PREV

• Introduction: Definitions of ODE, PDE and basics
• The Cauchy’s problem for quasi-linear first-order PDEs, First order nonlinear equations
• Applications of PDE
• Formulation of partial differential equation
• Some classical Partial differentiation equations and classification of 2nd order PDE
• Solution of 1st and 2nd order PDE: Separation of variable
• Parabolic and hyperbolic PDEs in Cartesian and cylindrical coordinates
• Basic concepts and definitions, Mathematical problems, Linear operator
• Solutions of elliptic, parabolic and hyperbolic PDEs
• Mid Term Exam
• Canonical forms and Cauchy’s problem for second order PDEs in two independent variables
• Winter Break
• Laplace transform: Introduction and properties of Laplace transform and Dirac delta function
• Inverse Laplace transform, convolution theorem, solution of PDEs by Laplace transform, Fourier integral representation
• Fourier sine and cosine representation, finite Fourier transforms
• Solutions of heat, wave and Laplace equations by Fourier transform.
• Final Term Exam