Chapter 7

प्रस्तावना

This section introduces the textbook 'Numerical Analysis and Vector Calculus', designed according to the curriculum of Vardhman Mahaveer Open University, Kota, for B.Sc. Part II, Mathematics, Paper III. The preface emphasizes the importance of using appropriate English terminology in mathematics and acknowledges the contributions of various authors and standard reference books. It states that the book is structured to assist students in both academic study and competitive examinations. The preface assures students that the material is factual and reliable, and that the book is written with the intention of providing proper guidance for learning and exam preparation.

• The book is tailored to the syllabus of Vardhman Mahaveer Open University, Kota.
• It is intended for B.Sc. Part II Mathematics, Paper III.
• English mathematical terms are used appropriately throughout.
• Content is based on standard reference books and expert authorship.
• The book is suitable for both academic and competitive exam preparation.
• 📌 Numerical Analysis: A branch of mathematics focused on obtaining numerical solutions to mathematical problems.
• 📌 Vector Calculus: The branch of mathematics dealing with vector fields and operations on them.

इकाई-1 : परिमित अन्तर (Finite differences)

This section provides the outline for Unit 1, titled 'Finite Differences'. It lists the subtopics that will be covered, including objectives, introduction, forward and backward difference operators, their properties, difference tables, fundamental theorems, shift operator, differential operator, relationships among operators, finding unknown terms for equally spaced arguments, summary, glossary, answers to self-assessment questions, and exercises. The unit aims to introduce students to the concept of finite differences and their applications in numerical analysis.

• Unit 1 focuses on finite differences and related operators.
• Topics include forward and backward differences, shift and differential operators, and their properties.
• The unit covers methods for estimating unknown function values at equally spaced arguments.
• 📌 Finite Differences: Differences between function values at discrete points, used for numerical estimation.
• 📌 Forward Difference Operator (Δ): An operator that computes the difference between successive function values.
• 📌 Backward Difference Operator (∇): An operator that computes the difference between a function value and its predecessor.