In Engineering Mathematics plays a vital role. These are Mathematics basic concept for BE entrance exam. Given concepts are especially targeted for:

- IOE, Pulchowk ( TU )
- Indian Embassy
- Ministry of Education ( MOE )
- Kathmandu University
- Pokhara University
- Purbanchal University &
- Other Institutions

The 100 marks paper consists of both subjective and objective questions. While objective questions are multiple choice questions. In engineering Mathematics learning should to conceptual. Such type of competitive examinations required sound knowledge of Mathematics.

**The basic concept of Set Theory**

- A collection of any well-defined objects is termed as set.
- Each of the objects in a set is known as a member or an element of the set.
- Sets are denoted by capital letters in English alphabet like A, B, C,……..X, Y, Z and the elements are denoted by small letters in English alphabet.
- While a set having only one element is called singleton set.
- A set having fixed number of elements is called finite set otherwise it is called infinite set.
- A set having no elements is called null set or empty set or void set. For example the set of boys students in Kanya campus. It is denoted by ¢ or {}.
- Finally, the null set is the subset of any non-empty set.

The collection of all possible subsets of a set is called power set. Two sets are said to be disjoint if they have no common elements. Two sets are said to be intersecting if they have at least one element common.

**Real Number System in Engineering Mathematics**

- The set of integers, Z = {…..-3,-2,-1, 0, 1, 2, 3…}
- And the set of natural numbers, N= {1, 2, 3, 4…}
- While the set of whole numbers, W = {0, 1, 2, 3…..}
- The set of rational numbers, Q = { x: x = a/b where b is not zero}

**Elementary properties of inequalities**

- If a>b and b>c then a>c
- If a>b and c is any real number then a+c> b+c and a-c> b-c
- If a>b and c>0 then ac>bc and a/c>b/c
- If a>b and c<0 then ac<bc and a/c< b/c
- If a>b and c>d then a+c>b+d
- If a>b and c>d then ac>bd where a,b,c,d are positive integers.

**Functions and Relations**

A relation obtained by interchanging the first and second element in the ordered pairs of a relation is called inverse relation of the given relation.

Range set is the subset of target set. If the range set is not equal to co-domain then the function is called into function. And if the range set is equal to co-domain then the function is called onto function. So a function which is both one to one and onto is called bijective function. Only bijective functions have their inverses. These are the basic and important concepts.

### Engineering Mathematics Basic Concepts

**Logarithms**

- Functions which are not algebraic are transcendental functions viz. exponential, logarithm and trigonometric.
- So inverse of an exponential function is known as logarithmic function.
- While logarithms to base 10 are called common logarithms. While the logarithms of base ‘e’ are called natural logarithms.
- The integral part of a logarithm is called characteristics and the fractional part when expressed as a decimal is called the Mantissa.
- So the characteristic of the logarithm of a number greater than unity are less by one, than the number of digits in its integral part and is non-negative.

Hence the above given are the basic concept of Maths. Therefore everyone preparing for entrance exam should know them. Due to high pressure of students competition is tough. So students should have sound knowledge on Maths.

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