Applied Mathematics – II (English)

95 70

Regulation 2023

ISBN 978-81-19432-54-7

 

Unit I COORDINATE GEOMETRY

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 II INVERSE TRIGONOMETRIC FUNCTIONS

THEORY
Recapitulation of domain and range of sin𝑥,cos𝑥,tan𝑥,cosec𝑥,sec𝑥 and cot𝑥 and their graphs – Definition of inverse trigonometric functions – Domain and range of sin−1𝑥,cos−1𝑥,tan−1𝑥,cosec−1𝑥,sec−1𝑥,cot−1𝑥 and their graphs – Principle values of inverse trigonometric functions – Simple problems.

Unit III COMPLEX NUMBERS

THEORY
Definition of a complex number – Real and imaginary parts – Modulus and argument – Polar form of a complex number – Conjugate of a complex number – Representation of complex numbers on Argand plane – Addition, subtraction, multiplication and division of complex numbers – De-Moivre’s theorem (without proof) – Simple problems.

Unit IV 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 – Maxima and minima – Simple problems.

Unit V 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.

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