“Integral Calculus” textbook authored by Maity and Ghosh. (NCBA)

Name: "Integral Calculus" textbook authored by Maity and Ghosh. (NCBA) - Booksbp.com
SKU: 9788173817328
Price: 390.00 INR
Availability: InStock

Original price was: ₹485.00.Current price is: ₹390.00.

SKU: 9788173817328

1. Bibliographic & Publishing Information

Primary Title: Integral Calculus
Authors: Prof. Kantish Chandra Maity & Prof. Ramkrishna Ghosh
Publisher: New Central Book Agency (NCBA) Private Ltd.
Country of Origin: India
Target Audience: Undergraduate students majoring in Mathematics, Physical Sciences, and Engineering.

2. Core Curriculum & Structural Syllabus

The textbook is structured into progressive modules designed to transition a student from elementary integration techniques to advanced multivariate analysis:

Part I: Single Variable Integration

Indefinite Integrals: Extensive methods of integration including integration by parts, partial fractions, trigonometric substitutions, and reduction formulas.
Definite Integrals: Fundamental Theorem of Calculus, evaluation of definite integrals, and properties of definite integrals.
Improper Integrals: Convergence tests (Comparison test, Dirichlet’s test, Abel’s test) for integrals with infinite limits or discontinuous integrands.
Beta and Gamma Functions: Definitions, properties, and applications to calculating complex definite integrals.

Part II: Geometric & Physical Applications

Rectification: Calculating the arc length of Cartesian, parametric, and polar curves.
Quadrature: Evaluation of areas bounded by plane curves.
Volumes and Surfaces of Revolution: Application of single integrals to calculate three-dimensional spaces and surface areas created by rotating curves around axes.

Part III: Advanced Calculus

Multiple Integrals: Evaluation techniques for double and triple integrals.
Change of Variables: Shifting coordinates (e.g., from Cartesian to Polar, Cylindrical, or Spherical systems) and calculating the Jacobian.
Line, Surface, and Volume Integrals: Vector integration frameworks including applications of Green’s, Stokes’, and Gauss’s Divergence theorems.

3. Pedagogical Style & Legacy

Problem-Centric Layout: The book is renowned for its high density of worked-out examples alongside exceptionally challenging exercise sets at the end of each chapter.
Rigorous Proofs: Unlike purely applied engineering mathematics books, it provides strict analytical proofs for underlying theorems (e.g., Riemann integration foundations).
Companion Literature: A popular companion solution manual titled “Masterguide to Maity & Ghosh’s Integral Calculus” is heavily relied upon by students for self-study and exam preparation.