Elementary Calculus
The complete B.Sc syllabus for Elementary Calculus (MASC-01), the first-semester core mathematics course of the Bachelor of Science programme at Chhattisgarh state universities (NEP four-year UG, 2024-28) — sequences, continuity and differentiability; mean-value theorems and expansions of functions; curvature, asymptotes and curve tracing; and integration. Available in English and Hindi editions.
Elementary Calculus · English
by Dr. H.K. Pathak · ₹480 — covers this full syllabus.
Prathamik Kalan (प्रारंभिक कलन) · Hindi
by Dr. H.K. Pathak · ₹440 — covers this full syllabus.
Course contents — unit by unit
Unit 1 · Indian Mathematicians; Sequences, Continuity & Differentiability
Contributions and biography of Indian mathematicians — Bodhayan, Apasthamb, Katyayan, Mahaveeracharya, Brahmagupta and Bhaskaracharya (in the special context of Leelavati). Convergence of sequences and series of real numbers; definition of limit and continuity of a real-valued function; differentiability and its geometrical interpretation; elementary differentiation.
Unit 2 · Expansion of Functions
Rolle's theorem, Lagrange's mean-value theorem and Cauchy's mean-value theorem and their geometrical interpretations; successive differentiation and Leibnitz theorem; Maclaurin's and Taylor's theorems for the expansion of a function.
Unit 3 · Curvature, Asymptotes & Curve Tracing
Curvature; asymptotes of general algebraic curves, parallel asymptotes and asymptotes parallel to the axes; symmetry, concavity and convexity, points of inflection, tangents at the origin, multiple points, position and nature of double points; tracing of Cartesian, polar and parametric curves.
Unit 4 · Integration
Elementary integration, integration of transcendental functions, reduction formulae, and the definite integral.