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This is a preparatory course for Statistics and Financial Mathematics that also provides a solid foundation for other teaching subjects that incorporate mathematics. |
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A basic understanding of mathematics is necessary: powers and their properties, equations and inequalities of the 1° and 2°, irrational, logorhythmic and exponential, fractional inequalities. |
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The course aims to provide the basic foundation in mathematics necessary for Degree Courses in the Economic sector, with a particular emphasis on Mathematical Analysis, Linear Algebra and Classical Analytical Geometry |
Sets and logical propositions. Operations and relationships between sets. Set product. Applications among sets: compound and inverse, images and counterimages, several formulae relative to the applications. Finite and infinite sets, countable and non countable. Calculus combinations: dispositions, permutations, combinations, dispositions and combinations with repetition. Triangle of Tartaglia and the binomial of Newton. Various formulae. Elementary Probability. Natural numbers and the principal of induction. Integers, rational and real numbers. Properties of real numbers: orders and operations. Continuity of R and its consequences: fundamental theorems. Separate and contiguous classes.
Intervals in R. Theorem of Cantor. Topology of lines. Points of accumulation and the theorem of Bolzano-Weierstrass. Decimal writing in real numbers.
Real Functions of real variables. Graphs. Monotone, even, odd and periodical functions. Inversions. Goniometrics. Continuous functions and relative theorems. Fundamental theorems of connection and unity; their corollaries. Limits. Case of sum, product, quotient in finite and infinite cases. Compounds. Limits of the more usual functions. Fundamental theories on limits. Case of successions; the number and that of Nepero.
Exponential and logorhythmic functions; noteable limits. Notions of the infinite and the infinitesmal. Proprieties and principals relative to infinite and infinitesmal orders.
Derivatives. Meaning and rules of calculation. Crescenza, relative maximum and minimum to absolutes and links to derivatives. Fundamental theorems of Rolle, Cauchy and Lagrange and their consequences. Limits of the derivative and theorem of L’Hopital. Linear approximation. Differentials. Formulae of Taylor. Local and global convex and concave forms. Necessary or sufficient conditions.
Primitive sets and the defined whole. Fundamental Theorems and the rules of calculus.
Linear Algebra: space vectors, linear dependence, subspaces and their properties. Bases and dimensions. R2 and R3 spaces. Generative systems. Matrices. Linear applications. Determining factors.
Elementary Analytical Plane Geometry. Elementary Plane and Space Topology.
Functions in many variables. Continuity and limits. Partial and directional derivatives. Free and confined maximum and minimum concepts.
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It is suggested that the exercises connected to the videolessons be carried out. During the course group and individual exercises will be organized. |
Prof.
Assem Deif
- University of Cairo (Cairo - Egypt)
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