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Mathematics II

Prof. Michael Lambrou
(University of Crete (Heraklion/Crete - Greece))

Content language:Arabic

Course description

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

Prerequisites

Differential and integral calculus. Linear Algebra.

Program

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

Appointed teaching professor

Professor not available

Video Professor

Prof. Michael Lambrou - University of Crete (Heraklion/Crete - Greece)

List of video lessons

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

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Mathematics II