# GITAM University Mathematics I Syllabus

B.Tech. (BT)First Semester

Bridge Course –I (BPC Stream) EURMT106: Mathematics – I

Code: EURMT 106 Category: BC

Credits: 3 Hours : 3 per week

Department: Engg. Mathematics

Aim of the Course is to impart knowledge of basics in Mathematics to enable them

understand advanced concepts / applications easily.

UNIT-1

Differential Calculus : (12 hours)

Limits & Continuity :

Definition of right hand limit, left hand limit, limit. Limits of f + g,

g

f , f o g (with out

proof), standard limits 1)

x a

x a

x a

n n

?

?

?

lim

2)

?

?

?

sin

0

lim

?

3)

n

n n

??

?

??

? ?

?

1 1

0

lim

4)

x

e

x

x 1

0

lim ?

?

5)

x

a

x

x 1

0

lim ?

?

(without proofs)

Definition of continuity and simple illustrations.

Differentiation:

Introduction – definition – differentiation of a function at a point and on an interval –

Derivative of a function – Differentiation of sum, difference, product and quotient of

functions- Differentiation of algebraic, exponential, logarithmic functions –

composite, implicit, parametric, hyperbolic and inverse hyperbolic functions-

Logarithmic differentiation – derivative of a function with respect to another function.

Derivatives of first and second order.

UNIT II.

Indefinite Integrals (10 periods)

Integration as the inverse process of differentiation standard forms – properties of

integrals- integration by method of substitution covering algebraic, trigonometric and

exponential functions – Integration by parts – logarithmic functions, Inverse

trigonometric functions.

UNIT III

Integrals of special types and definite integrals (10 hours)

integrals of the following types of functions.

2 2 2 2

2 2 2 2 2 2 2 2 1 , 1 , 1 , 1 , x a , a x

x a a x x a a x

? ?

? ? ? ?

Integration of rational functions using partial fractions.

Definite Integrals Definition of a definite integral and its properties (without

proof) – Formulae ,

/ 2

0 ?

?

Sinn? d? cos ,

/ 2

0 ?

?

n? d? ?

/ 2

0

cos

?

n? Sinm? d? (without proof).

UNIT IV

Coordinate Geometry – 1 (12 hours)

Locus: Definition and Equation of Locus

Straight lines:

Recapitulation of general equation of a straight line – forms of equation of a straight

line: slope Intercept form, intercept form, point – slope form, Two point form.

Normal form x cos ? + y cos ? = P , symmetric form

sin? cos?

1 1 x x y ? y

?

?

= r – Reduction

of general equation into different forms- point of intersection of two straight lines,

family of straight lines. Line passing through the point of intersection of two given

lines – condition for concurrency of three straight lines- angle between two

intersecting lines, condition for perpendicularity and parallelism- length of the

perpendicular from a point to a straight line, distance between two parallel lines.

(Proofs of the theorems are not required)

UNIT V.

Coordinate Geometry – 2 Circles: (10 periods)

Equation of a circle – standard form – centre and radius – equation of a circle with a

given line segment as diameter – equation of a circle through 3 non collinear points –

parametric equations of a circle, position of a straight line in the plane of the circle –

condition for a straight line to be a tangent – chord joining 2 points on a circle –

equation of the tangent at a point on the circle – point of contact – equation of normal.

Relative positions of 2 circles – circles touching each other – externally, internally, of

common tangents -Angle between 2 intersecting circles – conditions for

orthogonality. (Proofs of the theorems are not required)

Conic sections:

Standard and different forms of Parabola, Ellipse and Hyperbola – parametric

equations of Parabola, Ellipse and Hyperbola

Textbooks Prescribed :

1. Engineering Mathematics Dr. V. Ramamoorthy, Dr.A Solai Raju. S. Ramamoorthy,

S. Ganesh. Pub. Viodayal Karuppur, Kambakonam RMS. Anuradha Agencies.

2. Intermediate Mathematics Volume I & II, V.Venkateswara Rao, N.Krishna Murthy,

B.V.S.Sharma, Chand& Company Ltd.

References :

A first Course in Mathematics for Engineers, Chandrika Prasad. Prasad Mudranakya,

Allahabad

Note: The figures in parentheses indicate approximate number of expected hours of

Instruction.