24 Semester I 15E101 Calculus and Its Applications 3 2 0 4
SEMESTER I 15E101 CALCULUS AND ITS APPLICATIONS 3 2 0 4 DIFFERENTIAL CALCULUS: Basic concepts - Limits, continuity, differentiation, functions of several variables, partial derivatives. (6+4) INTEGRAL CALCULUS: Double integrals - double integrals over rectangles, double integrals as volumes, Fubini‘s theorem (concept and statement only) double integrals in polar form, changing the order of integration, triple integrals in rectangular co-ordinates, triple integrals in spherical and cylindrical co-ordinates. (8+5) ORDINARY DIFFERENTIAL EQUATIONS OF FIRST ORDER: Basic concepts, separable differential equations, exact differential equations, integrating factors, linear differential equations, Bernoulli equation, modelling of electric circuits. (8+5) LINEAR DIFFERENTIAL EQUATIONS OF SECOND ORDER: Homogeneous linear equations of second order, linearity principle, initial value problem, general solution, second order homogeneous equations with constant coefficients, Euler – Cauchy equation, solution by variation of parameters, modelling of electric circuits. (7+5) VECTOR CALCULUS: Gradient of a scalar field, directional derivative, divergence of a vector field, curl of a vector field. Integration in vector field – line integrals, work, circulation and flux, path independence, conservative fields, surface integrals. Green‘s, Gauss divergence and Stoke‘s theorems (concepts and statements only), evaluation of line, surface and volume integrals. (16+11) Total L: 45+T: 30=75 TEXT BOOKS: 1. Thomas G B and Finney R L, ―Calculus and Analytic Geometry‖, Pearson Education, New Delhi, 2012. 2. Erwin Kreyszig, ―Advanced Engineering Mathematics‖, Wiley India Pvt. Ltd, New Delhi, 2012. REFERENCES: 1. Wylie C R and Barrett L C, ―Advanced Engineering Mathematics‖, Tata McGraw-Hill, New Delhi, 2013. 2. Peter V.O Neil, ―Advanced Engineering Mathematics‖, Cengage, New Delhi, 2010.
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