Università telematica internazionale UNINETTUNO

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

Mathematics I

Language: English
Course description
The course provides an introduction to the mathematical analysis and linear algebra. The course starts with the real numbers and the related one-variable real functions by studying limits, and continuity. Then it approach the core of calculus, differentatial and integral theory for one-variable real functions. The aspects of linear algebra are also included in the course: in particular by studying the linear spaces and the theory and calculus of matrices.
Prerequisites
Analytic geometry on the plane. Elementary functions. Algebraic, trigonometric, exponential and logarithmic equations and inequalities.
Objectives
• Calculus of limits; • Differentianting one-variable real functions, in particular elementary real functions; • Study of the behaviour of any one-variable real function; • Calculus of integrals.
Program
• Elementary logic. Sets, relations, functions. Transformations on graphics. Compositions of functions; inverse functions. • Limits and continuity. Calculus of limits. Discontinuities. Asymptotic. Sequences. Landau symbols. Basic results on limits and on global properties of continuous functions. • Derivatives and derivation rules. Second derivatives and convexity. Differential calculus results (Fermat, Rolle, Lagrange, Cauchy, De L’Hopital Theorems). Taylor approximations. • Primitives and definite integrals. Integration rules. Improper integrals. symbols. Basic results on limits and on global properties of continuous functions.
  • Derivatives and derivation rules. Second derivatives and convexity. Differential calculus results (Fermat, Rolle, Lagrange, Cauchy, De L'Hopital Theorems). Taylor approximations.
  • Primitives and definite integrals. Integration rules. Improper integrals.
  • Book
    • Advanced Engineering Mathematics, A Jeffrey; Harcourt/Academic Press; 2002; • H Anton; Elementary Linear Algebra, Wiley; 1991; • R. Bartle & D. Sherbert, Introduction to Real Analysis, Wiley, 1982; • R. Haggerty, Fundamentals of Mathematical Analysis, Addison-Wesley, 1992; • Linear Algebra: S Lipschutz, McGraw-Hill • Dolciani, M. et al : Introductory Analysis , Houghton Mifflin , Boston , 1991. • Fouad Rajab: Differential and integral, knowledge house (Dar Al Maarfa), Al Cairo, 1972. • Sadek Bshara: Differential and integral calculus, Agency of Modern Publishing, Alexandrina Egypt 1962.
    Professor
    Professor not available
    Video professors
    Prof. Assem Deif - University of Cairo (Cairo - Egypt)
    List of lessons
        •  Lesson n. 1: Introduction 
        •  Lesson n. 2: Real Numbers 
        •  Lesson n. 3: Real functions 
        •  Lesson n. 8: Limits 
        •  Lesson n. 9: Limit theorem 
        •  Lesson n. 10: Continuity 

    Headquarter

    Corso Vittorio Emanuele II, 39
    00186 Roma - ITALIA
    Tax code number: 97394340588
    P.IVA: 13937651001

    Certified mail

    info@pec.uninettunouniversity.net

    Student Secretariat

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

    Videoconferencing

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

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