Chapter 9

प्रस्तावना

The preface introduces the book '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 book uses appropriate English terminology alongside Hindi to facilitate understanding. Various units are written by expert authors, who have referred to standard texts to ensure factual accuracy. The preface acknowledges the contributions of these authors and expresses gratitude. It also highlights that the book is useful for competitive examinations and provides proper guidance to students. The nature of mathematics is considered, and the content is structured to support both learning and teaching.

• Book designed as per university curriculum for B.Sc. Mathematics.
• Uses English terminology for clarity.
• Units written by subject experts using standard references.
• Useful for competitive exams.
• Acknowledges contributors and authors.
• 📌 Numerical Analysis: A branch of mathematics dealing with numerical solutions to mathematical problems.
• 📌 Vector Calculus: The study of calculus with vectors, including differentiation and integration of vector fields.

इकाई-1 : परिमित अन्तर (Finite differences)

Unit 1 is titled 'Finite Differences'. The unit outline lists the topics covered, including objectives, introduction, forward and backward difference operators, their properties, difference tables, fundamental theorem of difference calculus, shift operator, and relations among operators. The unit also includes vocabulary, self-assessment answers, and exercises. The objectives state that after studying this unit, students will be able to calculate forward and backward differences of a given function, understand the properties and relationships among operators (Δ, ∇, E, D), and estimate unknown values of a function at given points when values at equidistant points are known.

• Unit covers finite differences and related operators.
• Includes objectives, introduction, properties, and applications.
• Students learn to estimate function values at unknown points.
• Relations among difference, shift, and differential operators are discussed.
• 📌 Finite Differences: Numerical methods for estimating values of functions using differences at discrete points.
• 📌 Forward Difference Operator (Δ): Calculates the difference between successive values.
• 📌 Backward Difference Operator (∇): Calculates the difference between a value and its preceding value.