BSc Physics Notes: Semester 3

Semester 3

 

List of the Subjects 

CORE: MATHEMATICAL PHYSICS-II 

CORE: THERMAL PHYSICS

CORE: DIGITAL SYSTEMS  AND APPLICATIONS

GE: DIFFERENTIAL EQUATIONS 

                        




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PHYSICS-C V:  MATHEMATICAL PHYSICS-II 

(Credits: Theory-04, Practicals-02)

Theory:  60 Lectures 

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(The  emphasis  of  the  course  is  on  applications  in  solving  problems  of  interest  to physicists.  Students are to be examined on the basis of problems, seen and unseen. )


  Topics Covered in the Notes 


Fourier  Series:  Periodic  functions. Orthogonality of sine  and  cosine  functions,  Dirichlet Conditions  (Statement  only). Expansion  of  periodic functions  in  a  series  of  sine  and cosine  functions  and  determination  of  Fourier  coefficients.  Even  and  odd  functions  and their  Fourier  expansions.  Application.  Summing  of  Infinite  Series.  Term-by-Term differentiation and integration of Fourier Series. Parseval  Identity. 

                                                       (16  Lectures) 


Frobenius  Method  and  Special  Functions: Singular Points  of  Second  Order  Linear Differential  Equations  and  their  importance.  Frobenius  method  and  its  applications  to differential  equations.  Legendre,  Bessel,  Hermite  and  Laguerre  Differential  Equations. Properties  of  Legendre  Polynomials:  Rodrigues  Formula,  Generating  Function, Orthogonality. Simple  recurrence relations . Expansion  of  function in  a series of  Legendre Polynomials.  Bessel Functions  of the  First Kind: Generating  Function,  simple  recurrence relations. Zeros of Bessel Functions  (Jo(x) and J1(x))  and Orthogonality. 

                                                        (24 Lectures) 


Some  Special  Integrals:  Beta  and  Gamma  Functions  and  Relation  between  them. Expression of  Integrals in terms of Gamma Functions.

                                                           (4 Lectures) 


Partial  Differential  Equations:  Solutions  to  partial  differential  equations,  using separation  of  variables:  Laplace's  Equation  in  problems  of  rectangular  geometry. Solution of wave equation for vibrational modes of a stretched string, rectangular and circular membranes.    

                                                            (15 Lectures)  



Suggested Books in Syllabus:

  • Mathematical Methods for Physicists: Arfken, Weber, 2005, Harris, Elsevier. 
  • Fourier Analysis by M.R. Spiegel, 2004, Tata McGraw-Hill. 
  • Mathematics for Physicists, Susan M. Lea, 2004, Thomson Brooks/Cole. 
  • Differential Equations, George F. Simmons, 2006, Tata McGraw-Hill. 
  • Engineering Mathematics, S.Pal and S.C. Bhunia, 2015, Oxford University Press 
  • Mathematical methods for Scientists & Engineers, D.A.McQuarrie, 2003, Viva Books 







Click to download the Notes in Pdf Format












References:
  • Class Notes
  • Mathematical Physics By H K Das
  • YouTube  Jaipal Mathematics Channel 









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PHYSICS-C VI:  THERMAL PHYSICS
 (Credits: Theory-04, Practicals-02)     
 Theory:  60 Lectures 

___________________________________________________
(Include related problems for each topic)


Topics Covered in the Notes



Introduction to Thermodynamics Zeroth  and  First  Law  of  Thermodynamics:  Extensive  and  intensive  Thermodynamic Variables,  Thermo-dynamic  Equilibrium,  Zeroth  Law  of  Thermo-dynamics  &  Concept  of Temperature,  Concept  of  Work  &  Heat,  State  Functions,  First  Law  of  Thermodynamics and  its differential form,  Internal Energy,  First Law &various processes,  Applications of First  Law:  General  Relation  between  CP  and  CV,  Work  Done  during  Isothermal  and Adiabatic Processes, Compressibility  and Expansion Co-efficient.   
                                                           (8 Lectures) 


