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| Vector Analysis |
| Week 4, |
| 1 | Gradient, Divergence, Curl in all Cordinate system, |
| 2 | Vector Identities Problems |
| 3 | Line Integrals, Green Theorem, Surface Integrals |
| 4 | Gauss Divergence, Stokes’s thm Problems, |
| 5 | Curves in spaces, tangent, normal eqns , |
| 6 | Curvature , Torsion, Serret Ferret Formula |
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| ODE |
| Week 5,6, |
| 1 | Formation,Iintegarting factors |
| 2 | Eqn of 1st Order |
| 3 | Trajectory |
| 4 | P X Y Solvable |
| 5 | Claurit, Singular Soln |
| 6 | Linear Differential eqns with Const Coeff |
| 7 | Cauchy Euler Eqn |
| 8 | Method of Variation of parametrs |
| 9 | Simultaneous Differential Eqn |
| 10 | Linear Eqn Order 2 |
| 11 | Normal, Variable Transformation |
| 12 | Laplace Transform |
| 13 | Inverse Laplace Transform |
| 14 | Application of Laplace to ODE |
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| Partial Differential Eqns |
| Week 7,8 |
| 1 | Formation of PDE and examples |
| 2 | Linear PDE Order 1 |
| 3 | Non Linear PDE ,Charpit method |
| 4 | Standard form Solns |
| 5 | Jacobi , Cauchy Strip |
| 6 | Homogeneous Linear PDE const coeff |
| 7 | Non Homogeneous PDE |
| 8 | Euler Cauchy Methods |
| 9 | Canonical Forms |
| 10 | Boundary Value Problems, Heat Eqn |
| 11 | Wave Eqn |
| 12 | Laplace |
| 13 | Polar Sysytem, |
| 14 | Cylindrical, Spherical Syytem |
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| Calculus and Real Analysis: |
| Week 9,10,11 |
| 1 | Limits , Continuity |
| 2 | Differentiability and Problems |
| 3 | Mean Value theorem |
| 4 | Indeterminate form Problems |
| 5, 6 | Max min- Lagrange and 2Dimension |
| 7 | Jacobians |
| 8 | Asymptotes, Partial Derivative |
| 9 | Riemann Definitions |
| 10 | Theorem and Problems on Riemann |
| 11,12 | Improper Integrals |
| 13,14 | Sequences Basic |
| 15,16 | Series Problems |
| 17 | Uniform Convergence |
| 18 | Uniform Convergence- Continuity, Differentiability, Integrability Problems |
| 19 | Multiple Integrals |
| 20 | Double and Triple integrals , Areas |
| 21 | Surface , Volumes |
| 22 | Beta Gamma Functions |
| 23 | Integration under Differentiation sign |
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| Complex Analysis: |
| Week 12, |
| 1 | Analytic functions |
| 2,3 | Complex Integral |
| 4 | Laurent, Taylor Series |
| 5 | Singularities, Power Series,Meromorphic functions |
| 6,7 | Residue Theorem, Contour Integration |
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| Analytic Geometry: |
| Week 13,14 : |
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| 1 | Intro, Direction Cosines, Projections |
| 2 | Planes |
| 3 | Straight Lines |
| 4 | Straight Lines |
| 5 | Shortest Distance, Tetrahedron, |
| 6 | Skew Lines, |
| 7 | Spheres,Cylinder |
| 8 | Cones, |
| 9 | Cental Conicoid |
| 10 | Central Conicoid |
| 11 | Cental Conicoid |
| 12 | Paraboloid |
| 13 | Generating Lines |
| 14 | Generating Lines |
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| Linear Programming |
| Week 15 |
| 1 | Definitions, |
| 2 | Graphical Methods |
| 3,4 | Simplex Methods Practise and Duality |
| 5,6 | Assignment Problems |
| 7,8 | Transportaion Problems |
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| Mechanics |
| Week 16: |
| 1 | Moment of inertia, |
| 2 | Lagrange Problems 1 |
| 3 | Lagrange Problems 2 |
| 4 | Hamilton Problems 1 |
| 5 | Hamilton Problems 2 |
| 6 | D Alembert’s principle |
| 7 | Motion of rigid bodies in two dimensions.(Selected problems only) |
| 8 | Motion in 2D( Selected Problems Only) |
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| Fluid Dynamics |
| Week 17,18 : |
| 1 | Kinematics ,Lagrange , Velocity, Continuity |
| 2 | Boundary Conditions , |
| 3 | Path Line, Velocity Potential |
| 4 | Euler Eqns |
| 5 | Impulse Motion, energy Conservation |
| 6 | Bernaui Eqns |
| 7 | Stream Fns, Source Sink |
| 8 | Source Sink, Circle Images |
| 9 | Irrotational Motion |
| 10 | Navier Stoke Eqns |
| 11 | Laminar Flow |
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| ALGEBRA: |
| Week 19,20 |
| 1 | Intro, Binary Operations, Group |
| 2 | Subgroups and Problems |
| 3 | Cyclic Subgroups |
| 4 | Cosets |
| 5 | Normal Subgroups and Problems |
| 6 | Homomorphism and its theorems |
| 7 | Permutation Group |
| 8 | Sylow Theorem Problems |
| 9 | Rings and Sub Rings |
| 10 | Ideals , Quotient Rings |
| 11 | Ring Homomorphism, Embedding |
| 12 | Maximal Ideals, Prime Ideals |
| 13 | ED, PID |
| 14 | UFD, Eisenstein’s criteria. |
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| Here we will understand the basic concept thoroughly, Do Important Theorems and Important Problems only . This is a Ocean, so we will limit ourself with important things only. |
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| Dynamics |
| Week 21 |
| 1 | Basic Concept, Rectilinear motion |
| 2 | SHM |
| 3 | Projectiles |
| 4 | Plane Kinematics |
| 5 | Central Orbits |
| 6 | Planetary Motion |
| 7 | Constrained motion in Plane |
| 8 | Constrained motion in Circle |
| 9 | Motion in Resisting Medium |
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| Statics |
| Week 22 |
| 1,2 | Principle of Virtual work |
| 3,4 | Stability , UnStability Problems |
| 5 | Equilibrium |
| 6,7 | Catenary Problems |
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Launch your Graphy