Partial Differential Equations
This course will enable the students to -
- Classify the fundamental principles of partial differential equations to solve hyperbolic, parabolic and elliptic equations.
- Apply a range of techniques to find solutions of standard partial differential equations.
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Course |
Learning outcomes (at course level) |
Learning and teaching strategies |
Assessment Strategies |
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Course Code |
Course Title |
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24DMAT 615(A)
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Partial Differential Equations (Theory)
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CO145: Solve linear homogeneous partial differential equations with constant coefficients using appropriate methods. CO146: Apply analytical methods to solve non-linear homogeneous partial differential equations with constant coefficients. CO147: Explain the idea behind elliptic differential equations and identify the answers. CO148: Discover the idea behind parabolic differential equations and apply the proper techniques to solve them. CO149: Prepared with the knowledge of hyperbolic differential equations and the ability to solve PDEs using various analytical techniques. CO150: Contribute effectively in course-specific interaction.
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Approach in teaching: Interactive Lectures, Discussion, Power Point Presentations, Informative videos
Learning activities for the students: Self learning assignments, Effective questions, presentations, Assigned tasks |
Quiz, Individual and group projects, Open Book Test, Semester End Examination
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Linear Homogeneous partial differential equations with constant coefficients and their solutions.
Non-Homogeneous linear partial differential equations with constant coefficients, Reducible to linear partial differential equations.
Solution of Boundary Value Problems by the method of separation of Variables, Laplace equation in Cartesian and polar coordinates, Solution of Laplace equation of two dimensions.
Heat equation, solution of one and two dimensional Heat equation in Cartesian Coordinates, Uniqueness of the solution and Maximum-Minimum principle.
Derivation of one and two dimension Wave equations and their solution, D’Alembert’s solution of Wave equation, Uniqueness of the solution for the Wave equation.
- S.K. Pundir and Rimple Pundir, Advanced partial differential Equations (with Boundary value problems), Pragati Prakashan.
- M. D. Raisinghania, Advanced Differential Equations. S. Chand & Company Ltd. New Delhi, 2001.
- M. D. Raisinghania, Ordinary and Partial Differential Equations. S. Chand & Company Ltd. New Delhi.
- I.N. Sneddon, Elements of Partial Differential Equations, McGraw Hill, 1957.
- Fritz John, Partial Differential Equations, Springer-Verlag, New York Inc, 1982.
- S.L. Ross, Differential equations, 3rd Ed., John Wiley and Sons, India, 2004
e- RESOURCES
- https://s2pnd-matematika.fkip.unpatti.ac.id/wp-content/uploads/2019/03/Walter-A-Strauss-Partial-differential-equations-_-an-introduction-Wiley-2009.pdf
- https://www.usb.ac.ir/FileStaff/3223_2019-10-28-13-12-55.pdf
- https://nptel.ac.in/courses/111103021
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