UPSC Mathematics Optional Syllabus
The UPSC Mathematics Optional syllabus is quite comprehensive and covers a wide range of topics. Here's a breakdown of the syllabus for the two papers:
Paper-I (250 Marks)
- Section A (Linear Algebra, Calculus and Analytic Geometry):
- Vector spaces over R and C, linear dependence and independence, subspaces, bases, dimension.
- Linear transformations, rank and nullity, matrix of a linear transformation.
- Functions, limits, continuity, differentiation, applications of derivatives.
- Integration, definite and indefinite integrals, applications of integrals.
- Three-dimensional geometry: Straight lines, spheres, cones, cylinders, paraboloids, ellipsoids, hyperboloids.
- Section B (Ordinary Differential Equations, Vector Analysis and Dynamics and Statics):
- Ordinary differential equations (ODEs) of first and second order.
- Gradient, divergence, curl and applications.
- Equilibrium of a particle, work and energy, motion under constant force.
Paper-II (250 Marks)
- Section A (Modern Algebra, Real Analysis, Complex Analysis and Linear Programming):
- Groups, subgroups, cyclic groups, cosets, Lagrange's Theorem.
- Rings, fields.
- Analytic functions, complex integration, Cauchy's integral theorem.
- Linear programming problem formulations and graphical solution methods.
- Section B (Partial Differential Equations, Numerical Analysis and Computer Programming, Mechanics and Fluid Dynamics):
- Partial differential equations (PDEs) of first order.
- Numerical differentiation, integration and solution of ODEs.
- Binary system, arithmetic and logical operations, basic computer programming concepts.
- Motion of a rigid body in two dimensions.
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