## Instructor ### Professor

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