MA1L003
Undergraduate (BTech)
· Generally offered: Autumn
Calculus and Ordinary Differential Equations
L 3 T 1 P 0 Credits 4 Hours 4
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.
Full syllabus document →
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.