Chapter 12

प्रस्तावना

The preface introduces the book 'Numerical Analysis and Vector Calculus,' developed according to the syllabus of Vardhman Mahaveer Open University, Kota, for the B.Sc. Part II Mathematics third paper. The book is designed keeping in mind the nature of mathematics, with appropriate use of English terminology. Various units of the book have been written by expert authors, who have also referred to standard texts to ensure factual accuracy. The preface expresses gratitude to these authors. The book is also intended to guide students preparing for competitive examinations.

• Book is tailored for B.Sc. Part II Mathematics, third paper.
• English mathematical terminology is used for clarity.
• Content is factually accurate, based on standard references.
• Useful for competitive exam preparation.
• 📌 Numerical Analysis: A branch of mathematics dealing with numerical solutions to mathematical problems.
• 📌 Vector Calculus: A field of mathematics focused on differentiation and integration of vector fields.

इकाई की रूप रेखा

This section outlines the structure of Unit 1: Finite Differences. It lists the topics and subtopics covered, providing a roadmap for the unit. The main topics include objectives, introduction, forward and backward difference operators, their properties, difference tables, fundamental theorem of difference calculus, shift operator, differential operator, relations among operators, finding unknown values in equally spaced data, summary, glossary, answers to self-assessment questions, and exercise questions.

• Unit 1 covers finite differences and related operators.
• Includes both forward and backward differences.
• Explains properties and relationships among operators.
• Covers practical applications like finding unknown values.
• 📌 Finite Differences: Discrete analogs of derivatives used in numerical analysis.
• 📌 Forward Difference Operator (Δ): Operator representing the difference between successive values.
• 📌 Backward Difference Operator (∇): Operator representing the difference between a value and its predecessor.