UPSC Mathematics Question Bank for UPSC Civil Service Examination: QUESTION BANK FOR UPSC MATHEMATICS

The eBook contains topic wise questions for UPSC Mathematics Optional paper. All Topics are covered

This book is a complete guide to Practice different type of problems from each topic.

This book will save TIME in collecting books from different source , study material from different institutes, pdfs, internet information etc. All questions are available at one place.

This book will be useful for Last minute preparation to cover all topics ,check preparation and fill the voids to complete it.

UPSC MATHEMATICS Optional will definitely make you Topper. But you need to PRACTICE, PRACTICE and more PRACTICE. This book will provide you more PRACTICE.

The topics covered are :

01 Matrix Linear Algebra,Problems on Matrices  ,Rank Normal Form, Matrix Inverse,Linear Eqns, Diagonalisation Problems, Cayley Hamilton Problems, Quadratic Problems, Vector Spaces, Linear Dependence ,Basis Problems, Eigen Values, Linear Transformation, Problem Set

02 Calculus and Real Analysis  ,Limts, Continuity, Differentiabi, Max Min Single Variabl, Max Min Two Variable, Max Min Multi Vraiable, Lagrange Multiplier, Mean Value Theorem, MVT Taylor Maclauren,Improper Integrals, Indeterminants, Differntiation under Integral Sign, Jacobians, Length of Arc, Areas, Volumes, Surfaces ,Partial Differntiation ,PD Eulers, Total Differntiation, Definite Integral as Sum, Beta Gamma 1,Beta Gamma 2,Asymptote,Multiple Integrals, Rieman Integrals, Sequences, Series, Uniform Convergence, Several Variable Functions

03 Analytic Geometry ,Directional Cosines, Planes, Straight Lines ,Shortest Distance, Sphere ,Cylinder, Cones. Conicoids

04 ODE,First Order Linear, Orthogonal Trajectory Degree, Calaurit Singular Solns ,Constant Coeff Cauchy Euler, Variation Parameter Normal Form

05 Statics Dynamics  ,Work Energy Rectilinear ,SHM , Projectile ,Central Orbits ,Catenary Problems ,Stable UNstable Equilibrium ,Virtual Work

06 Vector Analysis                                          ,Gradient Divergence ,Green Gauss Divergence ,Differential Geometry

07 Algebra                                                             Group, SubGroups, Orders, Cosets Lagrange, Cyclic Group, Normal Subgroup, Cosets, Homomorphism, Rings ,Ideal Ring Homo, Embedding Max prime Ideals ,ED PID

08 Complex Analysis                                        ,Analytic Function, Complex Inegration ,Taylor Laurent Series, Poles Residue, Counter Integration , Rouches Theorem, Singularity, Power Series

09 PDE                                                                           ,Formation Linear, Orthogonal Charpit Multivariable, Claurit Complete Integrals Charpit, Homogeneous NonHomogeneous ,Boundary Problems

10 Numerical Analysis                                          ,Algebraic Eqns, Interpolation, Integration ,ODE

11 Mechanics                                                           Lagrange Hamiltonian

Fluid Dynamics   Lagrange Velocity Acceleration , Boundary Problems, Continuity Eqns ,Euler Bernauli Problems ,Velocity POtential, Source Sink,Vortex motion, Misc Problems