# Advanced Mathematics Personal Study Notes- Part II by Mohamed F. El-Hewie

By Mohamed F. El-Hewie

this is often half II of my own examine notes in complex arithmetic. It involves theoretical research, solved examples, and routines at the following topics:

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
Conformal Mapping
Inverse Transformation
Series of complicated numbers
Cauchy's Theorem
Cauchy’s Theorem of Residue
Cauchy's fundamental formula
-----
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

Best differential equations books

Darboux Transformations in Integrable Systems: Theory and their Applications to Geometry: 26 (Mathematical Physics Studies)

The Darboux transformation process is likely one of the premier equipment for developing particular strategies of partial differential equations that are referred to as integrable structures and play very important roles in mechanics, physics and differential geometry. This publication provides the Darboux variations in matrix shape and offers only algebraic algorithms for developing the specific suggestions.

Microstructured Materials: Inverse Problems (Springer Monographs in Mathematics)

Advanced, microstructured fabrics are prevalent in and know-how and comprise alloys, ceramics and composites. targeting non-destructive evaluate (NDE), this e-book explores intimately the mathematical modeling and inverse difficulties encountered while utilizing ultrasound to enquire heterogeneous microstructured fabrics.

Introduction to Hamiltonian Dynamical Systems and the N-Body Problem: 90 (Applied Mathematical Sciences)

Bobbing up from a graduate direction taught to math and engineering scholars, this article presents a scientific grounding within the thought of Hamiltonian structures, in addition to introducing the speculation of integrals and relief. a few different issues are lined too.

Asymptotic Integration of Differential and Difference Equations (Lecture Notes in Mathematics)

This booklet provides the idea of asymptotic integration for either linear differential and distinction equations. this kind of asymptotic research is predicated on a few primary rules by means of Norman Levinson. whereas he utilized them to a distinct category of differential equations, next paintings has proven that an analogous ideas bring about asymptotic effects for a lot wider sessions of differential and likewise distinction equations.