MOOC Massive Open Online Courses (Academic Year 2018/2019)

Mathematics II

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

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MOOC Massive Open Online Courses (Academic Year 2018/2019)

Mathematics II

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MOOC Massive Open Online Courses (Academic Year 2018/2019)

Mathematics II

Slides