Second  Law  of  Thermodynamics:  Reversible  and  Irreversible  process  with  examples. Conversion  of  Work  into  Heat  and  Heat  into  Work.  Heat  Engines. Carnot’s  Cycle, Carnot  engine & efficiency .Refrigerator  &  coefficient  of  performance,  2nd  Law  of Thermodynamics:  Kelvin-Planck  and  Clausius  Statements  and  their  Equivalence. Carnot’s  Theorem.  Applications  of  Second  Law  of  Thermodynamics:  Thermodynamic Scale of Temperature and its Equivalence to Perfect Gas Scale.     
                                                            (10 Lectures) 


Entropy:  Concept  of  Entropy,  Clausius  Theorem.  Clausius  Inequality,  Second  Law  of Thermo-dynamics  in  terms  of  Entropy. Entropy  of  a  perfect  gas.  Principle  of  Increase  of Entropy.  Entropy  Changes  in  Reversible  and  Irreversible  processes  with  examples. Entropy  of  the  Universe.  Entropy  Changes  in  Reversible  and  Irreversible  Processes. Principle  of  Increase  of  Entropy.  Temperature–Entropy  diagrams  for  Carnot’s  Cycle. Third Law of  Thermodynamics.  Unattainability  of Absolute  Zero.   
                                                          (7 Lectures) 


Thermodynamic  Potentials:  Thermodynamic  Potentials:  Internal  Energy,  Enthalpy, Helmholtz  Free  Energy,  Gibb’s  Free  Energy.Their  Definitions,  Properties  and Applications.  Magnetic  Work,  Cooling  due  to  adiabatic  demagnetization,  First  and second  order  Phase  Transitions  with  examples,  Clausius  Clapeyron  Equation  and Ehrenfest equations             
                                                           (7 Lectures) 


Maxwell’s  Thermodynamic  Relations:  Derivation  of  Maxwell’s  thermodynamic Relations  and  their  applications,  Maxwell’s  Relations:  (1)  Clausius  Clapeyron  equation, (2) Value of Cp-Cv,  (3) Tds Equations, (4) Energy  equations.    (7 Lectures) Kinetic  Theory of Gases Distribution  of  Velocities:  Maxwell-Boltzmann Law of Distribution of  Velocity  in  an Ideal  Gas  and  its Experimental  Verification.  Mean,  RMS  and  Most  Probable  Speeds. Degrees of  Freedom.  Law  of  Equipartition  of  Energy  (No  proof  required).  Specific  heats of Gases.     
                                                             (7 Lectures) 


Molecular  Collisions:  Mean  Free  Path.  Collision  Probability.  Estimation  of  Mean  Free Path.  Transport  Phenomenon  in  Ideal  Gases:  (1)  Viscosity,  (2)  Thermal  Conductivity and (3) Diffusion. Brownian Motion and its Significance.                                                                        (4 Lectures) 


Real  Gases:Behavior  of  Real  Gases:  Deviations  from  the Ideal  Gas  Equation. Andrew Experiments  on  CO2  Gas.  Virial  Equation.  Critical  Constants.  Continuity  of  Liquid  and Gaseous  State.  Vapour  and  Gas.  Boyle  Temperature.  van  der  Waal’s  Equation  of  State for  Real  Gases.  Values  of  Critical  Constants.  Law  of  Corresponding  States.  Comparison with  Experimental  Curves.  p-V  Diagrams.  Free  Adiabatic  Expansion  of  a  Perfect  Gas. Joule-Thomson  Porous  Plug  Experiment.  Joule-Thomson  Effect  for  Real  and  van  der Waal Gases.  Temperature of Inversion. Joule-Thomson Cooling.     
                                                          (10 Lectures) 





Suggested Books in Syllabus:
  •  Heat and Thermodynamics, M.W.  Zemansky, Richard Dittman, 1981, McGraw-Hill. 
  •  A Treatise on Heat, Meghnad Saha, and B.N. Srivastava, 1958, Indian  Press   
  • Thermal Physics, S. Garg, R. Bansal and Ghosh, 2nd  Edition, 1993, Tata McGraw-Hill 
  • Thermodynamics,  Kinetic  Theory  &  Statistical  Thermodynamics,  Sears  &  Salinger. 1988, Narosa. 
  • Thermal Physics, A. Kumar and S.P. Taneja, 2014, R. Chand Publications.   







