Linear Transformations

Vector Spaces and Linear Transformations

Transformations or Mappings, Group Homomorphism and Isomorphism, Linear Transformations on Vector Spaces, Non-singular Transformations, Vector Space Isomorphism.

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Algebra and Matrix Representations of Linear Transformations

Operations on Linear Transformations, Operations on Linear Operators, Algebra of Linear Transformations, Representation of Linear Transformations by Matrices.

Class-notes Download Link

Linear Operators in Quantum Mechanics

Space of Wave Functions, Hermitian and Anti Hermitian Operators, Expectation Value and Uncertainty, Eigenvalues and Eigenvectors, Degeneracy.

Class-notes Download Link

Reference:

• S P Kuila, ``Vector Analysis, Tensor Analysis and Linear Vector Space"
• B.S. Vatssa, ``Elements of Modern Algebra"
• Arfken and Weber, "Mathematical Methods for Physicists"
• S Lipschutz, ``Schaum's Outlines: Linear Algebra"

Atanu Kumar

Assistant Professor

Department of Physics

Chandernagore College

atanukum@gmail.com

Some Special Integrals

Topics Covered:

Beta  and Gamma Functions  and  Relation between  them. Expression  of  Integrals in terms  of  Gamma Functions.  Error  Function  (Probability  Integral).

Target Audience: 

3rd Semester Physics Honours Students of Chandernagore College

Class-notes Download Link: 

Some Special Integrals

Lectures:

Part I

Part II

Part III

Reference:

• Arfken and Weber, "Mathematical Methods for Physicists"
• D Biswas, "Mathematical Methods in Physics"

Atanu Kumar

Assistant Professor

Department of Physics

Chandernagore College

atanukum@gmail.com

Linear Vector Space: Introduction

Topics Covered:

Abstract Systems, Binary Operations and Relations, Introduction to Groups and Fields, Vector Spaces and Subspaces, Linear Independence and Dependence of Vectors, Basis and Dimensions of a Vector Space, Change of Basis, Inner Product and Norm, Orthogonal and Orthonormal Set of Vectors.

Target Audience: 

5th Semester Physics Honours Students of Chandernagore College

Class-notes Download Link: 

Linear Vector space: Introduction

Lectures:

Part I

Part II

Reference:

• S P Kuila, ``Vector Analysis, Tensor Analysis and Linear Vector Space"
• B.S. Vatssa, ``Elements of Modern Algebra"
• Arfken and Weber, "Mathematical Methods for Physicists"
• S Lipschutz, ``Schaum's Outlines: Linear Algebra"

Atanu Kumar

Assistant Professor

Department of Physics

Chandernagore College

atanukum@gmail.com

Physical Principles in Astrophysics

Topics Covered:

Gravitation in Astrophysics (Virial Theorem, Newton vs Einstein), Systems in Thermodynamic Equilibrium

Classnotes Download Link:

Physical Principles in Astrophysics

Lecture:

Part I

Part II 

Assignment Download Link:

Assignment II

Solutions of Assignment II

References:

1. Hannu Kartunen et. al., "Fundamental Astronomy"
2. Baidyanath Basu, "An Introduction to Astrophysics"
3. IGNOU Study Materials

Atanu Kumar

Assitant Professor

Department of Physics

Chandernagore College

atanukum@gmail.com

Astronomical Techniques

Topics Covered:

Basic Optical Definitions for Astronomy (Magnification, Light Gathering Power, Resolving Power and Diffraction Limit, Atmospheric Windows), Optical Telescopes (Types of Reflecting Telescopes, Telescope Mountings, Space Telescopes), Detectors and Their Use with Telescopes (Types of Detectors, Detection Limits with Telescopes)

Classnotes Download Link: 

Astronomical Techniques

Lectures:

Part I

Part II

Part III

References:

1. Hannu Kartunen et. al., "Fundamental Astronomy"
2. Baidyanath Basu, "An Introduction to Astrophysics"
3. IGNOU Study Materials

4. https://www.nasa.gov/content/about-the-hubble-story

Atanu Kumar

Assitant Professor

Department of Physics

Chandernagore College

atanukum@gmail.com

Parameters of a Star

Topics Covered:

Brightness, Radiant Flux and Luminosity, Apparent and Absolute Magnitude scales, Distance Modulus; Determination of Temperature and Radius of a Star; Determination of Masses from Binary orbits.

Classnotes Download Link: 

Parameters of a Star

Lectures:

Part I

Part II

References:

1. Hannu Kartunen et. al., "Fundamental Astronomy"
2. Baidyanath Basu, "An Introduction to Astrophysics"
3. IGNOU Study Materials

Atanu Kumar

Assitant Professor

Department of Physics

Chandernagore College

atanukum@gmail.com

Wave Motion II: Longitudinal Waves

Topics Covered:

Particle and Wave Velocities. Pressure of a Longitudinal Wave. Velocity of Longitudinal Waves in a Fluid in a Pipe. Newton's Formula for Velocity of Sound. Laplace's Correction. Energy Transport. Intensity of Wave.

Target Audience: 

2nd Semester (2020) Physics Honours Students of Chandernagore College.

