By Mohamed F. El-Hewie

9. capabilities of advanced Variable

Introduction to advanced numbers

The actual and imaginary elements of a fancy number

Modulus and Argument of a fancy number

Complex quantity as vectors

Cartesian and Polar illustration of complicated numbers

Pure actual and Imaginary numbers

Representation of complicated numbers on a Riemann Sphere

Algebraic operations on advanced numbers.

Conformal Mapping

Inverse Transformation

Series of complicated numbers

Cauchy's Theorem

Cauchy’s Theorem of Residue

Cauchy's fundamental formula

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10. idea of Probability

Mathematical definition of probability

Exclusive events

Independent events

Rules governing chance of self reliant events

Dependent events

Binomial legislations of probability

Random variables

Discrete distribution

Continuous distribution

Joint distribution of numerous variables

Expectation

Parameters of a frequency distribution

Sheppard’s correction

Binomial frequency distribution

Stirling’s formulation for the approximation of factorials of huge numbers

Chekychef’s Theorem

Normal frequency distribution or Gaussian distribution

Poission’s distribution

Law of enormous numbers

Correlation

Scatter diagram

Standard blunders of the suggest SEM

11. Laplace Transforms

The Laplace transformation.

The Laplace transformation of the sum of 2 functions

Sectionally or piecewise non-stop functions

Functions of exponential order

Inverse Laplace transforms

Transforms of derivatives

Transforms of integrals

The first shift theorem of multiplying the item functionality via eat

Laplace’s resolution of linear differential equations with consistent coefficients

The moment translation or transferring property

The unit impulse function

The unit doublet

Differentiation of transform

The Heaviside's enlargement formulae

Using Laplace Transformation in fixing Linear Partial Differential Equations

12. usual and Partial Differential Equations

Total Differential Equations

Ordinary differential equations

Linear simultaneous equations with consistent coefficients

Simultaneous overall Differential Equations

First Order differential equations

Separable Equations

Homogeneous Equations

Differential equations of the second one order

Linear differential equations of the second one order

Partial Differential Equations of the 1st Order

Non linear partial differential equations of the 1st order

Damped mechanical oscillations

Electrical oscillations- RCL circuit

13. functions in Engineering and Physics

14. Solved difficulties and routines

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