| Lectures: 4 Periods/Week | Sessional Marks: 30 |
| University Exam: 3 Hours | University Examination Marks: 70 |
UNIT-I
Partial Differential Equations:
Introduction, Formation of partial differential equations. Solutions
of partial differential equations, Equations solvable by direct
integration, Linear equations of the first order, Non-linear equations of the first order.
Charpits method, Homogeneous linear equations with constant
coefficients, Rules for finding the complementary function, Rules for finding the particular integral,
Non-homogeneous linear equations.
UNIT-II
Applications of partial differential equations:
Introduction, Variable separable method, One dimensional wave equation, One dimensional heat equation-steady and unsteady states, Two dimensional
heat flow-steady state heat flow- Laplace's equation in Cartesian coordinates.
UNIT-III
Numerical Methods:
Solution of Algebraic and Transcendental equations: Introduction, Newton-
Raphson method, Solution of simultaneous linear equations: Gauss Siedal Iteration method.
Finite Differences & Interpolation:
Introduction, Finite difference operators, Symbolic relations,
Differences of a polynomial, Factorial notation, Newton's forward and backward difference
interpolation formula, Interpolation with unequal intervals - Lagrange's interpolation.
Numerical Integration:
Trapezoidal rule, Simpson's one-third rule.
UNIT-IV
Difference Equations:
Introduction, Formation, Linear difference equations - Rules for finding the
complementary function, rules for finding theparticular integral.
Numerical solution of ordinary and partial differential equations:
Euler's method, Picards method, Runge-Kutta method of fourth order (for first order equations, simultaneous equations), Classification of
partial differential equation of second order, Solutions of Laplace's and Poisson's equations by iteration method.
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