62
BASIC ENGINEERING MATHEMATICS
ACE Academy
BASIC ENGINEERING MATHEMATICS
TOPIC 4
STATISTICS
PROBABILITY &
The probability p of an event A has defined as follows. If A can occur in s ways out of a total
of n equally likely ways then
p = p(A) = s/n
SAMPLE

ACE Academy
DIFFERENTIAL EQUATIONS
89
Basic Engineering Mathematics
TOPIC 5
EQUATIONS
DIFFERENTIAL
DIFFERENTIAL EQUATIONS OF FIRST ORDER
A differential equation is an equation which involves differential coefficients or
differentials.
Ex: i) ex dx + ey d

DIFFERENCES BETWEEN ONE AND
MULTI DIMENSIONAL SIGNAL
PROCESSING
o More data for M-D signal processing.
1. 1-D Speech —) 10K samples per second.
2. M-D Television —~> 500 x 500 pixels per frame,
30 frames a second, 7.5 Mega samples per
second.
0 Mathematic

160
BASIC ENGINEERING MATHEMATICS
BASIC
TOPIC 9
METHODS
ENGINEERING
ACE Academy
MATHEMATICS
NUMERICAL
ROOT FINDING : Consider the equation
f(x) = 0 . (1)
If f (x) is continuous in [a, b] and f (a) and f (b) are of opposite signs i.e. [f(a) . f(b)<0]
then

ACE Academy
BASIC
COMPLEX VARIABLES
ENGINEERING
139
MATHEMATICS
TOPIC 8
VARIABLES
COMPLEX
Complex Variables (Complex Numbers):
A Complex number may be defined as an ordered pair (x, y), where x and y are real numbers.
Which are called real and imaginary p

ACE Academy
TRANSFORM THEORY
115
Basic Engineering Mathematics
TOPIC 7
THEORY
TRANSFORM
LAPLACE TRANSFORMS
Definition : Let f(t) be a function of t defined for all positive values of t. Then the Laplace
transform of f(t), denoted by Lcfw_f (t) and is defi

ACE Academy
FOURIER SERIES
BASIC
ENGINEERING
109
MATHEMATICS
TOPIC 6
FOURIER SERIES
PERIODIC
FUNCTIONS
If at equal intervals of abscissa x, the value of each ordinate f(x) repeats itself
i.e. f(x) = f(x+) for all x, then y=f(x) is called a periodic functi

50
BASIC ENGINEERING MATHEMATICS
ACE Academy
BASIC ENGINEERING MATHEMATICS
TOPIC 3
VECTOR CALCULUS
* Vector differential operator, Del, written as is defined by
=i + j +k
x
y
z
GRADIENT
Let f(x, y, z) be a differentiable function. Gradient of f(x, y, z)

22
BASIC ENGINEERING MATHEMATICS
ACE Academy
Basic Engineering Mathematics
TOPIC 2
CALCULUS
STANDARD
DERIVATES
d (uv) = u dv + v du
dx
dx
dx
d
dx
u = v (du / dx) u (dv / dx)
v
v2
du = du . dy (Chain Rule)
dx
dy dx
d (ax + b) n =n (ax + b)n 1 . a
dx
d (ax)

Basic Engineering Mathematics
(Common to ECE, EEE & EIE)
TOPIC 1
ALGEBRA
LINEAR
* Matrix multiplication is associative( if conformability is assured) .
i.e. A(BC) = (AB)C
* Matrix multiplication is distributive w. r. t addition of matrices .
A.(B + C) = A