  Click to download the Notes in Pdf Format


                                                                        Handwritten



 





                                     DU  Vle 







References:
  • Class Notes
  • Thermal Physics by Garg , Bansal & Ghosh
  • Du VLE Notes 








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PHYSICS-C VII: DIGITAL SYSTEMS  AND APPLICATIONS 

(Credits: Theory-04, Practicals-02)       

Theory:  60 Lectures 

_________________________________________________



Topics Covered in the Notes



Introduction  to  CRO:  Block  Diagram  of  CRO.  Electron  Gun,  Deflection  System  and Time  Base.  Deflection  Sensitivity.  Applications  of  CRO:  (1)  Study  of  Waveform,  (2) Measurement of Voltage, Current, Frequency, and Phase Difference. 

                                                         (3 Lectures) 


Integrated  Circuits  (Qualitative  treatment  only):  Active  and  Passive  components. Discrete  components.  Wafer.  Chip.  Advantages  and  drawbacks  of  ICs.  Scale  of integration:  SSI,  MSI,  LSI  and  VLSI  (basic  idea  and  definitions  only).  Classification  of ICs. Examples of Linear and Digital lCs.     

                                                          (2  Lectures) 


Digital  Circuits:  Difference  between  Analog  and  Digital  Circuits.  Binary  Numbers. Decimal  to  Binary  and  Binary  to  Decimal  Conversion.  BCD,  Octal  and  Hexadecimal numbers.  AND,  OR  and  NOT  Gates  (realization  using  Diodes  and  Transistor).  NAND and  NOR  Gates  as  Universal  Gates.  XOR  and  XNOR  Gates  and  application  as  Parity Checkers.           

                                                        (6 Lectures) 


Boolean  algebra:  De  Morgan's  Theorems.  Boolean  Laws.  Simplification  of  Logic Circuit  using  Boolean  Algebra.  Fundamental  Products.  Idea  of  Minterms  and  Maxterms. Conversion  of  Truth  table  into  Equivalent  Logic  Circuit  by  (1)  Sum  of  Products  Method and (2) Karnaugh Map.                                                             (6 Lectures) 


Data processing circuits: Multiplexers, De-multi-plexers, Decoders, Encoders. 

                                                          (4 Lectures) 


Arithmetic  Circuits:  Binary  Addition.  Binary  Subtraction  using  2's  Complement.  Half and Full Adders.  Half &  Full Subtractors, 4-bit binary  Adder/Subtractor.    

                                                          (5 Lectures) 


Sequential  Circuits:  SR,  D,  and  JK  Flip-Flops.  Clocked  (Level  and  Edge  Triggered) Flip-Flops. Preset  and  Clear operations. Race-around conditions in JK Flip-Flop. M/S JK Flip-Flop.                                                                        (6 Lectures) 


Timers:  IC 555: block diagram and applications: Astable  multivibrator  and Monostable multivibrator.         

                                                        (3 Lectures) 


Shift  registers:  Serial-in-Serial-out,  Serial-in-Parallel-out,  Parallel-in-Serial-out  and Parallel-in-Parallel-out Shift Registers (only  up to  4 bits).                                                                    (2 Lectures) 


Counters(4  bits):  Ring  Counter.  Asynchronous  counters,  Decade  Counter.  Synchronous Counter.

                                                         ( 4 Lectures)


Computer  Organization:  Input/Output Devices. Data storage (idea of RAM  and  ROM). Computer  memory.  Memory  organization  and  addressing.  Memory  Interfacing.  Memory Map.            

                                                           (6 Lectures)


 Intel  8085  Microprocessor  Architecture:  Main  features  of  8085.  Block  diagram. Components.  Pin-out  diagram.  Buses.  Registers.  ALU.  Memory.  Stack  memory.  Timing and  Control  circuitry.  Timing  states.  Instruction  cycle,  Timing  diagram  of  MOV  and MVI.                                                                                       (9  Lectures)


 Introduction to Assembly Language:1  byte,  2  byte  and  3  byte instructions.

