Recorded
📅 VALIDITY- 8 MONTHS ⭐ COMPETE COURSE ⭐ VIDEO LECTURE OF FULL SYLLABUS ⭐ COMPLETE PDF NOTES FOR EACH CLASS ⭐ DOUBT CLEARING
Live classes and doubt sessions for this semester, for selected batches. Ask us on WhatsApp for the next batch and its fee.
Typed English PDF notes and handwritten notes for every paper of this semester.
Study only the paper you need: recorded classes and notes for one paper of your choice.
Unit-wise syllabus from the Odisha State Higher Education Council model curriculum. Tap a paper to open it.
The primary objective of this course is to introduce students to the extension of the studies of single variable differential and integral calculus to functions of two or more independent variables, with the geometry and visualization of curves and surfaces. It also makes students aware of the techniques of multiple integration and higher order derivatives.
Functions of several variables, limit and continuity of functions of two variables, partial differentiation, total differentiability, sufficient condition for differentiability, chain rule for one and two independent parameters, directional derivatives, the gradient, maximal and normal property of the gradient, tangent planes.
Extrema of functions of two variables, method of Lagrange multipliers, constrained optimization problems, double integration over rectangular region, double integration over non-rectangular region, double integrals in polar coordinates.
Triple integrals, triple integral over a parallelepiped and solid regions, volume by triple integrals, cylindrical and spherical coordinates, change of variables in double integrals and triple integrals.
Definition of vector field, divergence and curl, line integrals, applications of line integrals: mass and work, fundamental theorem for line integrals, conservative vector fields, independence of path, Green's theorem, surface integrals, integrals over parametrically defined surfaces, Stokes' theorem, the divergence theorem.
The objective of this course is to explore geometry of curves and surfaces in R² and R³ with their intrinsic properties and curvatures.
Theory of Space Curves: space curves, arc length, tangent, normal and binormal, osculating plane, curvature, torsion, Serret-Frenet formulae, contact between curves and surfaces, osculating circles and spheres, involutes and evolutes, existence of space curves, helices.
Theory of surfaces: parametric curves on surfaces, surfaces of revolution, helicoids, metric, direction coefficients, first fundamental forms.
Geodesics, canonical geodesic equations, nature of geodesics on a surface of revolution, normal property of geodesics, torsion of a geodesic, geodesic curvature, Gauss-Bonnet theorem, Gaussian curvature, surfaces of constant curvature.
Second fundamental forms, principal curvatures, lines of curvature, Rodrigue's formula, conjugate and asymptotic lines, developables, developable associated with space curves and curves on surfaces, minimal surfaces, fundamental theory of surfaces.
PYQs for this semester will be uploaded soon. Ask on WhatsApp for PYQ solutions in the AIFM app.
Demo classes for this semester are coming soon. Meanwhile, watch free classes on our YouTube channel.
It has 2 papers: Multivariable Calculus, Differential Geometry. The unit-wise syllabus is on this page, and the syllabus PDF can be opened or downloaded.
AIFM EDUCATION offers 4 courses for this semester (Recorded, Live, PDF Notes, Single Paper). Fees start from ₹3,000.
PYQs for this semester will be added to this page soon. PYQ solutions are available in the AIFM EDUCATION app.
Yes. It follows the NEP 2020 model curriculum of the Odisha State Higher Education Council, used by universities across Odisha. Classes are explained in Odia, with notes in English.
Message us on WhatsApp. We’ll explain the classes, notes, fee and how to enrol.
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