A Textbook Of Engineering Mathematics Sem 1 KTU

The hyperbolic functions have similar names to the trigonometric functions, but they are defined in terms of the exponential functions

A sequence is a function whose domain is the set N of all natural numbers whereas the range may be any set S. In other words, a sequence in a set S is a rule which assigns to each natural number a unique element of S.

A series of the form a0 + a1x + a2x2 + ..... + an xn + ..... = Σ is called a power series

Any first degree equation in x, y, z represents planes in 3 space. Hence planes are represented by linear equations in the cartesian system

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).
z is called the dependent variable while x and y are called independent variables.
For example, the area of a triangle is determined when its base and altitude are known.
Thus, area of a triangle is a function of two variables, base and altitude.

Let z = f(x, y) be a function of two independent variables x and y. If y is kept constant
and x alone is allowed to vary, then z becomes a function of x only. The derivative of z, with
respect to x, treating y as constant, is called partial derivative of z w.r.t. x

If to each value of a scalar variable t, there corresponds a value of a vector r , then r is
called a vector function

The multiple integral is a definite integral of a function of more than one real variable, for example, f(x, y) or f(x, y, z).Integrals of a function of two variables over a region in R2are called double integrals, and integrals of a function of three variables over a region of R3 are called triple integrals.

Vector integration refers to four types of integrals of vectors: ordinary integrals, indefinite or definite. line integrals: the vector values with respect to points on a line. surface integrals: sum the vector values with respect to an area (performed as a double integral for each coordinate)

Appendix I

Appendix II