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BU Question CC-1 2017 [ Theory Paper ] [C/C++ Programming Lab Paper 2017]
CORE COURSE (HONOURS IN PHYSICS)
Semester I
CC- I: MATHEMATICAL PHYSICS- I (Credits: Theory-04, Practicals-02)
F.M. = 75 (Theory - 40, Practical – 20, Internal Assessment – 15)
Internal Assessment[Class Attendance (Theory) – 05, Theory (Class Test/Assignment/ Tutorial) – 05, Practical (Sessional Viva-voce) - 05]
Class Notes
Theory: 60 Lectures
The emphasis of course is on applications in solving problems of interest to physicists. The students are to be examined entirely on the basis of problems, seen and unseen.
Unit 1: Calculus :
Recapitulation: Limits, continuity, average and instantaneous quantities, differentiation. Plotting functions. Intuitive ideas of continuous, differentiable, etc. functions and plotting of curves. Approximation: Taylor and binomial series (statements only). (2 Lectures). [Notes] [ New to Physics? Solve these]
Assignment -1 [03 August, 2017][pdf here]
First Order and Second Order Differential equations: First Order Differential Equations and Integrating Factor. Homogeneous Equations with constant coefficients.Wronskian and general solution.Statement of existence and Uniqueness Theorem for Initial Value Problems.Particular Integral. (13 Lectures) [Notes] [Home Works] [Solution of Home Work]
Calculus of functions of more than one variable: Partial derivatives, exact and inexact differentials. Integrating factor, with simple illustration.Constrained Maximization using Lagrange Multipliers. (6 Lectures) . [Notes] (Home Works)
Class Test 1 [On 29 Nov, 2021] [Question here]
Unit 2: Vector Calculus
Recapitulation of vectors: Properties of vectors under rotations. Scalar product and its invariance under rotations.Vector product, Scalar triple product and their interpretation in terms of area and volume respectively.Scalar and Vector fields. (5 Lectures). [Notes] [Home Works]
Vector Differentiation: Directional derivatives and normal derivative.Gradient of a scalar field and its geometrical interpretation.Divergence and curl of a vector field.Del and Laplacian operators.Vector identities. (8 Lectures). [Notes] [Home Works]
Vector Integration: Ordinary Integrals of Vectors. Multiple integrals, Jacobian.Notion of infinitesimal line, surface and volume elements.Line, surface and volume integrals of Vector fields. Flux of a vector field. Gauss' divergence theorem, Green's and Stokes Theorems and their applications (no rigorous proofs). (14 Lectures). [Notes] [Home Works]
Unit 3: Orthogonal Curvilinear Coordinate: Orthogonal Curvilinear Coordinates. Derivation of Gradient, Divergence, Curl and Laplacian in Cartesian, Spherical and Cylindrical Coordinate Systems. (6 Lectures) [Notes]
Unit 4: Introduction to Probability: Independent random variables: Probability distribution functions; binomial, Gaussian, and Poisson, with examples. Mean and variance. Dependent events: Conditional Probability. Bayes' Theorem and the idea of hypothesis testing. (4 Lectures) [Notes]
Home Work on unit 3 and unit 4
Unit 5: Dirac Delta function and its properties: Definition of Dirac delta function. Representation as limit of a Gaussian function and rectangular function. Properties of Dirac delta function. (2 Lectures): [Notes] [Home Works]
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Lecture Notes on Computational Physics Lab :
CC- I : MATHEMATICAL PHYSICS- I
Practical :
The aim of this Lab is not just to teach computer programming and numerical analysis but to emphasize its role in solving problems in Physics.
Highlights the use of computational methods to solve physical problems
The course will consist of lectures (both theory and practical) in the Lab
Evaluation done not on the programming but on the basis of formulating the problem
Aim at teaching students to construct the computational problem to be solved
Students can use any one operating system Linux or Microsoft Windows
Introduction and Overview[here]
Basics of Scientific computing[here]
Solve Differential Equations
..
Codes
Introduction to numerical methods
Interpolation: How to fit data with functions/straight lines/curves
Any question about the slides and codes, please talk to me in the class and/or write an email at somenath.jalal@gmail.com