Advanced Calculus
The complete B.Sc syllabus for Advanced Calculus (MASE-01), the third-semester Discipline-Specific Elective of the Bachelor of Science programme at Chhattisgarh state universities (NEP four-year UG, 2024-28) — limit, continuity and differentiability of functions of several variables; Fourier series; maxima and minima; and Beta and Gamma functions with multiple integrals. Available in English and Hindi editions.
Advanced Calculus · English
by Dr. H.K. Pathak · ₹450 — covers this full syllabus.
Ucch Kalan (उच्च कलन) · Hindi
by Dr. H.K. Pathak · ₹470 — covers this full syllabus.
Course contents — unit by unit
Unit 1 · Functions of Several Variables — Limits & Mean-Value Theorems
Limit and continuity of functions of two and three variables; mean-value theorems for functions of two variables — first mean-value theorem and Taylor's theorem; partial differentiation and Euler's theorem on homogeneous functions; change of variables.
Unit 2 · Partial Derivatives & Fourier Series
Partial derivation and differentiability of functions of two variables, Schwartz's theorem, Young's theorem, implicit function theorem; Fourier series and the Fourier expansion of a piecewise-monotonic function.
Unit 3 · Jacobians, Maxima & Minima
Jacobians; maxima, minima and saddle points of functions of two variables; Lagrange's multipliers method; envelopes and evolutes.
Unit 4 · Beta & Gamma Functions, Multiple Integrals
Beta and Gamma functions; double and triple integrals; Dirichlet's integrals; change of order of integration.