30 MIN
LESSON
Mathematics I & II & III & IV & V
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General information
nick  ELGAZZAR 

country  Egypt 
languages  Arabic, English 
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Education
 Hig hly experienced Tutor with diverse subject expertise. Friendly and energetic professional with Bachelor of Science in Mechanical Engineering and advanced knowledge of mathematics engineering and Basic sciences.
Adept at improving both group and individual concept understanding and performance.  Tutor wide range of secondary school and college students
 < strong>Present math engineering science and social studies topics on individual levels.
Hold group and oneonone tutoring sessions < strong>Specialize in homeschool student support and college prep studies
Experience: 3 years
About me
I section topics of maths in five courses I teachs this topic in university and I can teahe them online .
Mathematics I : This course covers: Basic rules of differentiation / Trigonometric and their derivatives / Inverse of trigonometric and their derivatives / Logarithmic and their derivatives / Exponential and their derivatives / Derivatives of hyperbolic s and their inverse / Parametric differentiation / Implicit differentiation / L’Hospital rule / Partial Differentiation / Maclaurin’s expansions / Physical application / Curve sketching Conic sections
Mathematics II : This course covers: Definition of indefinite integrals & table of famous integrals / Simple rules of integration & the fundamental theorem of calculus / Integration by parts / Integration by parts & integration of rational s / Integration of rational s / Integration of trigonometric powers / Trigonometric substitution / Integration of quadratic forms and the reduction formulas / Definite integration & Area and volume / Length of curve & Average of a & numerical integration / Matrix Algebra: Matrix addition / scalar multiplication / matrix multiplication and inverse of matrix / Solution of systems of linear equations using inverse of matrix and Gauss / Elimination method
Mathematics III : This course covers: First order ordinary Differential Equations: Separable of variables / Initial value problem / Homogeneous Equations / First order Differential Equations: Total differential and Exact Equations  Linear Equations. First order ordinary Differential Equations: Bernoulli’s Equation / Revision of First order Differential Equations. / Second order ordinary Differential Equations with constant coefficients: / Fundamental set of solutions / Linear independence of solutions:/ Wronskian. / General solution of homogeneous equations./ Second order ordinary Differential Equations with constant coefficients:/ Nonhomogeneous Equations (Method of undetermined coefficients)./ Second order ordinary Differential Equations with constant coefficients:/ onhomogenous Equations Method of undetermined coefficients (Case of duplication)./ Second Order ordinary Differential Equation with variable coefficients: / [EulerCauchy Equations] . / Laplace transform: Basic definition / First Shifting Theorem (sshifting)./ Laplace transform: / Transform Differentiation / Transform Integration./ Laplace transform:/ Unit Step Function / Second Shifting Theorem (tshifting)./ Convolution Theorem./ Inverse Laplace Transform./ Applications:/ Solution of D.E. using Laplace Transform. / Solution of integral equation (Volterra Integral Eq.) using Laplace Transform. / Fourier series:/ Fourier series for s of period 2P. / Fourier series:/ Fourier series for Even and Odd s
Mathematics IV :Vector Algebra / Dot and cross product and Applications  Partial Differentiation / and Derivatives of vector s  Gradient / Divergence / curl/ Laplacian  Line Integrals / line Integrals Independent of the path / Exactness  Conservative vector fields  Double Integrals in Cartesian and polar coordinates / Green’s Theorem  Surface Integrals / Stokes` Theorem  Triple Integrals / Divergence (Gauss‟ Theorem)  Review on Integrals Theorems
Mathematics V :Series solution for ordinary differential equations with variable coefficients: Taylor`s and power series. Special s: Gamma, Beta, Bessel and Legendre s. Partial differential equations: method of separation of variables. Applications on partial differential equations: heat equation, wave equation, Laplace equation. Conformal mapping: complex s as mapping, linear fractional mapping, Schwarz – Christoffel mapping