Mathematical Physics & Newtonian Mechanics (Physics) Rpp

 Author: J.C. Upadhyay (M.Sc., Ph.D., F. Inst. P., London)
Edition: 2024-25 (New Edition)
Pages: 592
Target Audience: B.Sc. 1st Semester (Physics)
Publisher: Ramprasad Publication, Agra
Language: English
Type of Book: Paperback (Test Book with Multiple Choice Questions as per NEP-2020)

Description:

“Mathematical Physics & Newtonian Mechanics” is a comprehensive and detailed textbook written by J.C. Upadhyay, a respected physicist with deep expertise in the field. This book is designed to serve as an essential guide for B.Sc. 1st Semester Physics students, combining two critical areas of physics: Mathematical Physics and Newtonian Mechanics. The book is structured in alignment with the NEP-2020 guidelines, making it highly relevant to current academic requirements.

With a vast range of topics covered, from basic mathematical techniques to the principles of classical mechanics, this text serves both as a detailed learning tool and a practical resource for solving problems. Each topic is carefully curated to provide theoretical insight and practical problem-solving strategies, helping students build a strong foundation in physics.

Contents Overview

Part A: Basic Mathematical Physics
The first part of the book dives into vector algebra, vector calculus, and coordinate systems, providing students with the mathematical tools necessary to tackle complex physical problems. The sections are laid out in a systematic way, making it easy for students to follow and understand.

1. Vector Algebra
   • Introduces basic concepts such as vectors, scalars, and their properties.
   • Covers operations like vector addition, subtraction, and dot product and cross product with applications in physics.
   • Advanced topics include coordinate rotation, coordinate reflection, and parity transformation, which are vital in understanding symmetries in physics.
2. Vector Calculus
   • Focuses on differentiation of vectors, scalar and vector fields, and physical applications of concepts like gradient, divergence, and curl.
   • Key theorems such as Gauss’s, Stoke’s, and Green’s theorems are explained with physical interpretations and applications.
3. Coordinate Systems
   • Explores different coordinate systems, including Cartesian, polar, cylindrical, and spherical, with practical examples.
   • Describes how to calculate velocity and acceleration in different systems and introduces non-inertial coordinate systems and pseudo-accelerations.
4. Introduction to Tensors
   • Provides a detailed introduction to tensors, their properties, and applications in physics.
   • Concepts like contravariant and covariant tensors, Kronecker delta, and Levi-Civita tensors are covered, helping students navigate more complex topics in mathematical physics.

Part B: Newtonian Mechanics & Wave Motion
The second part of the book introduces Newtonian mechanics, providing a historical context and critical analysis of Newton’s laws. This section is designed to help students understand the fundamental laws that govern motion and energy.

1. Newton’s Laws of Motion and Frame of Reference
   • Discusses the development of mechanics up to Newton’s time and provides an analysis of inertial and non-inertial frames of reference.
   • Explains Galilean transformations and the concept of fictitious forces in non-inertial frames.
2. Conservation of Energy
   • Covers the concepts of work, kinetic energy, and potential energy.
   • Discusses conservative forces and non-conservative forces, and the general law of conservation of energy.
3. Dynamics of a System of Particles
   • Introduces the concept of center of mass, conservation of linear and angular momentum, and the dynamics of a system of particles.
   • Examines collisions, both elastic and inelastic, in one and two dimensions.
4. Dynamics of a Rigid Body
   • Explains rotational motion, moment of inertia, and the dynamics of rigid bodies, including rolling motion and rotational kinetic energy.
   • Includes detailed calculations of moments of inertia for various objects.
5. Elasticity
   • Explores stress, strain, and Hooke’s law, with detailed examples of elastic behavior in materials.
   • Discusses the concepts of torsion, bending of beams, and methods to determine elastic constants.
6. Two-Body Central Force Problem
   • Describes the motion of planets and satellites under gravitational forces, with a focus on Kepler’s laws and the motion of celestial bodies.
   • Includes a detailed explanation of gravitational potential and escape velocity.
7. Simple Harmonic Motion (SHM)
   • Covers the theory and equations governing simple harmonic motion.
   • Discusses damped and forced harmonic oscillations and the phenomenon of resonance.
8. Wave Motion
   • Provides a comprehensive overview of wave motion, covering progressive waves, transverse waves, and longitudinal waves.
   • Includes discussions on energy transmission, stationary waves, and group velocity.

Special Features:

• Multiple Choice Questions (MCQs):
  Each chapter ends with a series of Multiple Choice Questions to help students test their understanding and prepare for exams.
• Clear Explanations and Examples:
  Complex concepts are broken down into simpler explanations, with detailed examples and step-by-step problem-solving strategies.
• Illustrations and Diagrams:
  The book is richly illustrated with diagrams and figures to visually aid understanding, especially for concepts involving vectors, motion, and waves.

Why This Book?

“Mathematical Physics & Newtonian Mechanics” is an essential resource for B.Sc. 1st Semester Physics students. The structured layout, combined with the author’s clear explanations and focus on practical applications, ensures that students gain a solid understanding of the key concepts in both mathematical physics and Newtonian mechanics. Whether used for classroom study or self-learning, this book is an indispensable guide for students aiming to excel in their physics courses.