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Mathematics II
Slides
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