UPSC IAS Mathematics Books References 

Paper-I

1. Linear Algebra - K.C. Prasad, K B Datta
2.Calculus - Santhi Narayan
3.Analytic Geometry - Shantinarayan, HC Sinha, DK Jha and Sharma
4.Ordinary Differential eqs:- MD Raising Lumina, Golden seris-NP Bali
5. Dynamics, Statitics and Hydrostatics - M.Ray
6. Vector analysis - Shantinarayan

Paper-II

1.Algebra - K C Prasad, KB Datta
2. Real Analysis - Shantinarayan,Royden
3. Complex Analysis - GK Ranganath
4. Linear Programming - SD sharma
5.Partial Diff.eqs. - Singhania
6. Numerical analysis and Computer Progg. - V. Rajaraman, SS Shasri
7. Mechanics & Fluid dynamics - AP Mathur, Azaroff leonid

Other Books

 Modern Algebra - A. R. Vashisth
 Algebra - J. N. Sharma and S. N. Goyal
 Linear Algebra - Schaum Series (Lipshutz) or Sharma and Vashisth
 Matrices - Schaum Series (Frank Ayres) or Vashisth
 Calculus - I. A. Menon
 Coordinate Geometry - R. L. Soni
 Differential Calculus - Gorakh Prasad
 Analytical Solid Geometry - Shanti Narayanan
 Text Book of Coordinate Geometry - Rai Ballabh
 Mechanism - D. S. Mathur
 Statistical Mechanism - Carson Horg .
 Solid Mechanism - Kazmioo
 Mathematics Dictionary - James
 Differential Equations - Schaum Series (Frank Ayres) or N.M. Kapur or Raisinghania
 Numerical Analysis - S.S. Sastry
 Complex Analysis - Schaum Series or J.N. Sharma
 Operations Research - Kanti Swaroop or Manmohan