Subject Code: MA1L001	Subject Name: Mathematics-I	L-T-P: 3-1-0	Credit: 4
Pre-requisite(s): Nil
*Calculus:* Rolle’s theorem, Lagranges theorem, Cauchy’s mean value theorem (Taylor’s and Maclaurin theorems with remainders), Indeterminate forms, Concavity and convexity of a curve, points of inflexion, maximum, minimum of a function, 2nd derivative test for max min, Asymptotes and curvature, Cartesian curve tracing, polar curve tracing. *Calculus of Several Variables: Limit, continuity and differentiability of functions of several variables, partial derivatives and their geometrical interpretation, differentials, derivatives of composite and implicit functions, derivatives of higher order and their commutativity, Euler’s theorem on homogeneous functions, harmonic functions, Taylor’s expansion of functions of several variables, maxima and minima of functions of several variables, Lagrange’s method of multipliers. Vector Calculus:* Double and triple integrals, Scalar and vector fields, level surfaces, directional derivative, Gradient, Curl, Divergence, line and surface integrals, theorems of Green, Gauss and Stokes. Beta and Gamma functions. *Ordinary Differential Equations:* First order differential equations, exact, linear and Bernoulli’s form, second order differential equations with constant coefficients, Euler’s equations, particular integrals by: variation of parameters, undetermined coefficients, operator method, system of differential equations. Text Books: Narayan S. and Mittal P. K. Differential Calculus and Integral Calculus, S. Chand & Company Ltd. Thomas G. B. and Finney R. L. Calculus and Analytic Geometry, Pearson Kreyszig E. Advanced Engineering Mathematics, John Wiley & Sons Simmons G. F. and Robertson J. S. Differential Equations with applications and Historical notes, Tata McGraw-Hill Publishing Company Limited, New Delhi, India Reference Books: Bartle R. G. and Sherbert D. R. Introduction to Real Analysis, Wiley India Jain R. K. and Iyengar S. R. K. Advanced Engineering Mathematics, Narosa Apostol T. M. Calculus - Vol.2, Wiley India Ross S. L. Differential Equations, Wiley India Coddington E. A. An Introduction to Ordinary Differential Equations, Prentice Hall

Subject Code: MA1L001

Subject Name: Mathematics-I

L-T-P: 3-1-0

Credit: 4

Pre-requisite(s): Nil

Calculus: Rolle’s theorem, Lagranges theorem, Cauchy’s mean value theorem (Taylor’s and Maclaurin theorems with remainders), Indeterminate forms, Concavity and convexity of a curve, points of inflexion, maximum, minimum of a function, 2nd derivative test for max min, Asymptotes and curvature, Cartesian curve tracing, polar curve tracing.
Calculus of Several Variables: Limit, continuity and differentiability of functions of several variables, partial derivatives and their geometrical interpretation, differentials, derivatives of composite and implicit functions, derivatives of higher order and their commutativity, Euler’s theorem on homogeneous functions, harmonic functions, Taylor’s expansion of functions of several variables, maxima and minima of functions of several variables, Lagrange’s method of multipliers.
Vector Calculus: Double and triple integrals, Scalar and vector fields, level surfaces, directional derivative, Gradient, Curl, Divergence, line and surface integrals, theorems of Green, Gauss and Stokes. Beta and Gamma functions.
Ordinary Differential Equations: First order differential equations, exact, linear and Bernoulli’s form, second order differential equations with constant coefficients, Euler’s equations, particular integrals by: variation of parameters, undetermined coefficients, operator method, system of differential equations.

Text Books:

Narayan S. and Mittal P. K. Differential Calculus and Integral Calculus, S. Chand & Company Ltd.
Thomas G. B. and Finney R. L. Calculus and Analytic Geometry, Pearson
Kreyszig E. Advanced Engineering Mathematics, John Wiley & Sons
Simmons G. F. and Robertson J. S. Differential Equations with applications and Historical notes, Tata McGraw-Hill Publishing Company Limited, New Delhi, India

Reference Books:

Bartle R. G. and Sherbert D. R. Introduction to Real Analysis, Wiley India
Jain R. K. and Iyengar S. R. K. Advanced Engineering Mathematics, Narosa
Apostol T. M. Calculus - Vol.2, Wiley India
Ross S. L. Differential Equations, Wiley India
Coddington E. A. An Introduction to Ordinary Differential Equations, Prentice Hall