                                                             (4 Lectures) 




Suggested Books in Syllabus: 

  • Digital  Principles  and  Applications,  A.P.Malvino,  D.P.  Leach  and  Saha,  7th  Ed., 2011, Tata McGraw
  • Fundamentals of Digital  Circuits, Anand Kumar, 2nd  Edn, 2009,  PHI  Learning  Pvt.  Ltd. 
  • Digital Circuits and systems, Venugopal, 2011, Tata McGraw Hill. 
  • Digital  Electronics G K Kharate ,2010, Oxford University  Press 
  • Logic circuit design, Shimon P. Vingron, 2012, Springer. 
  • Digital Electronics, Subrata Ghoshal, 2012, Cengage Learning. 
  • Digital Electronics, S.K. Mandal, 2010, 1st  edition, McGraw  Hill 
  • Microprocessor  Architecture  Programming  &  applications  with  8085,  2002,  R.S. Goankar, Prentice Hall. 









 Click to download the Notes in Pdf Format








References:
  • Class Notes
  • Fundamentals of Digital  Circuits, Anand Kumar.
  • Microprocessor  Architecture  Programming  &  applications  with  8085 by R.S. Goankar.







__________________________________________________

GE-3: Differential equations  
Total Marks: 150 
Theory: 75,  Examination: 3 Hrs. 

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Topics Covered in the Notes



Course Objectives: This course includes a variety of methods to solve ordinary and partial differential equations with basic applications to real life problems. It provides a solid foundation to further in mathematics, sciences and engineering through mathematical modeling.   

Course Learning Outcomes: This course will enable the students to learn:  
i) To analyze real-world scenarios to recognize when ordinary (or systems of) or partial differential equations are appropriate for creating an appropriate model.
 ii) To reduce a higher order equation to a system of first order simultaneous equations. 
iii) Explicit methods of solving higher-order linear differential equations.   Course Contents:   



Unit 1: Ordinary Differential Equations and Applications                                                                        First order exact differential equations. Integrating factors, rules to find integrating factor. Linear equations and Bernoulli equations, Orthogonal trajectories and oblique trajectories. Basic theory of higher order linear differential equations, Wronskian and its properties. Solving differential equation by reducing its order. 
                                                       (Lectures: 20) 


Unit 2.  Explicit Methods of Solving Higher-Order Linear Differential Equations  Linear homogenous equations with constant coefficients. Linear non homogenous equations. The method of undetermined coefficients. The method of variation of parameters, The Cauchy-Euler equation. Simul-taneous differential equations.   
                                                      (Lectures: 16)  
                                                                          

Unit 3.  First and Second Order Partial Differential Equations  Partial differential equations: Basic Concepts and definitions. Mathematical problems, First order equations: Classification, Construction, Geometrical interpretation. Method of characteristics, General solutions of first order partial differential equations. Canonical forms and method of separation of variables for first order partial differential equations. Classification of second order partial differential equations. Reduction to canonical forms. Second order partial differential equations with constant coefficients, General solutions. 
                                                       (Lectures: 20) 








Suggested Books in Syllabus:
  • Kreyszig, Erwin. (2011). Advanced Engineering Mathematics (10th ed.). Wiley India.
  • Myint-U, Tyn and Debnath, Lokenath (2007).  Linear Partial Differential Equations  for Scientist and Engineers (4th ed.). Birkk√§user Boston. Indian Reprint.
  • Ross, Shepley. L. (1984). Differential equations (3rd ed.). John Wiley & Sons. 









Click to download the Notes in Pdf Format











References:
  • Class Notes
  • Mathematical Physics by H K Das.
  • Kreyszig , Advanced Engineering Mathematics.






with regards,

By Bsc Physics Notes

Vaibhav Tyagi
Personal Homepage : Click Here
PhD in Atmospheric Sciences
Indian Institute of Technology Indore, MP
M.Sc. Physics (2020-2022)
Indian Institute of Technology
Palakkad , Kerala 

B.Sc. Honours Physics (2017-2020)
Deen Dyal Upadhyaya College
University of Delhi

2 comments:

  1. Please upload 3rd semester previous year question papers.

    ReplyDelete
  2. I got both the files sent to my email id. Thank you .

    ReplyDelete