Classnotes Download Link:

Wave Motion II: Longitudinal Waves

Lectures:

Part I

Part II

Reference:

N K Bajaj, "The Physics of Wave and Oscillations",

Atanu Kumar

Assistant Professor

Department of Physics

Chandernagore College

atanukum@gmail.com 

Complex Analysis: Evaluation of Definite Integrals

Topics Covered:

Evaluation of Definite Integrals by Cauchy' Residue Theorem.

Target Audience:

4th Semester (2020) Physics Honours Students of Chandernagore College.

Classnotes Download Link:

Evaluation of Definite Integrals L2

Lecture:

Assignments Download Link:

Assignment II

Solutions of Assignment II

References:

(i) Arfken & Weber, "Mathematical Methods for Physicists"

(ii) Spigel et. al., "Outlines of Complex Variables"

Atanu Kumar

Assistant Professor

Department of Physics

Chandernagore College

atanukum@gmail.com

Basics of Positional Astronomy: Measurement of Time

Topics Covered:

Measurement of Time, Sidereal Time, Apparent Solar Time, Mean Solar Time, Equation of Time, Calendar.

Target Audience:

6th Semester (2020) Physics Honours Students of Chandernagore College.

Classnotes Download Link:

Measurement of Time

Lectures 

Part I 

Part II

Assignments Download Link

Assignment I

Solutions of Assighnment I

References:

(i) Hannu Kartunen, et. al., "Fundamental Astronomy"

(ii) Pankaj Jain, "An Introduction to Astronomy"
(iii) IGNOU Study Materials

Atanu Kumar

Assistant Professor

Department of Physics

Chandernagore College

atanukum@gmail.com

Wave Motion I

Topics Covered:

Longitudinal and Transverse Waves. Plane and Spherical Waves.  Progressive (Travelling) Waves. Differential Equation of  a Plane Progressive Wave. Solution of One Dimensional Wave Equation.

Target Audience: 

2nd Semester (2020) Physics Honours Students of Chandernagore College.

Class Notes Download Link

Lecture: 

Part I

Part II

References:

1. N K Bajaj, "The Physics of Wave and Oscillations",
2. Frank S. Crawford, "Barkley Physics Course (Volume III): Waves",
3. Richard P Feynman, "Feynman Lectures on Physics (Volume I)".

Atanu Kumar

Assistant Professor

Department of Physics

Chandernagore College

atanukum@gmail.com 

Basics of Positional Astronomy: Astronomical Coordinates

Topics Covered:

Astronomical Coordinate Systems, Geographical Coordinate Systems, Horizon System, Equatorial System, Conversion of Coordinates.

Target Audience:

6th Semester (2020) Physics Honours Students of Chandernagore College.

Classnotes Download Link:

Astronomical Coordinates

Lectures:

Part I

Part II

Part III

References:

(i) Baidyanath Basu, "An Introduction to Astrophysics"

(ii) Pankaj Jain, "An Introduction to Astronomy"
(iii) IGNOU Study Materials

Atanu Kumar

Assistant Professor

Department of Physics

Chandernagore College

atanukum@gmail.com

Complex Analysis: Cauchy's Residue Theorem and its Applications

Topics Covered:

Classification of Singularities, Residue, Cauchy's Residue Theorem, Evaluation of Definite Integrals.

Target Audience:

4th Semester (2020) Physics Honours Students of Chandernagore College.

Classnotes Download Link:

Cauchy's Residue Theorem and its Applications L1

Lecture 1:

Part I

Part II

Part III

Part IV

Assignments Download Link:

Assignment I

References:

(i) Arfken & Weber, "Mathematical Methods for Physicists"

(ii) Spigel et. al., "Outlines of Complex Variables"

Atanu Kumar

Assistant Professor

Department of Physics

Chandernagore College

atanukum@gmail.com

Basics of Positional Astronomy: Celestial Sphere

Topics Covered:

Basic concepts of positional astronomy: Celestial Sphere, Geometry of a Sphere, Spherical Triangle, Diurnal Motion of the Stars.

Target Audience:

6th Semester (2020) Physics Honours Students of Chandernagore College.

Classnotes Download Link:

Celestial Sphere 

Astronomical Scales

Lectures:

Part I

Part II

Part III

Part IV

Part V

References:

1. Jim Kaler, "Measuring The Sky: A Quick Guide to the Celestial Sphere"

2. IGNOU Study Materials

3. Baidyanath Basu, "An Introduction to Astrophysics"

Atanu Kumar

Assistant Professor

Department of Physics

Chandernagore College

atanukum@gmail.com 

Superposition of Perpendicular Harmonic Oscillations

Topics Covered:

Superposition of two Perpendicular Harmonic Oscillations. Graphical and Analytical Methods. Lissajous Figures with equal an unequal frequency and their uses.

Target Audience: 

2nd Semester (2020) Physics Honours Students of Chandernagore College.

Class Notes Download Link

Lectures:

Part I  

Part II  

Part III  

Part IV  

Part V  

Part VI

Assignments Download Link

Reference:

N K Bajaj, "The Physics of Wave and Oscillations".

Atanu Kumar
Assistant Professor
Department of Physics
Chandernagore College
atanukum@gmail.com