Università telematica internazionale UNINETTUNO

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

Calculus 1


Video professors: Assem Deif - University of Cairo (Cairo - Egypt), Michael Lambrou - University of Crete (Heraklion/Crete - Greece)

Videolesson

Lesson n. 1: Introduction
   Real number and complex numbers

   Power

   Roots

   Notational conventions in fields

   Polynomials
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Lesson n. 2: Vectors
   Vectors

   Equal vectors

   Addition of two vectors

   Subtraction of two vectors

   Coordinates of a vector

   Norm of a vector
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Lesson n. 3: Inner Product
   Angle between two vectors

   Inner product of vectors

   Orthogonal vectors
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Lesson n. 4: Cross Product
   Cross product of vectors

   An important formula
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Lesson n. 5: Vector Spaces
   Definition

   Theorem
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Lesson n. 6: Matrices I
   Operations with Matrix

   Diagonal matrix

   The trace of a square matrix

   Scalar multiplication

   Identity matrix
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Lesson n. 7: Bases I
   Definition of linear combination

   Definition of linear independence

   Bases
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Lesson n. 8: Matrices II
   Definition

   Properties

   Inverse of a 2x2 matrix

   Types of matrices
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Lesson n. 9: Linear Systems
   Linear Systems

   Homogeneous linear system
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Lesson n. 10: Determinants
   Definition of determinant

   Addition of two rows or columns

   Determinants and systems
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Lesson n. 11: Linear Transformations
   Definition

   Examples
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Lesson n. 12: Bases II
   Extension of Sub-Basis

   Solution
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Lesson n. 13: Orthonormal Bases
   Definition

   Gram-Schmidt process
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Lesson n. 14: Matrix of a Transformation
   Matrix of a linear transformation

   Application
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Lesson n. 15: Eigenvalues
   Definition

   Theorem

   Cayley
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Lesson n. 16: Eigenvectors
   Recall the definition

   Eigenspaces

   Linear independence of eigenvectors
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Lesson n. 17: Diagonalization
   Definition

   Theorem
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Lesson n. 18: Straight Lines
   Vector form of a straight line

   General equation of a line

   Mid-point

   Perpendicular Bisector

   vector equation of a line (I)
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Lesson n. 19: Circle
   Distance between two points on the plans

   Parametric equations of a circle

   Tangent of a circle

   Relative positions
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Lesson n. 20: Conic Sections I
   The parabola

   The tangent of the parabola
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Lesson n. 21: Conic Sections II
   Ellipse

   Parametrical equations

   Eccentricity

   Hyperbola
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Lesson n. 22: 3D-Space
   Three dimensional space

   Midpoint in 3 dimensions

   Straight line
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Lesson n. 23: Planes in Space I
   Equation of a plane in space

   Parametric equation of a plane
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Lesson n. 24: Planes in Space II
   Intersection of two planes in space

   Geometric illustration
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Lesson n. 25: Spheres and Cylinders
   A cylinder in space

   Plane
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Lesson n. 26: Introduction
   Differential and Integral Calculus

   Limit

   Squaring of the parabola
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Lesson n. 27: Real Numbers
   Sets and relations

   The set R

   Algebraic and order properties

   Inequalities

   Neighborhood

   Cartesian product
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Lesson n. 28: Real Functions
   The Function as a Concept

   Characteristics of f

   Domain and range of a function
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Lesson n. 29: Classifications of functions
   The Function

   Even Function

   Odd Function

   Monotonically increasing

   Periodic Function

   New Equation
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Lesson n. 30: Basic functions
   Power function

   Exponential function

   Trigonometric functions

   Trigonometric identities

   Hyperbolic identities
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Lesson n. 31: Composite functions
   Composite functions in engineering

   Method of constructing fog
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Lesson n. 32: Inverse functions
   Steps to obtain f

   Logarithmic Function

   Solving the equation

   Theorem
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Lesson n. 33: Limits
   Limit of a sequence

   Limit of a Function

   One?sided limit
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Lesson n. 34: Limit theorem
   Basic theorems

   Squeeze Theorem
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Lesson n. 35: Continuity
   Definition of Continuity

   Continuity Theorems

   Continuity on an Interval

   The Extreme Value Theorem
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Lesson n. 36: Differentiation
   Definition of the Derivative

   Differentiability on an Interval

   Differentiation Laws

   Derivatives of Basic Functions
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Lesson n. 37: Derivative of the inverse, composite and implicit functions
   Derivative of the Inverse Function

   Derivative of the Composite Function

   Derivative of Implicit and parametric Functions

   Repeated Differentiation
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Lesson n. 38: Applications to the derivative
   Mean Value Theorem and Taylor Formula

   Approximations
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Lesson n. 39: Indeterminate forms and l'hospital rule
   Indeterminate quantities

   Cauchy mean value theorem

   L?Hospital Rule

   Convexity, Concavity and Extrema

   Convexity and Concavity
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Lesson n. 40: Maximum and minimum values of a function
   Definition of a Local Extrema

   1th test of Local Extrema

   2nd test of Local Extrema

   Definition of the Absolute Extrema
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Lesson n. 41: Curve sketching
   Mechanical techniques for drawing graphs

   Graphical Properties
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Lesson n. 42: Antiderivative or the indefinite integral
   Notion of the Indefinite integral

   Remarks about the Antiderivative

   Properties of the indefinite integral
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Lesson n. 43: Integration by substitution
   Theorem

   By Completing the Square
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Lesson n. 44: Integration by parts
   Theorem

   Reduction Formula
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Lesson n. 45: Trigonometric and hyperbolic integrals
   The equivalence of trigonometric and hyperbolic integrals

   Rules for even and odd powers

   When do the rules fail
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Lesson n. 46: Trigonometric and hyperbolic substitutions
   Types of substitutions

   By using a reduction formula

   A second method
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Lesson n. 47: Integration by partial fractions
   Partial fractions representation

   Some Integrals
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Lesson n. 48: The definite integral
   The Definite Integral as a Limit to Riemann Sum

   Riemann Sum

   Theorem
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Lesson n. 49: Properties of the definite integral
   Properties of integrable functions

   Useful theorems on parity

   Integral Mean value theorem
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Lesson n. 50: Fundamental theorem for calculus -
   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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