Instructor

Professor

Madhumita Bhattacharjee

Is Mathematics your boogeyman? I will simplify the concepts and make the subject interesting for you. Mathematics is a core pillar of engineering and you will use it extensively no matter what stream you specialize in. An engineering veteran with 20+ years of experience, I have authored an engineering reference book and been awarded the best teacher i several times.

Course curriculum

  • 1

    Module 1 (Laplace Transformation)

    • Basics of Laplace Transformation

      FREE PREVIEW

    • Laplace Transformation of Standard Functions

    • Linearity Property & Its Application

    • Problems on Linearity Property & Change of Scale Property

    • First Shifting Property

    • Second Shifting Property

    • Effect Of Multiplication of t

    • Problems on Multiplication of t

    • Effect of Division by t

    • Laplace Transform of Derivatives of Function

    • Problems on Laplace Transform of Derivatives of Function

    • Laplace Transform of Integrals

    • Evaluation of Integrals using LT
  • 2

    Module 2 (Inverse Laplace Transformation)

    • Basics Of Inverse Laplace Transform

    • Shifting Theorem to Obtain ILT

    • Method of partial fraction to Obtain ILT

    • Continuation of Method of partial fraction to obtain ILT

    • Convolution theorem to obtain ILT

    • Continuation of Convolution theorem to obtain ILT

    • Determination of ILT using Derivatives

    • Finding ILT by using Integral

  • 3

    Module 3 (Fourier Series)

    • Introduction & Determination of Fourier coefficients by Euler's formula

    • Determination of Fourier Expansion in the interval (0,2π)

    • Fourier Series & use of Parseval identity

    • Continuation of finding Fourier Series in the interval (0,2π)

    • Continuation of finding Fourier Series in the interval (0,2π)

    • Determination of Fourier Expansion in the interval (-π,π)

    • Continuation of Determination of Fourier Expansion in the interval (-π,π)

    • Fourier series of Even & Odd function in the interval (-π,π)

    • Continuation Fourier series of Even and Odd function in the interval (-π,π)

    • Determination of Fourier Expansion in the interval (c,c+2l)

    • Fourier Series in the interval (0,2l) & change of interval

    • Fourier Series in the interval (-l,l)

    • Fourier Series of Even and Odd function in the interval (-l,l)

    • Half Range Cosine and Sine series

    • Half Range Cosine Series alongwith deduction
  • 4

    Module 4 (Complex Variable)

    • Introduction of Complex Variable

    • Analytic function, Cauchy-Reimann Equation & Problems

    • Determination of Constants if function is given to be analytic

    • Analytic function when real part is given by using Milne -Thompson's method

    • Analytic function when imaginary part is given by using Milne -Thompson's method

    • Analytic function when u-v or u+v is given by using Milne -Thompson's method

    • Harmonic function & determination of conjugate harmonic function

    • Analytic function when harmonic function is given

    • Orthogonal trajectories
  • 5

    Module 5 (Linear Algebra- Matrix Theory)

    • Introduction to Eigen values & Eigen vectors of a Square Matrix

    • Properties & Problems on Eigen value & Eigen vectors

    • Determination of Eigen values & Eigen vectors when Eigen values are distinct

    • Determination of Eigen values & Eigen vectors when Eigen values are repeated

    • Determination of Eigen values and Eigen vectors when Eigen values are repeated but having same Eigen vectors

    • Characteristics roots & Characteristics vector of expression containing square matrix

    • Continuation To find Characteristic roots and Characteristic vector of expression containing square matrix

    • Cayley-Hamilton's Theorem & its application for solving problems

    • Continuation Cayley-Hamilton's Theorem & its application for solving problems

    • Similarity of a Matrix and Diagonalisable matrix

    • To show whether the given matrix is diagonalisable

    • To show that the given matrix is not diagonalisable

    • Function of a Square Matrix

    • Continuation of Function of Square matrix

    • Continuation of Function of Square matrix
  • 6

    MODULE 6 - Partial Differential Equation (PDE)

    • Introduction to PDE & Numerical method for one dimensional wave equation

    • Numerical method to solve One dimensional wave equation

    • One dimensional Heat Flow equation

    • Numerical method to solve One dimensional Heat Flow equation

    • Numerical method for solving PDE using Bender Schmidt Formula

    • Continuation of Numerical method for solving PDE using Bender Schmidt Formula

    • Numerical method for solving PDE using Crank Nicholson Simplified Formula

    • Crank Nicholson Simplified Formula for solving problem
  • 7

    Module 7- Probability

    • Introduction & Basics of Probability

    • Total Probability Theorem & Bayes Theorem

    • Total Probability Theorem & Bayes Theorem

    • Discrete & Continuous Random Variable

    • ...Cont of Discrete & Continuous Random Variable

    • Expectation of Random Variable with Mean and Variance

    • ...Cont for Expectation of Random Variable with Mean and Variance

    • Moment Generating Function

    • ... Cont of Moment Generating Function

    • Numerical on Moment of Continuous Random Variable
  • 8

    Module 8- Vector Differentiation & Integral

    • Pre-requisite to Vector Calculus

    • Vector Differentiation, Basics of Gradient & Directional Derivative

    • Divergence & Curl of Vector point function

    • Properties Of Vector Field, Solenoidal & Irrotational

    • Numerical on Solenoidal & Irrotational vector

    • Vector Integration; Line Integral

    • Numerical on Line Integral & Work Done

    • Green's Theorem & its application

    • Work done by Green's Theorem

    • Verification of Green's Theorem

    • Stoke's Theorem & its application

    • Numerical on Stokes Theorem_1

    • Numerical on Stoke's Theorem_2