B.Tech Engineering Mathematics – 2 Tuition Classes

The objective of this course is to familiarize the prospective engineers with techniques in ordinary differential equations, Laplace transform, sequence and series, Fourier series and complex variables. It aims to equip the students to deal with advanced level of mathematics and applications that would be essential for their disciplines. The students will learn:

• The effective mathematical tools for the solutions of differential equations that model physical processes.
• The basic knowledge of Laplace transform and its applications in solving differential equations.
• The tool for convergence of series and expansion of function using Fourier series for learning advanced Engineering Mathematics.
• The tools of differentiation of functions of complex variables that are used in various techniques dealing with engineering problems.
• The tools of integration of functions of complex variables that are used in various techniques dealing with engineering problems

Ordinary Differential Equation of Higher Order Tuition Classes

Linear differential equation of nth order with constant coefficients, Simultaneous linear differential equations, Second order linear differential equations with variable coefficients, Solution by changing independent variable, Method of variation of parameters, Cauchy-Euler equation, Application of differential equations in solving engineering problems. Hence, call 9818003202 for the best engineering tuition classes.

Laplace Transform Tuition Classes

Laplace transform, Existence theorem, Properties of Laplace Transform, Laplace transform of derivates and integrals, Unit step function, Laplace transform of periodic function, Inverse Laplace transform, Convolution theorem. Application of Laplace Transform to solve ordinary differential equations and simultaneous differential equations. Hence, call for the best laplace transform tuition classes.

Sequence and Series Tuition Classes

Definition of Sequence and series with examples, Convergence of series, Tests for convergence of series, Ratio test, D’ Alembert’s test, Raabe’s test, Comparison test. Fourier series, Half range Fourier sine and cosine series. Hence, call for the sequence and series tuition classes.

Complex Variable–Differentiation Tuition Classes

Functions of complex variable, Limit, Continuity and differentiability, Analytic functions, Cauchy- Riemann equations (Cartesian and Polar form), Harmonic function, Method to find Analytic functions, Milne’s Thompson Method, Conformal mapping, Mobius transformation and their properties. Hence, call for the complex variable differentiation tuition classes.

Complex Variable –Integration Tuition Classes

Complex integration, Cauchy- Integral theorem, Cauchy integral formula, Taylor’s and Laurent’s series, singularities and its classification, zeros of analytic functions, Residues, Cauchy’s Residue theorem and its application. Hence, call for the complex variable integration tuition classes.

At the end of this course, the students will be able to:

Remember the concept differentiation to evaluate LDE of nth order with constant coefficient and LDE with variable coefficient of 2nd order.

Understand and apply the concept of Laplace Transform to evaluate differential equations

Understand the concept of convergence to analyze the convergence of series and expansion of the function for Fourier series.

Apply the concept of analyticity, Harmonic function and create the image of function applying conformal transformation

Apply the concept of Cauchy Integral theorem, Cauchy Integralformula, singularity and calculus of residue to evaluate integrals.