
Couse Deliverables:
| Date | Day | Class Day | Topics | Sub Topics |
| 03 Jun 2026 | Wednesday | Day 1 | Orientation, Introduction to vector Analysis | |
| 04 Jun 2026 | Thursday | Day 2 | Vector Analysis | Vector differential calculus: Scalar and vector fields; Limits, Continuity and differentiation of vector field of a scalar variable; Tangent Vector to a curve Application to geometry: Curves in space; Curvature and torsion; Serret-Frenet’s formulae. Del, Gradient, Divergence and Curl. Vector identities and vector equations. |
| 05 Jun 2026 | Friday | Day 3 | Curvilinear coordinates and Level Surfaces Vector integral Calculus | Integrations along the volume Green’s theorem and its applications Gauss-divergence theorem and its applications Stokes’ theorems and its applications |
| 08 Jun 2026 | Monday | Day 4 | Analytic Geometry | Introduction to coordinate systems and locus in three dimensions and direction cosines and direction ratios etc. Plane Straight lines |
| 09 Jun 2026 | Tuesday | Day 5 | Sphere Cylinder | |
| 10 Jun 2026 | Wednesday | Day 6 | Cone | |
| 11 Jun 2026 | Thursday | Day 7 | Conicoid | |
| 12 Jun 2026 | Friday | Day 8 | Ordinary Differential Equations (ODE) | Formulation of differential equations. Equations of first order and first degree: Solution of Linear differential equations with constant coefficient and Euler-Cauchy equation and Legendre equation |
| 15 Jun 2026 | Monday | Day 9 | Solution of second order linear equations with variable coefficients Equations of first order but not of first degree Clairaut’s equation and reduction of Clairaut’s equation and Singular solution Orthogonal trajectory | |
| 16 Jun 2026 | Tuesday | Day 10 | Laplace and Inverse Laplace transforms and their properties; Laplace transforms of elementary functions Solution of initial value problems for 2nd order linear equations with constant coefficients by using Laplace transforms | |
| 17 Jun 2026 | Wednesday | Day 11 | Partial Differential Equations (PDE) | Family of surfaces in three dimensions and formulation of partial differential equations Solution of quasilinear partial differential equations of the first order Integral Surfaces (Solution Surfaces through given curve) Orthogonal Surfaces Linear partial differential equations of the second order with constant coefficients |
| 18 Jun 2026 | Thursday | Day 12 | Solution of non-linear partial differential equations of the first order – Charpits Method Jacobi Method Cauchy’s method of characteristics | |
| 19 Jun 2026 | Friday | Day 13 | Application of PDE | |
| 22 Jun 2026 | Monday | Day 14 | Linear Algebra | Vector spaces over Q, R and C and Subspaces Linear dependence and independence Basis and Dimension |
| 23 Jun 2026 | Tuesday | Day 15 | Linear transformations | |
| 24 Jun 2026 | Wednesday | Day 16 | Algebra of Matrices, Row and column reduction, Echelon form, Rank of a matrix, Inverse of a matrix, Symmetric, Skew-symmetric, Hermitian, Skew-Hermitian, Orthogonal and unitary matrices Solution of system of linear equations Eigenvalues and eigenvectors and Cayley-Hamilton theorem Similarity of Matrices | |
| 25 Jun 2026 | Thursday | Day 17 | Modern Algebra | Groups Order of an element Permutation groups |
| 26 Jun 2026 | Friday | Day 18 | Subgroups Cosets, Lagrange’s Theorem Cyclic groups | |
| 29 Jun 2026 | Monday | Day 19 | Normal subgroups Quotient Group Homomorphism of groups | |
