Maths III

About the course

Mathematics-III covers Fourier Series and Laplace Transformations. We also study about Partial Differentiation Equation along with its Applications. Towards the Middle, we discuss Functions of Complex Variables and Basic Transformations. The course also discusses popular Statistical and Numerical Techniques in detail.

What will you learn?

The complete online syllabus of this course comprises 8 Learning Modules | 126 Topics of Learning | 5.4 Hours of Learning

Module

• Fourier Series and Euler’s Formula
• Laplace Transformations
• Special Functions
• Partial Differential Equations
• Functions of Complex Variable
• Basic Transformations
• Statistical Techniques
• Numerical Techniques

Topics of Learning

• Fourier series and Periodic Function
• Even and odd functions
• Change of Interval
• Half Range Expansions
• Definition of Laplace Transforms
• Laplace transforms of various standard functions
• Properties of Laplace transforms
• Inverse Laplace transforms
• Transform of Derivatives and Integrals
• Convolution Theorem
• Laplace transform of unit step function
• Applications to solution of ordinary linear differential equations with constant coefficients
• Frobenius method for power series solution of differential equations
• Bessel’s equation
• Bessel functions of the first and second kind
• Legendre’s equation
• Legendre polynomial
• Formation of partial differential equations
• Equations solvable by direct integration
• Linear partial differential equations
• Homogeneous Partial Differential Equations with Constant Coefficients
• Solution of two-dimensional Laplace equation(Cartesian co-ordinates)
• Method of separation of variables for solving partial differential equations.
• Wave equation up to two-dimensions
• Laplace equation in two-dimensions,
• Heat conduction equations up to two-dimensions
• Equations of transmission lines.
• Definition of Limit
• Definition of continuity
• Derivative of Complex Functions
• Derivative of Analytic Functions
• Necessary and sufficient conditions for analytic function
• Cauchy-Riemann equation (Cartesian and polar co-ordinates)
• Harmonic Functions
• Determination of conjugate functions
• Miller’s Thomson method
• Bilinear Transformations
• Complex Integration
• Line integrals in the complex plane
• Cauchy’s integral theorem
• Cauchy’s integral formula for analytic function and its derivatives
• Taylor’s and Laurent’s expansions
• Singular Points
• Poles
• Residue
• Cauchy’s Residue theorem
• Evaluation of real integrals by contour integration (F(cosx, sinx)
• Introduction to Moments
• Moment generating functions
• Skewness
• Kurtosis
• Curve fitting
• Method of least squares
• Fitting of straight lines
• Polynomials
• Exponential curves
• Correlation
• Linear, non –linear and multiple regression analysis
• Binomial, Poisson and Normal distributions
• Chi-square test
• Analysis of variance (one way)
• Time series and forecasting (moving and semi-averages)
• Statistical quality control methods
• Regula-falsi method
• Newton-Raphson method
• Finite differences
• Difference Tables
• Newton’s forward and backward interpolation
• Lagrange’s and Newton’s divided difference formula for unequal intervals.
• Gauss- Seidal method
• Crout method
• Numerical differentiation
• Numerical integration
• Trapezoidal Rules
• Simpson’s one third and three-eight rules
• Euler’s method
• Picard’s Method
• Forth-order Runge- Kutta mehthods

For a quick review, please watch our videos here 👉🏻 Online Video-Tutorials For Mathematics-III