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    Mathematics I



    Prof. Assem Deif
    (University of Cairo (Cairo - Egypt))
    Content language:Italian
    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.
    Appointed teaching professor
    Professor not available
    Video Professor
    Prof. Assem Deif - University of Cairo (Cairo - Egypt)
    List of video lessons
    Lesson n. 1: Introduction  Go to this videolesson
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    		 Assem Deif
    Lesson n. 2: Real Numbers  Go to this videolesson
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    Lesson n. 3: Real Functions  Go to this videolesson
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    Lesson n. 5: Basic functions  Go to this videolesson
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    Lesson n. 6: Composite functions  Go to this videolesson
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    Lesson n. 7: Inverse functions  Go to this videolesson
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    Lesson n. 8: Limits  Go to this videolesson
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    Lesson n. 9: Limit theorem  Go to this videolesson
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    Lesson n. 10: Continuity  Go to this videolesson
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    Lesson n. 11: Differentiation  Go to this videolesson
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    Lesson n. 16: Curve sketching  Go to this videolesson
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    Lesson n. 19: Integration by parts  Go to this videolesson
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    Lesson n. 23: The definite integral  Go to this videolesson
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