Course Code : PMAT 32322
Title : Mathematical Methods
Pre-requisites : PMAT 22293
Learning Outcomes:
At the end of this course, the student should be able to
- classify partial differential equations using various techniques learned
- solve hyperbolic, parabolic and elliptic equations using fundamental principles
- apply range of techniques to find solutions of standard PDEs
- demonstrate accurate and efficient use of Fourier analysis techniques and their applications in the theory of PDE’s
- solve real world problems by identifying them appropriately from the perspective of partial derivative equations.
Course Contents:
Partial Differential Equations (PDEs): Classification of PDE, First order partial differential equations: Lagrange’s method and Charpit’s method
Second order partial differential equations: Linear Partial Differential Equations with Constant Coefficients, Partial Differential Equations of Order two with Variables Coefficients, Classification of Partial Differential Equations Reduction to Canonical or Normal Form: Parabolic, elliptic and hyperbolic partial differential equations.
Fourier Series: Fourier Series, Even and Odd Functions, Half-Range Expansions, Fourier Integral, Fourier Cosine and Sine Transforms
Solutions of PDEs: Separations of variables, Fourier Transforms, Laplace Transforms, D’Alembert’s Solution of the Wave Equation
Method of Teaching and Learning: A combination of lectures and tutorial discussions.
Assessment: Based on tutorials, tests and end of course examination.
Recommended Reading:
- Kreyszig, E. (10th Ed., 2011). Advanced Engineering Mathematics, Wiley.
- 2. Zill, D.G. (7th Ed., 2020). Advanced Engineering Mathematics, Jones & Bartlett Learning.
- 3. Raisinghania, M.D. (19th Ed., 2018). Advanced Differential Equations, S.Chands, India.