Università telematica internazionale UNINETTUNO

Ingegneria civile e ambientale (Academic Year 2019/2020) - Strutture e infrastrutture

Mathematical Methods


Videolesson

Lesson n. 1: Sequences
   Outline

   Numerical Sequences

   Convergence of sequences
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Lesson n. 2: Series Vai alla videolezione
Lesson n. 3: Criteria for series convergence
   Outline

   Criteria for series convergence

   Ratio and root test
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Lesson n. 4: Sequences and series of functions
   Outline

   Sequences of functions

   Derivatives and integrals of limits

   Series of functions
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Lesson n. 5: Power Series
   Outline

   Power Series

   Radius of convergence

   Differentiation and integration of power series
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Lesson n. 6: Taylor series
   Outline

   Maclaurin series

   Polynomial approximation

   Taylor expansion of functions
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Lesson n. 7: Fourier series
   Outline

   Trigonometric expansion of functions

   Orthogonal functions

   Behaviour at discontinuties
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Lesson n. 8: Functions of two variables
   Outline

   Functions of two variables

   Graph
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Lesson n. 9: Continuity and Partial derivatives
   Outline

   Limit of functions of two variables

   Continuity

   Partial derivatives

   Higher - order partial derivatives
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Lesson n. 10: Differentiability
   Outline

   Differentiability of functions

   Chain rules

   Directional derivatives
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Lesson n. 11: Functions of three or more variables
   Outline

   Functions of many variables

   Partial derivatives

   Chain Rules

   Cylindrical and spherical transformations
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Lesson n. 12: Extreme of functions
   Outline

   Maxima, minima, saddle points

   Criteria for extrema

   Extrema on the boundary
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Lesson n. 13: Lagrange Multipliere
   Outline

   Extrema under constraints

   Lagrange multipliers
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Lesson n. 14: Double Integrals
   Outline

   Volume approximation by rectangles

   Double integrals

   Integration
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Lesson n. 15: Double integrals over regions
   Outline

   Double integrals over regions

   Iteration of integrals

   Techniques of integration
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Lesson n. 16: Change of variables
   Outline

   Change of variables into polars

   Change of variable formula for polars

   General change of variables

   Jacobians
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Lesson n. 17: Triple Integrals
   Outline

   Triple integrals over a rectangular domain

   Triple integrals over general domains

   Volumes as triple integrals
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Lesson n. 18: Evaluation of triple integrals
   Outline

   Techniques of evaluating triple integrals

   Iteration of integrals
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Lesson n. 19: Applications of integration
   Outline

   Volume of solids

   Mass of solids

   Center of mass

   Moment fo inertia

   Pappus Theorem
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Lesson n. 20: Differential equations
   Outline

   Idea of differential equations

   Separation of variables

   Homogeneous equations
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Lesson n. 21: First order differential equations
   Outline

   First order linear differential equations

   Integrating factor

   Exact equations
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Lesson n. 22: Second order linear differential equations
   Outline

   Second order differential equations

   Homogeneous equations

   Application
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Lesson n. 23: Second order inhomogeneous differential equations
   Outline

   Second order linear inhomogeneous differential equations

   Particular solutions

   Undetermined coefficients
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Lesson n. 24: Higher order differential equations
   Outline

   Higher order linear differential equations

   Homogeneous case

   Inhomogeneous case

   Methods of variation of parameters
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Lesson n. 25: Systems of differential equations
   Outline

   Linear systems of differential equations

   Method of D operators
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