Università telematica internazionale UNINETTUNO

Ingegneria civile e ambientale (Academic Year 2019/2020) - Costruzioni, Estimo e Topografia

Calculus 1


Enseignant vidéo: Abdelilah Dahlane - Université Cadi Ayyad (Marrakech - Morocco), Youssef el From - Université Cadi Ayyad (Marrakech - Morocco)

Leçon vidéo

Leçon n. 1: Introduction
   Real number and complex numbers

   Power

   Roots

   Notational conventions in fields

   Polynomials
Go to this lesson
Leçon n. 2: Vectors
   Vectors

   Equal vectors

   Addition of two vectors

   Subtraction of two vectors

   Coordinates of a vector

   Norm of a vector
Go to this lesson
Leçon n. 3: Inner Product
   Angle between two vectors

   Inner product of vectors

   Orthogonal vectors
Go to this lesson
Leçon n. 4: Cross Product
   Cross product of vectors

   An important formula
Go to this lesson
Leçon n. 5: Vector Spaces
   Definition

   Theorem
Go to this lesson
Leçon n. 6: Matrices I
   Operations with Matrix

   Diagonal matrix

   The trace of a square matrix

   Scalar multiplication

   Identity matrix
Go to this lesson
Leçon n. 7: Bases I
   Definition of linear combination

   Definition of linear independence

   Bases
Go to this lesson
Leçon n. 8: Matrices II
   Definition

   Properties

   Inverse of a 2x2 matrix

   Types of matrices
Go to this lesson
Leçon n. 9: Linear Systems
   Linear Systems

   Homogeneous linear system
Go to this lesson
Leçon n. 10: Determinants
   Definition of determinant

   Addition of two rows or columns

   Determinants and systems
Go to this lesson
Leçon n. 11: Linear Transformations
   Definition

   Examples
Go to this lesson
Leçon n. 12: Bases II
   Extension of Sub-Basis

   Solution
Go to this lesson
Leçon n. 13: Orthonormal Bases
   Definition

   Gram-Schmidt process
Go to this lesson
Leçon n. 14: Matrix of a Transformation
   Matrix of a linear transformation

   Application
Go to this lesson
Leçon n. 15: Eigenvalues
   Definition

   Theorem

   Cayley
Go to this lesson
Leçon n. 16: Eigenvectors
   Recall the definition

   Eigenspaces

   Linear independence of eigenvectors
Go to this lesson
Leçon n. 17: Diagonalization
   Definition

   Theorem
Go to this lesson
Leçon 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)
Go to this lesson
Leçon n. 19: Circle
   Distance between two points on the plans

   Parametric equations of a circle

   Tangent of a circle

   Relative positions
Go to this lesson
Leçon n. 20: Conic Sections I
   The parabola

   The tangent of the parabola
Go to this lesson
Leçon n. 21: Conic Sections II
   Ellipse

   Parametrical equations

   Eccentricity

   Hyperbola
Go to this lesson
Leçon n. 22: 3D-Space
   Three dimensional space

   Midpoint in 3 dimensions

   Straight line
Go to this lesson
Leçon n. 23: Planes in Space I
   Equation of a plane in space

   Parametric equation of a plane
Go to this lesson
Leçon n. 24: Planes in Space II
   Intersection of two planes in space

   Geometric illustration
Go to this lesson
Leçon n. 25: Spheres and Cylinders
   A cylinder in space

   Plane
Go to this lesson
Leçon n. 26: Introduction
   Differential and Integral Calculus

   Limit

   Squaring of the parabola
Go to this lesson
Leçon n. 27: Real Numbers
   Sets and relations

   The set R

   Algebraic and order properties

   Inequalities

   Neighborhood

   Cartesian product
Go to this lesson
Leçon n. 28: Real Functions
   The Function as a Concept

   Characteristics of f

   Domain and range of a function
Go to this lesson
Leçon n. 29: Classifications of functions
   The Function

   Even Function

   Odd Function

   Monotonically increasing

   Periodic Function

   New Equation
Go to this lesson
Leçon n. 30: Basic functions
   Power function

   Exponential function

   Trigonometric functions

   Trigonometric identities

   Hyperbolic identities
Go to this lesson
Leçon n. 31: Composite functions
   Composite functions in engineering

   Method of constructing fog
Go to this lesson
Leçon n. 32: Inverse functions
   Steps to obtain f

   Logarithmic Function

   Solving the equation

   Theorem
Go to this lesson
Leçon n. 33: Limits
   Limit of a sequence

   Limit of a Function

   One?sided limit
Go to this lesson
Leçon n. 34: Limit theorem
   Basic theorems

   Squeeze Theorem
Go to this lesson
Leçon n. 35: Continuity
   Definition of Continuity

   Continuity Theorems

   Continuity on an Interval

   The Extreme Value Theorem
Go to this lesson
Leçon n. 36: Differentiation
   Definition of the Derivative

   Differentiability on an Interval

   Differentiation Laws

   Derivatives of Basic Functions
Go to this lesson
Leçon 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
Go to this lesson
Leçon n. 38: Applications to the derivative
   Mean Value Theorem and Taylor Formula

   Approximations
Go to this lesson
Leçon n. 39: Indeterminate forms and l'hospital rule
   Indeterminate quantities

   Cauchy mean value theorem

   L?Hospital Rule

   Convexity, Concavity and Extrema

   Convexity and Concavity
Go to this lesson
Leçon 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
Go to this lesson
Leçon n. 41: Curve sketching
   Mechanical techniques for drawing graphs

   Graphical Properties
Go to this lesson
Leçon n. 42: Antiderivative or the indefinite integral
   Notion of the Indefinite integral

   Remarks about the Antiderivative

   Properties of the indefinite integral
Go to this lesson
Leçon n. 43: Integration by substitution
   Theorem

   By Completing the Square
Go to this lesson
Leçon n. 44: Integration by parts
   Theorem

   Reduction Formula
Go to this lesson
Leçon n. 45: Trigonometric and hyperbolic integrals
   The equivalence of trigonometric and hyperbolic integrals

   Rules for even and odd powers

   When do the rules fail
Go to this lesson
Leçon n. 46: Trigonometric and hyperbolic substitutions
   Types of substitutions

   By using a reduction formula

   A second method
Go to this lesson
Leçon n. 47: Integration by partial fractions
   Partial fractions representation

   Some Integrals
Go to this lesson
Leçon n. 48: The definite integral
   The Definite Integral as a Limit to Riemann Sum

   Riemann Sum

   Theorem
Go to this lesson
Leçon n. 49: Properties of the definite integral
   Properties of integrable functions

   Useful theorems on parity

   Integral Mean value theorem
Go to this lesson
Leçon 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
Go to this lesson

Siège de l'Université

Corso Vittorio Emanuele II, 39
00186 Roma - ITALIA
C.F.: 97394340588
P.IVA: 13937651001

Certified mail

info@pec.uninettunouniversity.net

Secrétariat des Etudiants

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

Vidéoconférence

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

Avez-vous besoin d’informations plus détaillées?

Donnez-nous vos données


Demandez des informations