GITAM University Mathematics I Syllabus

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.

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