Still no participant
Still no reviews
• Fourier series and its application to the solution of partial differential equations.
• Study of Second order linear differential equations and their importance
• Introduce the concepts of Laplace equation, its application, basic statistical data analysis and curve fitting.
• Expand a function in Fourier series.
• Find the solution of the wave, diffusion and Laplace equations using the Fourier series.
• Find the mean and the variance of a random variable.
• describe special functions and their recurrence relations
Fourier series: Periodic functions. Orthogonality of sine and cosine functions, Dirichlet Conditions (Statement only). Expansion of periodic functions in a series of sine and cosine functions and determination of Fourier coefficients. Complex representation of Fourier series. Expansion of functions with arbitrary period.
Practice-1 Introduction to Scilab, Advantages and disadvantages, Scilab environment, Command window, Figure window, Edit window
Practice-2 Variables and arrays, Initializing variables in Scilab, Multidimensional arrays, Subarray
Expansion of non-periodic functions over an interval. Even and odd functions and their Fourier expansions. Application. Summing of Infinite Series. Term-by-Term differentiation and integration of Fourier series. Parseval Identity.
Practice-3 Special values, Displaying output data, data file, Scalar and array operations Hierarchy of operations, Built in Scilab functions
Practice-4 Introduction to plotting, 2D and 3D plotting
Frobenius Method and Special Functions: Singular Points of Second order linear differential Equations and their importance. Frobenius method and its applications to differential equations. Legendre, Bessel, Hermite and Laguerre Differential Equations.
Practice-5 Branching Statements and program design, Relational & logical operators
practice-6 The while loop, for loop, details of loop operations, break & continue statements
Properties of Legendre Polynomials: Rodrigues Formula, Generating Function, Orthogonality. Simple recurrence relations. Expansion of function in a series of Legendre Polynomials. Bessel Functions of the First Kind: Generating Function, simple recurrence relations. Zeros of Bessel Functions (Jo(x) and J1(x))and Orthogonality.
Practice-7 Curve fitting for experimental Data. Solution of AX=B Using Gauss Elimination.
Practice-8 Numerical Integration using Trapizoidal Rule and Simpson's Rule
Some Special Integrals: Beta and Gamma Functions and Relation between them.Expression of Integrals in terms of Gamma Functions. Error Function (Probability Integral).
Practice-9 Find the eigen value and eigen vector of the input matrix. Solution Of Radioactive decay .
Theory of Errors: Systematic and Random Errors. Propagation of Errors. Normal Law of Errors. Standard and Probable Error. Least-squares fit. Error on the slope and intercept of a fitted line.
Practice-10 An introduction to Scilab file processing, file opening and closing, Binary I/o functions, comparing binary and formatted functions, Numerical methods and developing the skills of writing a program
Practice-11 Ohms law to calculate R, Hooke’s law to calculate spring constant.
Partial Differential Equations: Solutions to partial differential equations, using separation of variables: Laplace's Equation in problems of rectangular, cylindrical and spherical symmetry. Wave equation and its solution for vibrational modes of a stretched string, rectangular and circular membranes. Diffusion Equation.
Practice-12 Solution of simple pendulum and Double Pendulum using Euler and RK4 method
DirichletConditions, Expansion of periodic functions in a series of sine and cosine functions
Numerical problems to find Fourier series and Fourier's coefficient
Introduction to Scilab, Advantages and disadvantages, Scilab environment, Command window, Figure window, Edit window
(Using Scilab )
Special values, Displaying output data, data file, Scalar and array operation Hierarchy of operations, Built in Scilab functions
Term-by-term differentiation and integration of Fourier series
Solutions of Second order differential equation for different points.
Branching Statements and program design, Relational & logical operators
Assignment-5 , flipped class-5:-
Solutions of second order differential equation by using Frobenius method.
User defined functions, Introduction to Scilab functions, Variable passing in Scilab, optional arguments, preserving data between calls to a function,
Find the eigen value and eigen vector of the input matrix. Solution Of Radioactive decay
An introduction to Scilab file processing, file opening and closing, Binary I/o functions, comparing binary and formatted functions, Numerical methods and developing the skills of writing a program
Least-squares fit ,Error on the slope and intercept of a fitted line.
Ohms law to calculate R, Hooke’s law to calculate springconstant
Assignment-9, Flipped class-9 :-
Solutions to partial differential equations by using Complimentary function and particular integral
Assignment-10, Flipped class-10:-
Solution of Laplace's Equation in cylindrical Coordinate.
Radioactive decay, Current in RC, LC circuits with DC source, Newton’s law of cooling