please suggest me the standard book for Mathematics optional subject....

Hello,

Mathematics optional is very rewarding and concise in UPSC examination. You can refer below mentioned books for you preparation

Paper 1-

Linear Algebra-Schaum’s outline on Linear Algebra

Calculus-Mathematical Analysis by Malik and Arora,Differential Calculus (Krishna Series),Integral Calculus (Krishna Series)

Analytic Geometry-Analytic Geometry (3D) (Krishna Series),Golden Solid Geometry

Ordinary differential equatiins-Ordinary and Partial Differential Equations by MD Raisinghania,Advanced Differential Equations by MD Raisinghania

Vector Calculus-Vector Calculus (Krishna Series),Schaum’s outline on Vector Analysis

Statics and dynamics-Statics (Krishna Series),Dynamics (Krishna Series)

paper 2-

Modern Algebra-Group Theory by R Kumar (Vardhaman Publications),Ring Theory by R Kumar (Vardhaman Publications)

Real analysis-Mathematical Analysis by Malik and Arora

Complex analysis-Schaum’s Outlines Complex Variables

Linear programming problems-Operations Research (Krishna Series)

Partial differential equations-Ordinary and Partial Differential Equations by MD Raisinghania,Advanced Differential Equations by MD Raisinghania

Numerical analysis and computer programming-Numerical Methods by Jain and Iyengar,Grewal, Engineering Mathematics

Mechanics-Rigid Dynamics (Vol I) (Krishna Series)

Fluid dynamics-Fluid Dynamics, MD Raisinghania,Ordinary and Partial Differential Equations by MD Raisinghania,Advanced Differential Equations by MD Raisinghania

Hope it helps