diode Concepts
LoadLine Analysis of Diode circuits
IdealDiode Model
PiecewiseLinear Diode Model
ZenerDiode as Voltage Regulator
Rec(er Circuits
Waveshaping Circuits
Linear Small
Frequency Response of System*
1. Fourier Series
2. Transfer Function
3. Filters
4. Bode Plot
*Hambley Chapter 6
Fourier Analysis
v(t)
v (t ) = a o +
n =1
2nt
2nt
+ bn sin
a n cos
T
T
Treat signals as periodic, i.e., sums of sinusoids of different frequ
Exam 1 Review
Solutions Guide
1. All directions in the plane 3x + 2y z = 7 are perpendicular to (3, 2, 1), and
the ones in the plane x 4y + 2z = 0 are in turn perpendicular to (1, 4, 2). The
direction of the line of intersection of these two planes then m
1
Homework 2 Solution
M 20E C T
1
Chapter 1
1.1 Section 4, Problems 1, 4, 8, 12, 13
Problem 1.1.4. 1. Describe the surfaces r = const., = const., and z = const. 2. Describe the surfaces = const., = const., and = const. Solution. 1. r = const. is a cylinde
Homework 3 additional problems.
Reminder: the basic linear transformation matrices for 2D that I gave in class were
Counterclockwise rotation:
cos sin
sin cos
Scaling the x-direction by kx and the y -direction by ky :
Shearing x by k :
kx 0
0 ky
1k
0
Homework 4 additional problems.
Problems
1. Find the linear approximation to f (x, y, z ) = (2x2 3x, sin(xy ) around the point (0, 0)
and around the point (1, 1).
2. Find the linear approximation to g (t, x, y ) = (cos(xt), sin(yt), arctan(x2 + y 2 t2 ) a