%This function computes the value of -t(u(t+1)-u(t)
1. Solve the PDEs.
(a) uxx = 4y 2 u,
(b) uyy = 4xuy
Sol. (a) If u = u(x), then u(x) = Ae2yx + Be2yx . Thus the solution of this PDE is
u(x, y ) = A(y )e2yx + B (y )e2yx , where A(y ) and B (y ) are arbitrary.
(b) Setting uy = p, we have py
1. (a) Represent the data
403 399 398 401 400 401 401
by a stem-and-leaf plot, a histogram, and a boxplot.
(b) In(a), nd the mean and compare it with the median. Find the standard deviation and compare it with the interquartile range.
Understand the operating principle of a timer and an audio amp, and implement it
by connecting to a speaker.
Understand the characteristics and operating principles of a timer
Understand the characteristics and operating principles of an audio amp.
Understand the operation of a DAC according to its timing diagram, and
devise a circuit that can operate at a desired range.
DAC timing diagram range
Understand the characteristics and the operating principle of a DAC utilizing the
current mirror usi
Understand the usage of the ADC according to its timing diagram and
design a circuit that produces output within the desired range.
Understand the characteristic and o
Ch. 2. Filter
Understand what filter is, and understand the characteristics and operating
principles of RC filters and Tow-Thomas Biquad filters.
1. Understand the characteristics and operating principles of a 1st order RC
Ch. 1. Regulators and DC-DC Converters
Understand the usage and operating method of regulators and DC-DC converters
and implement a circuit that produces a desired voltage
1. Understand the characteristics and operating method of th
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) DC AC
1.(a) Show that multiplication by i (z iz ) is geometrically a counterclockwise
rotation through .
(b) Show that multiplication by = cos + i sin (z z ) is geometrically a
counterclockwise rotation through .
Sol. (a) Let z = x + iy (= 0).
1. Find the divergence and the curl of the vector function
F(x, y, z ) = (x2 + y 2 + z 2 )3/2 (xi + y j + z k).
, F2 = 2
, F3 = 2
(x2 + y 2 + z 2 )3/2
(x + y 2 + z 2 )3/2
(x + y 2 + z 2 )3/2
y 2 +
1. (a) Find a maximum likelihood estimate for = p in the case of the binomial
(b) Extend (a) as follows. Suppose that m times n trials were made and in the rst
n trials A happened k1 times, in the second trials A happened k2