# هندسة تكنولوجيات المعلومات والاتصالات (السنة الدراسية 2019/2020) - هندسة تكنولوجيات المعلومات والاتصالات (Helwan University)

## الشرائح

 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 Contents    Complex function theory    Working with functions and integrals    A transform to the rescue    Using complex numbers Contents    Representing complex numbers    Exponents and conjugates    Applications to roots and powers    Functions of a complex variable Contents    Mappings from the complex plane to itself    Limits of a complex variable    Complex derivatives    Polynomial functions Contents    Partial derivatives    Recognizing holomorphic functions    Vector calculus    Harmonic functions Contents    Polynomials and series    Absolute convergence    Radius of convergence    Analytic functions Contents    Paths and curves    The velocity integral    Integrals along curves    Length estimates Contents    Fundamental theorem of calculus    Regions in the plane    Existence of primitives    Integrating a holomorphic function Contents    Existence of primitives    A singular integrand    Integrating around circles    Deforming a contour Contents    Taylor series    Derivatives of holomorphic functions    Series of reciprocals    Convergence in an annulus Contents    Laurent coefficients    Simple closed contours    Cauchy’s Theorem for boundaries    Computing integrals using residues Contents    Isolated singularities    Poles and zeros    Computing and using residues    Trigonometric integrals Contents    Fundamental theorem of algebra    Rational functions    More integrals involving roots of unity    More trigonometric integrals Contents    Indented contours    Semicircular estimates    Logarithmic integrals    Summation of series Contents    Basic properties    Further examples    Transforms of derivatives    Solving an initial value problem Contents    Limiting values and integrals    New transforms from old    Some special integrals    Applications to finding inverse transforms Contents    Inverting rational functions    Known examples of inverse transforms    Contour integral interpretation    Applying the inversion theorem Contents    The set of test functions    Linear functionals    Distributions as limits    Derivatives of distributions Contents    Operations on distributions    Differentiation and limits    Principal value integrals    Infinite sums and series Contents    Motivating examples    Convolution as a product    Spaces of integrable functions    Convolution with a distribution Contents    First examples    Spectral analysis    Derivatives and products    Transform of a convolution Contents    The inversion theorem    Proof of inversion    Using a convolution    The Schwartz space Contents    Convergence in Schwartz space    Tempered distributions    The generalized Fourier transform    Generalized inversion Contents    Laplace versus Fourier    Laplace convolution    An application to beam bending    Laplace inversion Contents    Another differential equation    Solution by series    Laurent coefficients    Laplace transform of an integral Contents    A partial differential equation    The heat kernel    Final example    Acknowledgements

### مقر الجامعة

Corso Vittorio Emanuele II, 39
00186 Roma - ITALIA
الرقم الضريبي: 97394340588
P.IVA: 13937651001

### البريد الألكتروني المسجل

info@pec.uninettunouniversity.net

### مكتب الطلاب

tel: +39 06 692076.70
tel: +39 06 692076.71
e-mail: info@uninettunouniversity.net

### عقد المؤتمرات عبر الفيديو

Library 1st floor: 90.147.90.157
Meeting Room 5th floor: 90.147.90.158

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