| 30 Jun 2026 | Tuesday | Day 20 | Rings, Integral domains and Fields Subrings and Characteristic of a ring Ideals, Principal ideal domains & Quotient Ring etc. | |
| 01 Jul 2026 | Wednesday | Day 21 | Homomorphisms of ring | |
| 02 Jul 2026 | Thursday | Day 22 | Euclidean domains, unique factorization domains | |
| 03 Jul 2026 | Friday | Day 23 | Statics | Basic Concepts and Principle of virtual work |
| 04 Jul 2026 | Saturday | Day 24 | Test Paper 1 | Part A |
| 06 Jul 2026 | Monday | Day 25 | Common catenary | |
| 07 Jul 2026 | Tuesday | Day 26 | Stability of equilibrium Equilibrium of rigid bodies and Friction Equilibrium of a system of particles | |
| 08 Jul 2026 | Wednesday | Day 27 | Dynamics | Rectilinear motion Simple harmonic motion |
| 09 Jul 2026 | Thursday | Day 28 | Motion in a plane,Projectiles Constrained motion | |
| 10 Jul 2026 | Friday | Day 29 | Fluid Dynamics | Equation of continuity, Stream-lines, path of a particle, Potential flow-I |
| 11 Jul 2026 | Saturday | Day 30 | Test Paper 1 | Part B |
| 13 Jul 2026 | Monday | Day 31 | Sources and sinks-I | |
| 14 Jul 2026 | Tuesday | Day 32 | Vortex motion and Navier-Stokes equation for a viscous fluid | |
| 15 Jul 2026 | Wednesday | Day 33 | Euler’s equation of motion for inviscid flow-I | |
| 16 Jul 2026 | Thursday | Day 34 | Moment of inertia Motion of rigid bodies in two dimensions Generalized coordinates and D’ Alembert’s principle | |
| 17 Jul 2026 | Friday | Day 35 | Lagrange’s equations Hamilton equations | |
| 18 Jul 2026 | Saturday | Day 36 | Test Paper 2 | Part B |
| 20 Jul 2026 | Monday | Day 37 | Real Analysis & Calculus | Sequences of real numbers |
| 21 Jul 2026 | Tuesday | Day 38 | Series of real numbers | |
| 22 Jul 2026 | Wednesday | Day 39 | Functions of single variables: Limits; Continuity and uniform continuity; Differentiability; Increasing and decreasing; Indeterminate forms; maxima and minima | |
| 23 Jul 2026 | Thursday | Day 40 | Mean value theorems | |
| 24 Jul 2026 | Friday | Day 41 | Point wise convergence Uniform convergence Continuity Differentiability and integrability | |
| 25 Jul 2026 | Saturday | Day 42 | Test Paper 2 | Part A |
| 27 Jul 2026 | Monday | Day 43 | Riemann integral and Fundamental theorems of integral calculus etc; Improper integrals | |
| 28 Jul 2026 | Tuesday | Day 44 | Calculus | |
| 29 Jul 2026 | Wednesday | Day 45 | Complex Analysis | Introduction to Complex variable functions: Limit, Continuity, Differentiability, Singular points Cauchy-Riemann equations, Construction of Analytic functions |
| 30 Jul 2026 | Thursday | Day 46 | Complex integration Cauchy’s theorem and its applications Taylor’s series; Laurent’s series and Singularities Cauchy’s residue theorem | |
| 31 Jul 2026 | Friday | Day 47 | Contour integration; Miscellaneous | |
| 01 Aug 2026 | Saturday | Day 48 | Test Paper 1 | |
| 03 Aug 2026 | Monday | Day 49 | LPP | |
| 04 Aug 2026 | Tuesday | Day 50 | LPP | |
| 05 Aug 2026 | Wednesday | Day 51 | Numerical Analysis | |
| 06 Aug 2026 | Thursday | Day 52 | Numerical Analysis | |
| 07 Aug 2026 | Friday | Day 53 | Computer programing | |
| 08 Aug 2026 | Saturday | Day 54 | Test Paper 2 | |
| 12 Aug 2026 | Wednesday | Day 55 | Simulation Paper 1 +Paper 2 |
TEST:
8 Tests in total : 4 HLTs + 4 FLTs
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