SE IT SEM 3 – ENGINEERING MATHEMATICS III

Module 1 – Laplace Transform
15 Topics
1.2 Laplace Transform(L) of standard functions like e^at, sin(at), cos(at), sinh(at), cosh(at) and t^n, n>=0.
1.3.a Properties of Laplace transform : Linearity
1.3.b Properties of Laplace transform : First Shifting Theorem
1.3.c Properties of Laplace transform : Second Shifiting Theorem
1.3.d Properties of Laplace transform : Changes of scale
1.3.e Properties of Laplace transform : Multiplication by t
1.3.f Properties of Laplace transform : Division by t
1.3.g Properties of Laplace transform : Laplace Transform of derivatives and integrals
1.4 Evalution of real improper integrals by using Laplace Transformation
1.5.a Laplace Transform
1.5.b Periodic functions
1.5.c Heaviside’s
1.5.e Dirac Delta Function
1.5.f Special functions (Error and Bessel)
1.1 Definition of Laplace transform, Condition of Existence of Laplace Transform
Module 2 – Inverse Laplace Transform
7 Topics
2.1 Definition of Inverse Laplace transform
2.1.a Linearity Property
2.1.b Inverse Laplace Transform of Standard functions
2.1.c Inverse Laplace Transform using derivatives
2.2 Partial fractions method to find Inverse Laplace transform
2.3 Inverse Laplace Transform using Convolution Theorem(Without Proof)
2.4 Applications to solve initial and boundary value problems involving ordinary differential equations
Module 3 – Fourier Series
8 Topics
3.1 Dirichlet’s conditions
3.1.a Definition of Fourier Series and Parseval’s Identity
3.2 Fourier Series of periodic function with period 2 and 2pi
3.3 Fourier Series of even and odd functions
3.4 Half range Sine and Cosine Series
3.5.a Orthogonal and orthogomal set of functions
3.5.b Complex form of Fourier Series
3.5.c Fourier Transforms
Module 4 – Complex Variables
11 Topics
4.1 Function f(z) of Complex variables, Limit, continuity and Differentiability of f(z)
4.1.a Analytic Function: Necessary and Sufficient conditions for f(z) to be analytic
4.2 Cauchy-Riemann equations in cartesian coordinates
4.3 Milne-Thomson Methods
4.3.a Determine analytic function f(z) when real part(u), imaginary part(v), or its Combination(u+v/u-v) is given
4.4 Harmonic function
4.4.a Harmonic Conjugate
4.4.b Orthogonal trajectories
4.5.a Conformal Mapping
4.5.b Linear and Bilinear Mappings
4.5.c Cross ratio, Fixed points and Standard transformations
Module 5 – Statistical Techniques
5 Topics
5.1 Karl Pearson’s coefficient of correlations(r)
5.2 Spearman’s Rank Correlation Coeficient(R) (with repeated and non-repeated ranks)
5.3 Lines of Regression
5.4 Fitting of first and second degree curves
5.5.a Covariance, fitting of exponential curve
Module 6 – Probability
8 Topics
6.1 Definition and basics of probability
6.1.a Conditional Probability
6.2 Total Probability Theorems and Bayes Theorem
6.3 Discrete and Continuous random variable with Probability distribution and Probability density function
6.4 Expectation
6.4.a Variance Moment generating function
6.4.b Raw and central moments up to 4th order.
6.5.a Skewness and Kurtosis of distribution (data)
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2.4 Applications to solve initial and boundary value problems involving ordinary differential equations

SE IT SEM 3 – ENGINEERING MATHEMATICS III Module 2 – Inverse Laplace Transform 2.4 Applications to solve initial and boundary value problems involving ordinary differential equations
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