Fourier series
Convergence and divergence of infinite series of positive terms, definition
and illustrative examples*
Periodic functions, Dirichlet’s conditions, Fourier series of periodic functions
of period and arbitrary period, half range Fourier series. Complex form
of Fourier Series. Practical harmonic analysis.
7 Hours
UNIT-2
Fourier Transforms
Infinite Fourier transform, Fourier Sine and Cosine transforms, properties,
Inverse transforms
6 Hours
UNIT-3
Application of PDE
Various possible solutions of one dimensional wave and heat equations, two
dimensional Laplace’s equation by the method of separation of variables,
Solution of all these equations with specified boundary conditions.
D’Alembert’s solution of one dimensional wave equation.
6 Hours
UNIT-4
Curve Fitting and Optimisation
Curve fitting by the method of least squares- Fitting of curves of the form
y = ax+b, y = a x2 + b x + c, , y
bx b
y = a e = ax
Optimization: Linear programming, mathematical formulation of linear
programming problem (LPP), Graphical method and simplex method.
7 Hours
PART-B
UNIT-5
Numerical Methods - 1
Numerical Solution of algebraic and transcendental equations: Regula-falsi
method, Newton - Raphson method. Iterative methods of solution of a system
6ı
of equations: Gauss-seidel and Relaxation methods. Largest eigen value and
the corresponding eigen vector by Rayleigh’s power method.
6 Hours
UNIT-6
Numerical Methods – 2
Finite differences: Forward and backward differences, Newton’s forward and
backward interpolation formulae. Divided differences - Newton’s divided
difference formula, Lagrange’s interpolation formula and inverse
interpolation formula.
Numerical integration: Simpson’s one-third, three-eighth and Weddle’s rules
(All formulae/rules without proof)
7 Hours
UNIT-7
Numerical Methods
Convergence and divergence of infinite series of positive terms, definition
and illustrative examples*
Periodic functions, Dirichlet’s conditions, Fourier series of periodic functions
of period and arbitrary period, half range Fourier series. Complex form
of Fourier Series. Practical harmonic analysis.
7 Hours
UNIT-2
Fourier Transforms
Infinite Fourier transform, Fourier Sine and Cosine transforms, properties,
Inverse transforms
6 Hours
UNIT-3
Application of PDE
Various possible solutions of one dimensional wave and heat equations, two
dimensional Laplace’s equation by the method of separation of variables,
Solution of all these equations with specified boundary conditions.
D’Alembert’s solution of one dimensional wave equation.
6 Hours
UNIT-4
Curve Fitting and Optimisation
Curve fitting by the method of least squares- Fitting of curves of the form
y = ax+b, y = a x2 + b x + c, , y
bx b
y = a e = ax
Optimization: Linear programming, mathematical formulation of linear
programming problem (LPP), Graphical method and simplex method.
7 Hours
PART-B
UNIT-5
Numerical Methods - 1
Numerical Solution of algebraic and transcendental equations: Regula-falsi
method, Newton - Raphson method. Iterative methods of solution of a system
6ı
of equations: Gauss-seidel and Relaxation methods. Largest eigen value and
the corresponding eigen vector by Rayleigh’s power method.
6 Hours
UNIT-6
Numerical Methods – 2
Finite differences: Forward and backward differences, Newton’s forward and
backward interpolation formulae. Divided differences - Newton’s divided
difference formula, Lagrange’s interpolation formula and inverse
interpolation formula.
Numerical integration: Simpson’s one-third, three-eighth and Weddle’s rules
(All formulae/rules without proof)
7 Hours
UNIT-7
Numerical Methods
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