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Mathematiques II

Prof. Abdelilah Dahlane
(Université Cadi Ayyad (Marrakech - Morocco))

Langue du contenu:Anglais

Description du cours

Introduction to several variable functions and multiple integrals. Differential equations and systems, series of functions.

Connaissances requises

Differential and integral calculus. Linear Algebra.

Programme

NumericalSeries; series of functions. Taylor and power series. Fourierseries.
Real functions of several variables: limits, continuity and differentiation.
Multiple integrals.
Differential equations: separable variables, first and second order linear equations. Linear differential systems with constant coefficients

Chargé de Cours

Professeur non disponible

Enseignant vidéo

Prof. Abdelilah Dahlane - Université Cadi Ayyad (Marrakech - Morocco)

Liste des leçons vidéo

Leçon n. 1: Sequences Affichez les sujets de la leçon		Michael Lambrou
Outline Numerical Sequences Convergence of sequences
Leçon n. 2: Series		Michael Lambrou
Leçon n. 3: Criteria for series convergence Affichez les sujets de la leçon		Michael Lambrou
Outline Criteria for series convergence Ratio and root test
Leçon n. 4: Sequences and series of functions Affichez les sujets de la leçon		Michael Lambrou
Outline Sequences of functions Derivatives and integrals of limits Series of functions
Leçon n. 5: Power Series Affichez les sujets de la leçon		Michael Lambrou
Outline Power Series Radius of convergence Differentiation and integration of power series
Leçon n. 6: Taylor series Affichez les sujets de la leçon		Michael Lambrou
Outline Maclaurin series Polynomial approximation Taylor expansion of functions
Leçon n. 7: Fourier series Affichez les sujets de la leçon		Michael Lambrou
Outline Trigonometric expansion of functions Orthogonal functions Behaviour at discontinuties
Leçon n. 8: Functions of two variables Affichez les sujets de la leçon		Michael Lambrou
Outline Functions of two variables Graph
Leçon n. 9: Continuity and Partial derivatives Affichez les sujets de la leçon		Michael Lambrou
Outline Limit of functions of two variables Continuity Partial derivatives Higher - order partial derivatives
Leçon n. 10: Differentiability Affichez les sujets de la leçon		Michael Lambrou
Outline Differentiability of functions Chain rules Directional derivatives
Leçon n. 11: Functions of three or more variables Affichez les sujets de la leçon		Michael Lambrou
Outline Functions of many variables Partial derivatives Chain Rules Cylindrical and spherical transformations
Leçon n. 12: Extreme of functions Affichez les sujets de la leçon		Michael Lambrou
Outline Maxima, minima, saddle points Criteria for extrema Extrema on the boundary
Leçon n. 13: Lagrange Multipliere Affichez les sujets de la leçon		Michael Lambrou
Outline Extrema under constraints Lagrange multipliers
Leçon n. 14: Double Integrals Affichez les sujets de la leçon		Michael Lambrou
Outline Volume approximation by rectangles Double integrals Integration
Leçon n. 15: Double integrals over regions Affichez les sujets de la leçon		Michael Lambrou
Outline Double integrals over regions Iteration of integrals Techniques of integration
Leçon n. 16: Change of variables Affichez les sujets de la leçon		Michael Lambrou
Outline Change of variables into polars Change of variable formula for polars General change of variables Jacobians
Leçon n. 17: Triple Integrals Affichez les sujets de la leçon		Michael Lambrou
Outline Triple integrals over a rectangular domain Triple integrals over general domains Volumes as triple integrals
Leçon n. 18: Evaluation of triple integrals Affichez les sujets de la leçon		Michael Lambrou
Outline Techniques of evaluating triple integrals Iteration of integrals
Leçon n. 19: Applications of integration Affichez les sujets de la leçon		Michael Lambrou
Outline Volume of solids Mass of solids Center of mass Moment fo inertia Pappus Theorem
Leçon n. 20: Differential equations Affichez les sujets de la leçon		Michael Lambrou
Outline Idea of differential equations Separation of variables Homogeneous equations
Leçon n. 21: First order differential equations Affichez les sujets de la leçon		Michael Lambrou
Outline First order linear differential equations Integrating factor Exact equations
Leçon n. 22: Second order linear differential equations Affichez les sujets de la leçon		Michael Lambrou
Outline Second order differential equations Homogeneous equations Application
Leçon n. 23: Second order inhomogeneous differential equations Affichez les sujets de la leçon		Michael Lambrou
Outline Second order linear inhomogeneous differential equations Particular solutions Undetermined coefficients
Leçon n. 24: Higher order differential equations Affichez les sujets de la leçon		Michael Lambrou
Outline Higher order linear differential equations Homogeneous case Inhomogeneous case Methods of variation of parameters
Leçon n. 25: Systems of differential equations Affichez les sujets de la leçon		Michael Lambrou
Outline Linear systems of differential equations Method of D operators

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