MATHEMATICS
–II (G104)
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L
3
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T
1
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P
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Credit: 4
Curri. Ref. No.: G104
Prerequisite:
G103
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Total
marks: 100
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Total
Contact hrs :60
Lecture: 45Tutorial: 15Practical: 0
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Theory:
100= End
Term Exam: 70 +P.A: 30
Practical:
25= P.A
: 25
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RATIONALE
The purpose of teaching Engineering Mathematics-II
to diploma students is to enable them to understand advance uses of mathematics
and solving engineering problems. Continuity and sequence is necessary for logical
Development of subject. The topic
includes Coordinate Geometry, Differential Calculus, Integral Calculus and
Vector Algebra. This course will be helpful
for the learners those who like to go for higher studies.
THEORY Total Periods :
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UNIT
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TOPIC/SUB-TOPIC
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HRS.
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1
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CO-ORDINATE
GEOMETRY
Co-ordinate Systems:Cartesian& Polar Coordinates, Distance
between two points. Division of line segment. Area of a triangle. Locus of a point. Standard forms
of the equations of a straight line: Intersection of straight lines Angle
between them Bisector of the angle between them. Change of axes
Transformation of coordinates when origin is shifted and when axes are rotated. Pair of Straight lines:
x² + 2hxy + by² =0, Geometric figures, Circle, Parabola, Ellipse ,Hyperbola.
Definition & Properties of Geometric figures. Standard Equations of
Geometric figures
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10L+3T
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2
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DIFFERENTIAL
CALCULUS
Functions.Independent& Dependent Variables. Types of
functions. Limits: Concept of limits. Evaluation of limits. Differentiation
by 1st Principle: Differentiation of Sum, Product and Quotient of functions.
Differentiation of a function of a function. Differentiation of
Trigonometric, Inverse Trigonometric & Hyperbolic functions. Logarithmic
differentiation. Differentiation of Parametric
functions.PartialDifferentiation:PartialDifferentiation,Successive
Differentiation Higher order derivatives - up to nth order, Linear
differential Equation. Application of differentiation: Differential
coefficient. Application of coefficient. Equation for Tangent, Normal δ ,
Sub-tangent & Subnormal δ
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12L+5T
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3
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INTEGRAL
CALCULUS
Indefinite Integration: Definition. Methods of Integration:
Integration by Substitution. Integration by parts Integration by partial fractions. Reduction
formulae for integration of sinⁿx.cosⁿx. Definite Integrals: Definite
integral as limit of a sum. Fundamental properties. Definition of gamma
function. Evaluation of gamma function. Application of Integration: Area of a
plane curve.Length of plane curves.Work done.Volume Mean & RMS values.
Centre of gravity Simpson’s One- Third Rule. Evaluation of Multiple
Integrals:Evaluation of double integrals. Evaluation of triple integrals. Use
of constant limits.
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13L+5T
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4
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VECTOR ALGEBRA
Vector and Scalar
quantities.Type of vectors, geometric representation of vectorAddition and
subtraction of vectors, unit vectors i,j and k. Magnitude and direction of
vectors,Product of a vector by a scalar, product of two vectors (scalar &
vector), Applications of vectors to engineering problems
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10L+2T
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SUGGESTED LEARNING RESOURCES
Text Books:
1.
Differential Calculus By B.C. Das & B.N. Mukherjee
2.
Integral Calculus By B.C. Das & B.N. Mukherjee
3.
Elementary Co-ordinate Geometry and Solid figures By B. Das
Reference Books:
1.
Engineering Mathematics Part II By Shanti Narayan
2.
Engineering Mathematics Vol I & II ByVishwanath