DEPARTMENT OF PHYSICS
BSc. (Hons.) Physics
Category-I
DISCIPLINE SPECIFIC CORE COURSE – 1 (DSC-1) Mathematical Physics I
CREDIT DISTRIBUTION, ELIGIBILITY AND PRE-REQUISITES OF THE
COURSE
Credit distribution of the course
Course title & Eligibility Pre-requisite
Credits Practical/
Code Lecture Tutorial criteria of the course
Practice
Class XII pass Physics and
Mathematical with Physics and Mathematics
4 3 0 1
Physics I Mathematics as syllabus of
main subjects class XII
Learning Objectives
The emphasis of the course is on applications in solving problems of interest to physicists.
The course will teach the students to model a physics problem mathematically and then solve
those numerically using computational methods. The course will expose the students to
fundamental computational physics skills enabling them to solve a wide range of physics
problems. The skills developed during course will prepare them not only for doing
fundamental and applied research but also for a wide variety of careers.
Learning Outcomes
After completing this course, student will be able to,
• Draw and interpret graphs of various elementary functions and their combinations.
• Understand the vector quantities as entities with Cartesian components which satisfy
appropriate rules of transformation under rotation of the axes.
• Use index notation to write the product of vectors in compact form easily applicable
in computational work.
• Solve first and second order differential equations and apply these to physics
problems.
• Understand the functions of more than one variable and concept of partial derivatives.
• Understand the concept of scalar field, vector field, gradient of scalar field and
divergence and curl of vector fields.
• Perform line, surface and volume integration and apply Green’s, Stokes’ and Gauss’s
theorems to compute these integrals and apply these to physics problems
• Understand the properties of discrete and continuous distribution functions.
In the laboratory course, the students will learn to,
• Prepare algorithms and flowcharts for solving a problem.
• Design, code and test simple programs in Python/C++ to solve various problems.
61
, • Perform various operations of 1-d and 2-d arrays.
• Visualize data and functions graphically using Matplotlib/Gnuplot
SYLLABUS OF DSC – 1
THEORY COMPONENT
Unit 1 (18
Hours)
Functions: Plotting elementary functions and their combinations, Interpreting graphs of
functions using the concepts of calculus, Taylor’s series expansion for elementary
functions.
Ordinary Differential E quations: First order differential equations of degree one and
those reducible to this form, Exact and Inexact equations, Integrating Factor, Applications
to physics problems
Higher order linear homogeneous differential equations with constant coefficients,
Wronskian and linearly independent functions. Non-homogeneous second order linear
differential equations with constant coefficients, complimentary function, particular integral
and general solution, Determination of particular integral using method of undetermined
coefficients and method of variation of parameters, Cauchy-Euler equation, Initial value
problems. Applications to physics problems
Unit 2 (12
Hours)
Vector Algebra: Transformation of Cartesian components of vectors under rotation of the
axes, Introduction to index notation and summation convention. Product of vectors - scalar
and vector product of two, three and four vectors in index notation using 𝛿𝑖𝑖 and 𝜀𝑖𝑖𝑖 (as
symbols only – no rigorous proof of properties). Invariance of scalar product under rotation
transformation.
Vector D ifferential C alculus: Functions of more than one variable, Partial derivatives,
chain rule for partial derivatives. Scalar and vector fields, concept of directional derivative,
the vector differential operator 𝛻�⃗, gradient of a scalar field and its geometrical
interpretation. Divergence and curl of a vector field and their physical interpretation.
Laplacian operator. Vector identities.
Unit 3 (15
Hours)
Vector I ntegral C alculus: Integrals of vector-valued functions of single scalar variable.
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 (no proofs) and their applications
Probability D istributions: Discrete and continuous random variables, Probability
distribution functions, Binomial, Poisson and Gaussian distributions, Mean and variance of
these distributions.
62
BSc. (Hons.) Physics
Category-I
DISCIPLINE SPECIFIC CORE COURSE – 1 (DSC-1) Mathematical Physics I
CREDIT DISTRIBUTION, ELIGIBILITY AND PRE-REQUISITES OF THE
COURSE
Credit distribution of the course
Course title & Eligibility Pre-requisite
Credits Practical/
Code Lecture Tutorial criteria of the course
Practice
Class XII pass Physics and
Mathematical with Physics and Mathematics
4 3 0 1
Physics I Mathematics as syllabus of
main subjects class XII
Learning Objectives
The emphasis of the course is on applications in solving problems of interest to physicists.
The course will teach the students to model a physics problem mathematically and then solve
those numerically using computational methods. The course will expose the students to
fundamental computational physics skills enabling them to solve a wide range of physics
problems. The skills developed during course will prepare them not only for doing
fundamental and applied research but also for a wide variety of careers.
Learning Outcomes
After completing this course, student will be able to,
• Draw and interpret graphs of various elementary functions and their combinations.
• Understand the vector quantities as entities with Cartesian components which satisfy
appropriate rules of transformation under rotation of the axes.
• Use index notation to write the product of vectors in compact form easily applicable
in computational work.
• Solve first and second order differential equations and apply these to physics
problems.
• Understand the functions of more than one variable and concept of partial derivatives.
• Understand the concept of scalar field, vector field, gradient of scalar field and
divergence and curl of vector fields.
• Perform line, surface and volume integration and apply Green’s, Stokes’ and Gauss’s
theorems to compute these integrals and apply these to physics problems
• Understand the properties of discrete and continuous distribution functions.
In the laboratory course, the students will learn to,
• Prepare algorithms and flowcharts for solving a problem.
• Design, code and test simple programs in Python/C++ to solve various problems.
61
, • Perform various operations of 1-d and 2-d arrays.
• Visualize data and functions graphically using Matplotlib/Gnuplot
SYLLABUS OF DSC – 1
THEORY COMPONENT
Unit 1 (18
Hours)
Functions: Plotting elementary functions and their combinations, Interpreting graphs of
functions using the concepts of calculus, Taylor’s series expansion for elementary
functions.
Ordinary Differential E quations: First order differential equations of degree one and
those reducible to this form, Exact and Inexact equations, Integrating Factor, Applications
to physics problems
Higher order linear homogeneous differential equations with constant coefficients,
Wronskian and linearly independent functions. Non-homogeneous second order linear
differential equations with constant coefficients, complimentary function, particular integral
and general solution, Determination of particular integral using method of undetermined
coefficients and method of variation of parameters, Cauchy-Euler equation, Initial value
problems. Applications to physics problems
Unit 2 (12
Hours)
Vector Algebra: Transformation of Cartesian components of vectors under rotation of the
axes, Introduction to index notation and summation convention. Product of vectors - scalar
and vector product of two, three and four vectors in index notation using 𝛿𝑖𝑖 and 𝜀𝑖𝑖𝑖 (as
symbols only – no rigorous proof of properties). Invariance of scalar product under rotation
transformation.
Vector D ifferential C alculus: Functions of more than one variable, Partial derivatives,
chain rule for partial derivatives. Scalar and vector fields, concept of directional derivative,
the vector differential operator 𝛻�⃗, gradient of a scalar field and its geometrical
interpretation. Divergence and curl of a vector field and their physical interpretation.
Laplacian operator. Vector identities.
Unit 3 (15
Hours)
Vector I ntegral C alculus: Integrals of vector-valued functions of single scalar variable.
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 (no proofs) and their applications
Probability D istributions: Discrete and continuous random variables, Probability
distribution functions, Binomial, Poisson and Gaussian distributions, Mean and variance of
these distributions.
62
