# Management Engineering (Academic Year 2020/2021) - Economics path

## Slides

 Real number and complex numbers    Power    Roots    Notational conventions in fields    Polynomials Vectors    Equal vectors    Addition of two vectors    Subtraction of two vectors    Coordinates of a vector    Norm of a vector Angle between two vectors    Inner product of vectors    Orthogonal vectors Cross product of vectors    An important formula Definition    Theorem Operations with Matrix    Diagonal matrix    The trace of a square matrix    Scalar multiplication    Identity matrix Definition of linear combination    Definition of linear independence    Bases Definition    Properties    Inverse of a 2x2 matrix    Types of matrices Linear Systems    Homogeneous linear system Definition of determinant    Addition of two rows or columns    Determinants and systems Definition    Examples Extension of Sub-Basis    Solution Definition    Gram-Schmidt process Matrix of a linear transformation    Application Definition    Theorem    Cayley Recall the definition    Eigenspaces    Linear independence of eigenvectors Definition    Theorem Vector form of a straight line    General equation of a line    Mid-point    Perpendicular Bisector    vector equation of a line (I) Distance between two points on the plans    Parametric equations of a circle    Tangent of a circle    Relative positions The parabola    The tangent of the parabola Ellipse    Parametrical equations    Eccentricity    Hyperbola Three dimensional space    Midpoint in 3 dimensions    Straight line Equation of a plane in space    Parametric equation of a plane Intersection of two planes in space    Geometric illustration A cylinder in space    Plane Differential and Integral Calculus    Limit    Squaring of the parabola Sets and relations    The set R    Algebraic and order properties    Inequalities    Neighborhood    Cartesian product The Function as a Concept    Characteristics of f    Domain and range of a function The Function    Even Function    Odd Function    Monotonically increasing    Periodic Function    New Equation Power function    Exponential function    Trigonometric functions    Trigonometric identities    Hyperbolic identities Composite functions in engineering    Method of constructing fog Steps to obtain f    Logarithmic Function    Solving the equation    Theorem Limit of a sequence    Limit of a Function    One?sided limit Basic theorems    Squeeze Theorem Definition of Continuity    Continuity Theorems    Continuity on an Interval    The Extreme Value Theorem Definition of the Derivative    Differentiability on an Interval    Differentiation Laws    Derivatives of Basic Functions Derivative of the Inverse Function    Derivative of the Composite Function    Derivative of Implicit and parametric Functions    Repeated Differentiation Mean Value Theorem and Taylor Formula    Approximations Indeterminate quantities    Cauchy mean value theorem    L?Hospital Rule    Convexity, Concavity and Extrema    Convexity and Concavity Definition of a Local Extrema    1th test of Local Extrema    2nd test of Local Extrema    Definition of the Absolute Extrema Mechanical techniques for drawing graphs    Graphical Properties Notion of the Indefinite integral    Remarks about the Antiderivative    Properties of the indefinite integral Theorem    By Completing the Square Theorem    Reduction Formula The equivalence of trigonometric and hyperbolic integrals    Rules for even and odd powers    When do the rules fail Types of substitutions    By using a reduction formula    A second method Partial fractions representation    Some Integrals The Definite Integral as a Limit to Riemann Sum    Riemann Sum    Theorem Properties of integrable functions    Useful theorems on parity    Integral Mean value theorem The fundamental theorem    Improper integrals    Applications to the Integral    Calculating Areas    Solid of Revolution    Length of Curves    Surface Areas of Revolution

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