Mathematics Optional Syllabus for UPSC
The syllabus is divided into two papers: Paper I and Paper II.
Paper I (Pure Mathematics)
- Linear Algebra – Matrices, Determinants, Eigenvalues, Vector Spaces
- Calculus – Limits, Continuity, Differentiability, Maxima & Minima
- Analytic Geometry – Cartesian and Polar Coordinates, Conics
- Ordinary Differential Equations – First and Higher Order Differential Equations
- Vector Analysis – Gradient, Divergence, Curl, Green’s Theorem, Stoke’s Theorem
- Statics and Dynamics – Equilibrium, Simple Harmonic Motion, Work & Energy
Paper II (Applied Mathematics)
- Modern Algebra & Real Analysis – Groups, Rings, Real Sequences
- Complex Analysis – Analytic Functions, Contour Integration
- Linear Programming – Simplex Method, Duality
- Partial Differential Equations – First Order, Second Order Equations
- Numerical Analysis & Computer Programming – Errors, Newton’s Method, Algorithms
- Mechanics & Fluid Dynamics – Kinematics, Equations of Motion, Boundary Layers
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