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

## Slides

 Outline    Numerical Sequences    Convergence of sequences Outline    Criteria for series convergence    Ratio and root test Outline    Sequences of functions    Derivatives and integrals of limits    Series of functions Outline    Power Series    Radius of convergence    Differentiation and integration of power series Outline    Maclaurin series    Polynomial approximation    Taylor expansion of functions Outline    Trigonometric expansion of functions    Orthogonal functions    Behaviour at discontinuties Outline    Functions of two variables    Graph Outline    Limit of functions of two variables    Continuity    Partial derivatives    Higher - order partial derivatives Outline    Differentiability of functions    Chain rules    Directional derivatives Outline    Functions of many variables    Partial derivatives    Chain Rules    Cylindrical and spherical transformations Outline    Maxima, minima, saddle points    Criteria for extrema    Extrema on the boundary Outline    Extrema under constraints    Lagrange multipliers Outline    Volume approximation by rectangles    Double integrals    Integration Outline    Double integrals over regions    Iteration of integrals    Techniques of integration Outline    Change of variables into polars    Change of variable formula for polars    General change of variables    Jacobians Outline    Triple integrals over a rectangular domain    Triple integrals over general domains    Volumes as triple integrals Outline    Techniques of evaluating triple integrals    Iteration of integrals Outline    Volume of solids    Mass of solids    Center of mass    Moment fo inertia    Pappus Theorem Outline    Idea of differential equations    Separation of variables    Homogeneous equations Outline    First order linear differential equations    Integrating factor    Exact equations Outline    Second order differential equations    Homogeneous equations    Application Outline    Second order linear inhomogeneous differential equations    Particular solutions    Undetermined coefficients Outline    Higher order linear differential equations    Homogeneous case    Inhomogeneous case    Methods of variation of parameters Outline    Linear systems of differential equations    Method of D operators

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