Applied Mathematics – I (English)

95 70

Regulation 2023

ISBN 978-81-19432-71-4

 

Unit I COORDINATE GEOMETRY – 1

THEORY
Equation of a circle with given centre and radius – General equation of circles – Centre and radius of a circle from general equation – Concentric circles – Contact of circles – Orthogonal circles – Simple problems.

Unit II COORDINATE GEOMETRY – 2

THEORY
General equation of conics – Classification of conics – Standard equations of parabola – Vertex, focus, axis, directrix, focal distance, focal chord, latus-rectum of parabola – Standard equations of ellipse – Vertices, foci, major axis, minor axis, directrices, eccentricity, centre and latus-rectums of ellipse – Simple problems.

Unit III DIFFERENTIAL CALCULUS

THEORY
Limits of polynomials and rational functions – Limits of the form lim𝑥→0sin𝑎𝑥𝑏𝑥 and lim𝑥→0tan𝑎𝑥𝑏𝑥 (𝑥 in radians) (results only) – Definition of differentiability – Differentiation formulae for standard functions – Differentiation of sum, difference, product and quotient of functions – Chain rule – Second order derivatives – Radius of curvature – Simple problems

Unit IV INTEGRAL CALCULUS

THEORY
Integration formulae of standard functions as inverse operation of differentiation – Bernoulli’s formula – Definite integrals (Properties are excluded) – Area and volume using integration – Simple problems.

Unit V STATISTICAL PROCESS CONTROL

THEORY
Random variables – Continuous random variables – Normal distribution – Process average and process variation using arithmetic mean and variance – Central line (CL), upper control limit (UCL) and lower control limit (LCL) – Control charts – 𝑋̅ charts – Out-of-control signals – Simple problems.

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