A Textbook Of Engineering Mathematics Kerala Uni Sem 1 & 2

As the hyperbolic functions are defined in terms of the exponential function, the inverse
hyperbolic functions are expressible in terms of the inverse of the exponential function.

FUNCTIONS OF TWO VARIABLES
If three variables x, y, z are so related that the value of z depends upon the values of x and y,
then z is called a function of two variables x and y, and this is denoted by z = f(x, y).

The definite integral
a
b z f(x) dx is defined as the limits of the sum f(x1)δx1 + f(x2)δx2 + ⋅⋅⋅ +
f(xn)δxn when n → ∞ and each of the lengths δx1, δx2, ..., δxn tends to zero. Here δx1, δx2, ..., δxn
are n sub-intervals into which the range b – a has been divided and x1, x2, ..., xn are values of
x lying respectively in the first, second, ..., nth sub-interval.

A transformation is a mathematical device which converts one function into another.

Laplace transforms or Laplace transformation is widely used by scientists and engineers.
It is particularly effective in solving linear differential equations – ordinary as well as
partial. It reduces an ordinary differential equation into an algebraic equation.
Laplace transform directly gives the solution of differential equations with given initial
conditions without the necessity of first finding the general solution and then evaluating the
arbitrary constants.

A linear differential equation is the differential equation in which the dependent variable
and its derivatives occur only in the first degree and are not multiplied together.

Any one of the following operations on a matrix is called an elementary transformation (or Eoperation).

Appendix