Download APPLIED_MATHEMATICS_1.pdf

The Maharaja Sayajirao University of Baroda
Polytechnic,
Department of Electrical Engineering,
ACADEMIC YEAR
2015-2016
Near Shastri Bridge, Fatehgunj, Vadodara-390001, <<e-mail ID>>
Computer Engineering : (Higher Payment Program)
YEAR I
Semester I
CORE/Elective/Foundation 1:
AMT3107 : Applied Mathematics-1
CREDIT
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HOURS
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OBJECTIVES:
COURSE CONTENT / SYLLABUS
UNIT-I
Algebra
1.1
Arithmetic progression.
1.2
Geometric progression.
1.3
Sum of squares and cubes of finite number of natural members.
1.4
Mathematical Induction.
1.5
Exponential and Logarithmic functions.
1.6
Binomial Theorem (without proof) for any index.
1.7
Quadratic equations and inequations.
1.8
Permutations and combinatiosn.
Trigonometry
2.1
UNIT-II
UNIT-III
UNIT-IV
2.2
2.3
2.4
2.5
2.6
2.7
2.8
2.9
2.10
2.11
Angles and their measures.
Trigonometric ratios.
Trigonometric functions.
Periodicity of trigonometric functions.
Sums and Difference formulae (without proof) and their applications.
Trigonometric ratios of multiple and sub-multiple of angles (2A, 3A and A/2 only.)
Simple Trigonometric identities.
Sine and cosine formula.
Napier Analogy.
Law of projection and Half angle formula.
Inverse trigonometric functions.
Coordinate Geometry
3.1
Cartesian and polar coordinates of a point and their conversion.
3.2
Distance between two points.
3.3
External and Internal division formulae (without proof.)
3.4
Coordinates of centroid and incentre of a triangle.
3.5
Area of a triangle when its vertices are given.
3.6
Equation of straight line in various standard forms.
3.7
Intersections of straight lines.
3.8
Angle between two straight lines.
3.9
Perpendicular distance formula.
3.10
Circle.
3.11
Standard and general equation of a circle.
3.12
Finding equation of circle when center and radius is given.
3.13
Conic.
3.14
Definition of a conic.
3.15
Parabola, ellipse, hyperbola and their standard equations (without proof).
3.16
Finding equations of a conic when its focus, directrix and vertex are given.
Differential Calculus
4.1
Limit and continuity of a functions.
4.2
Standard limits.
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UNIT-V
UNIT-VI
4.3
Evaluation of a simple limits.
4.4
Differentiation - Definition and geometrical interpretation of derivative.
4.5
Physical meaning of derivative,
4.6
Differentiation from the first principle of Xn, ax, logax, sin x, cos x, tan x.
4.7
Derivative of sum, product, quotient and composite of two functions.
4.8
Differentiation of sec x, cosec x, cot x and inverse trigonometric functions.
4.9
Differentiation of functions in implicit and parametric forms.
4.10
Applications of Differentiation - Tangents and normals, maxima and minima.
Integral Calculus
5.1
Indefinite integrals.
5.2
Integration as inverse of differentiation.
5.3
Simple integration by substitution, integration by parts and by partial fractions.
5.4
Definite integral.
5.5
Geometrical interpretation of definite integral.
5.6
Properties of definite integrals.
5.7
Evaluation of simple definite integrals,
5.8
Reduction formulae.
5.9
Evaluation of
(m, n being positive integers).
5.10
Applcation Area under the curve and.
5.11
Volume and surface of solids formed by revolution of mens under curve, about x-axis.
Differential Equations
6.1
Order and degree of differential equation.
6.2
Solution of differential equations of first order and first degree - homogeneous
differential equation and solutions of differential equation in variable separable form.
6.3
Linear differential equation of first order.
REFERENCES
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