Mathematics I & II & III & IV & V
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Experience: 3 years
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:/ Non-homogeneous Equations (Method of undetermined coefficients)./ Second order ordinary Differential Equations with constant coefficients:/ on-homogenous Equations Method of undetermined coefficients (Case of duplication)./ Second Order ordinary Differential Equation with variable coefficients: / [Euler-Cauchy Equations] . / Laplace transform: Basic definition / First Shifting Theorem (s-shifting)./ Laplace transform: / Transform Differentiation / Transform Integration./ Laplace transform:/ Unit Step Function / Second Shifting Theorem (t-shifting)./ 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