Calculus, Geometry & Ordinary Differential Equation (MATHMJ101)
4 units: · L-T-P 3-1-0.
Detailed syllabus
Unit 1
Hyperbolic functions, higher order derivatives, Leibnitz rule and its applications to problems of typeeax+bsinx, eax+bcosx, (ax+b)nsinx, (ax+b)ncosx, concavity and inflection points, curvature, envelopes, asymptotes, curve tracing in cartesian coordinates, tracing in polar coordinates of standard curves, L’Hospital’s rule, applications in business, economics and life sciences.
Unit 2
Reduction formulae, derivations and illustrations of reduction formulae of the type ʃsin nx dx, ʃcosnx dx, ʃtan nx dx, ʃsec nx dx, ʃ(log x)n dx, ʃsinnx sinmx dx, parametric equations, parameterizing a curve, arc length of a curve, arc length of parametric curves, area under a curve, area and volume of surface of revolution, techniques of sketching conics.
Unit 3
Reflection properties of conics, rotation of axes and second degree equations, classification of conics using the discriminant, polar equations of conics. Spheres. Cylindrical surfaces. Central conicoids, paraboloids, plane sections of conicoids, generating lines, classification of quadrics, illustrations of graphing standard quadric surfaces like cone, ellipsoid.
Unit 4
General, particular, explicit, implicit and singular solutions of a differential equation. First order but not first degree. Exact differential equations and integrating factors, and equations reducible to this form, linear equation, Bernoulli equation and special integrating factors and transformations.
Source: official document