Physics

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Mathematical Physics 1

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This course gives an idea on various mathematical operations in physics. This course includes vector algebra, basic properties of matrices and different types of matrices. This course also include second order differentials equations and specials functions like Gamma functions and beta functions. This course helps the students to do various derivations and to form eqations of theories in physics.

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Course objective:

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• To introduce various Mathematical operations practiced in Physics
• To give an introduction about special functions.

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Course Outcome:

[/vc_column_text][vc_empty_space height=”20px”][vc_column_text]By successfully completing the course students will be able to do the Mathematical operation and solve the difference equations[/vc_column_text][vc_empty_space height=”20px”][vc_column_text]Course Duration: 35 hrs
Course Coordinator: Babitha V M[/vc_column_text][vc_column_text]

Course Content:

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Module 1 – Vectors

Rotation of co-ordinates, Orthogonal Curvilinear co-ordinates, Gradient, Divergence and Curl of Orthogonal Curvilinear co-ordinates, Rectangular, Cylindrical and Spherical polar coordinates, Laplacian operator, vector integration,enough exercise.

Module 2 – Matrices

Basic properties of matrices (review only), orthogonal matrices, Hermitian and unitory matrices, Similarity and unitary transformations, Diagonilization of matrices, Enough exercises.[/vc_column_text][/vc_column_inner][/vc_row_inner][vc_row_inner row_type=”row” type=”full_width” text_align=”left” css_animation=”” css=”.vc_custom_1685534994909{padding-top: 80px !important;}”][vc_column_inner width=”1/2″][vc_column_text]

Module 3 – Second Order Differential Equations

Partial differential equations of Physics, Separation of variables, Singular points, Ordinary series solution.Frobenius method. A second solution, Self adjoint differential equation, eigen functions and values, Enough exercises

Module 4 – Special Functions

Gamma function, Beta function. Delta function, Dirac delta function, Bessel functions of the first and secondkinds, Generating function, Recurrence relation, Orthogonality Neumann function. SphericalBessel function, enough exercises.[/vc_column_text][vc_empty_space height=”20px”][vc_column_text]

Reference:

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• GB Arfken and H.J. Weber: “Mathematical Methods for Physicists (5th Edition, 2001)”
• LL.Pipes and LR.Harvill: “Applied Mathematics for Engineers and Physicists (3rd Edition)”  (McGraw Hill)
• Erwin Kreyzig: “Advanced Engineering Mathematics – 8th edition” (Wiley) 4. M. Greenberg: “Advanced Engineering Mathematics-2nd edition (Pearson India 2002)
• A.W. Joshi: Matrices and tensors 6. Mathematical methods in the physical sciences, 2nd edn, Mary L. Boas, John Wiley & Sons
• Elementary Differential Equations and boundary value problems, William E. Boyce, Richard C. DiPrima, John Wiley & Sons, Inc.
• Mathematics of Classical and Quantum Physics, F. W. Byron and R. W. Fuller, Dover Publications, Inc., New York

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