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    Mathematics Optional — UPSC Notes

    UPSC Mathematics Optional notes for Papers I and II: theorems, standard results, solution methods and worked examples for every syllabus unit, in English and Hindi.

    How to study Mathematics OptionalShow

    What UPSC asks most

    Optional Papers I and II (250 marks each): proofs, standard results and long computations across 13 syllabus areas.

    Traps to avoid

    • Skipping hypotheses when quoting a theorem.
    • Arithmetic slips in long calculations; verify each answer by substitution.

    How to study it here

    1. Finish one chapter's theory, then solve its past questions with full steps under time.
    2. Keep a formula and theorem sheet per chapter and revise it weekly.

    Mains: Optional: write every step, state the results you use and box the final answer.

    Mathematics Optional

    UPSC Mathematics Optional: Papers I and II

    Mathematics Optional Playlist

    14 chapters • 0 completed

    1

    Exam Pattern, Syllabus and Strategy

    3 topics

    2

    Linear Algebra

    9 topics

    3

    Calculus

    9 topics

    4

    Analytic Geometry

    8 topics

    5

    Ordinary Differential Equations

    8 topics

    6

    Dynamics and Statics

    8 topics

    7

    Vector Analysis

    8 topics

    8

    Abstract Algebra

    10 topics

    9

    Real Analysis

    9 topics

    10

    Complex Analysis

    8 topics

    11

    Linear Programming

    7 topics

    12

    Partial Differential Equations

    8 topics

    13

    Numerical Analysis and Computer Programming

    8 topics

    14

    Mechanics and Fluid Dynamics

    8 topics

    Progress (0%)
    0 / 14 complete

    Chapter 11: Linear Programming

    7 topics•Estimated reading: 21 minutes
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    Mathematics Optional: chapter-wise UPSC notes

    Read any chapter as a full page in English or Hindi. 14 chapters · 111 topics.

    1. 1. Exam Pattern, Syllabus and Strategyहिंदी
    2. 2. Linear Algebraहिंदी
    3. 3. Calculusहिंदी
    4. 4. Analytic Geometryहिंदी
    5. 5. Ordinary Differential Equationsहिंदी
    6. 6. Dynamics and Staticsहिंदी
    7. 7. Vector Analysisहिंदी
    8. 8. Abstract Algebraहिंदी
    9. 9. Real Analysisहिंदी
    10. 10. Complex Analysisहिंदी
    11. 11. Linear Programmingहिंदी
    12. 12. Partial Differential Equationsहिंदी
    13. 13. Numerical Analysis and Computer Programmingहिंदी
    14. 14. Mechanics and Fluid Dynamicsहिंदी