This book “Mathematical Physics-II” for B.Sc. honours students is written according to new NEP-2020 SYLLABUS of all Odisha Universities, Autonomous Colleges and other Indian Universities as per UGC guidelines. In addition, this book will serve as a text book to the students preparing for IIT JAM, NEST, JEST, CUET and CPET to take admission in M.Sc. course in physics.
The contents of this book have been divided into four units that comprises of six chapters. The subject matter of each chapter are presented by introducing the concepts through definitions and significant results are proved systematically in a simple, lucid and logical manner for the easy grasp of the students. The structure of each chapter includes the text that illustrated through sufficient numbers of selected informative and modern solved examples followed by large number of unsolved examples are given as an exercise. At the end of each chapter objective and multiple choice based questions with their answers are provided.
While writing this book special importance is given to present the subject matter in a much simpler manner without any skipping of mathematical steps. Necessary diagrams are provided for better understanding of the text and problems.
Contents –
1. FOURIER SERIES – I
1.1 Periodic Functions – 1.2 Fourier Series – 1.3 Dirichlet condition for a Fourier Series – 1.4 Useful Integrals – 1.5 Evaluation of Fourier Co-efficients – 1.6 Functions Defined in two or more sub-intervals – 1.7 Fourier Representation of Even and Odd Function – 1.8 Cosine and Sine Series – 1.9 Extension of the interval from (–π, π) to (–L, L) – 1.10 Fourier Half-Range Series – 1.11 Complex Form of Fourier Series – 1.12 Applications of Fourier Series
Questions
Multiple Choice Questions (MCQs)
Long-type Questions
2. FROBENIUS METHOD
(Series Solutions of Ordinary Differential Equations) 2.1 Power Series – 2.2 Properties of Power Series – 2.3 Analytic Function – 2.4 Ordinary and Singular points of Differential Equations – 2.5 Power Series Solution of Differential Equation when x = 0 is an ordinary point – 2.6 Extended Power Series Method (Frobenius Method)
Questions
Multiple Choice Questions (MCQs)
Long-type Questions
3. SPECIAL FUNCTIONS
3.1 Legendre’s Differential Equation and Polynomials – 3.2 Rodrigue’s Formulae – 3.3 Legendre Polynomials – 3.4 Integral Representation of Legendre Polynomials – 3.5 Generating Function for Pn(x) – 3.6 Recurrence Relation for Pn(x) – 3.7 Orthogonality of Legendre Polynomials – 3.8 Hermite Differential Equation – 3.9 Hermite Polynomial – 3.10 Generating Function for Hermite Polynomials – 3.11 Rodrigue’s Formula for Hermite Polynomials – 3.12 Orthonormality of Hermite Polynomials – 3.13 Recurrence Formula for Hermite Polynomials – 3.14 Bessel’s Differential Equation – 3.15 Plots of some Bessel Functions – 3.16 Generating Function for Jn(x) – 3.17 Recurrence Formula – 3.18 Orthonormality of Bessel’s Function – 3.19 Laguerr’s Differential Equation – 3.20 Generating Function for Laguerre Polynomial – 3.21 Rodrigue’s Formula for Laguerre Polynomials – 3.22 Laguerre’s Polynomial – 3.23 Recurrence Relation for Laguerre Polynomials – 3.24 Orthogonal Property of Laguerre Polynomials
Questions
Multiple Choice Questions (MCQs)
Long-type Questions
4. POLYNOMIALS
4.1 Recurrence Formulae for Legendre’s Polynomials – 4.2 Recurrence Formulae for Hermite Polynomials – 4.3 Expansion of a Function f(x) in a series of Legendre polynomials – 4.4 Associated Legendre Differential Equation – 4.5 Associated Legendre’s Polynomials – 4.6 Evaluation of some Associated Legendre Polynomials – 4.7 Recurrence Relations – 4.8 Orthonormality Relaton for Pn m(x) – 4.9 Spherical Harmonics – 4.10 Spherical Harmonics in Cartesian Coordinates
Questions
Multiple Choice Questions (MCQs)
Long-type Questions
5. SOME SPECIAL INTEGRALS
5.1 Gamma Function – 5.2 Transformation of Γ-function – 5.3 Beta Function – 5.4 Transformation of Beta Function – 5.5 Some Important Relations of Γ and β Functions – 5.6 Error Function – 5.6.1 Relation between erf (x) and erfc (x) – 5.6.2 Relation between erfc (x) and erfc (–x) – 5.6.3 Derivatives of erf (x) – 5.6.4 Derivatives of erf (x) – 5.6.5 Asymptotic expression of erf (x) and erfc (x) – 5.6.6 Imaginary Error Function – 5.6.7 Relation between Normalized Gaussian function and the Effor function – 5.6.8 Relationship with Incomplete Gamma function
Questions
Multiple Choice Questions (MCQs)
Long-type Questions
6. PARTIAL DIFFERENTIAL EQUATIONS
6.1 Introduction – 6.2 Method of separation of variable – 6.3 Laplace’s Equation – 6.3.1 Solution of Laplace’s Equation in Cartesian Coordinates – 6.3.2 Laplace Equation in Two Dimension – 6.3.3 Laplace Equation in Problem of Rectangular Symmetry – 6.4 Solution of Laplace’s equation in Two-dimensional Cylindrical Co-ordinates (r, θ) : Circular Harmonics – 6.5 Solution of Laplace’s Equation in Three Dimensions Cylindrical Co-ordinates – 6.6 Solution of Laplace’s equation in spherical polar co-ordinates – 6.7 Conducting Sphere in an External Uniform Electric Field – 6.8 Dielectric Sphere in Uniform Electric Field – 6.9 One Dimensional Wave Equation and its Solution (Transverse vibration of stretched string)
Questions
Multiple Choice Questions (MCQs)
Long-type Questions
