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

Calculus 1



Videolesson

Lesson n. 1: Introduction
   Real number and complex numbers
   Power
   Roots
   Notational conventions in fields
   Polynomials 		Go to this lesson Michael Lambrou
Lesson 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 Michael Lambrou
Lesson n. 3: Inner Product
   Angle between two vectors
   Inner product of vectors
   Orthogonal vectors 		Go to this lesson Michael Lambrou
Lesson n. 4: Cross Product
   Cross product of vectors
   An important formula 		Go to this lesson Michael Lambrou
Lesson n. 5: Vector Spaces
   Definition
   Theorem 		Go to this lesson Michael Lambrou
Lesson n. 6: Matrices I
   Operations with Matrix
   Diagonal matrix
   The trace of a square matrix
   Scalar multiplication
   Identity matrix 		Go to this lesson Michael Lambrou
Lesson n. 7: Bases I
   Definition of linear combination
   Definition of linear independence
   Bases 		Go to this lesson Michael Lambrou
Lesson n. 8: Matrices II
   Definition
   Properties
   Inverse of a 2x2 matrix
   Types of matrices 		Go to this lesson Michael Lambrou
Lesson n. 9: Linear Systems
   Linear Systems
   Homogeneous linear system 		Go to this lesson Michael Lambrou
Lesson n. 10: Determinants
   Definition of determinant
   Addition of two rows or columns
   Determinants and systems 		Go to this lesson Michael Lambrou
Lesson n. 11: Linear Transformations
   Definition
   Examples 		Go to this lesson Michael Lambrou
Lesson n. 12: Bases II
   Extension of Sub-Basis
   Solution 		Go to this lesson Michael Lambrou
Lesson n. 13: Orthonormal Bases
   Definition
   Gram-Schmidt process 		Go to this lesson Michael Lambrou
Lesson n. 14: Matrix of a Transformation
   Matrix of a linear transformation
   Application 		Go to this lesson Michael Lambrou
Lesson n. 15: Eigenvalues
   Definition
   Theorem
   Cayley 		Go to this lesson Michael Lambrou
Lesson n. 16: Eigenvectors
   Recall the definition
   Eigenspaces
   Linear independence of eigenvectors 		Go to this lesson Michael Lambrou
Lesson n. 17: Diagonalization
   Definition
   Theorem 		Go to this lesson Michael Lambrou
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) 		Go to this lesson Michael Lambrou
Lesson 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 Michael Lambrou
Lesson n. 20: Conic Sections I
   The parabola
   The tangent of the parabola 		Go to this lesson Michael Lambrou
Lesson n. 21: Conic Sections II
   Ellipse
   Parametrical equations
   Eccentricity
   Hyperbola 		Go to this lesson Michael Lambrou
Lesson n. 22: 3D-Space
   Three dimensional space
   Midpoint in 3 dimensions
   Straight line 		Go to this lesson Michael Lambrou
Lesson n. 23: Planes in Space I
   Equation of a plane in space
   Parametric equation of a plane 		Go to this lesson Michael Lambrou
Lesson n. 24: Planes in Space II
   Intersection of two planes in space
   Geometric illustration 		Go to this lesson Michael Lambrou
Lesson n. 25: Spheres and Cylinders
   A cylinder in space
   Plane 		Go to this lesson Michael Lambrou
Lesson n. 26: Introduction
   Differential and Integral Calculus
   Limit
   Squaring of the parabola 		Go to this lesson Assem Deif
Lesson n. 27: Real Numbers
   Sets and relations
   The set R
   Algebraic and order properties
   Inequalities
   Neighborhood
   Cartesian product 		Go to this lesson Assem Deif
Lesson n. 28: Real Functions
   The Function as a Concept
   Characteristics of f
   Domain and range of a function 		Go to this lesson Assem Deif
Lesson n. 29: Classifications of functions
   The Function
   Even Function
   Odd Function
   Monotonically increasing
   Periodic Function
   New Equation 		Go to this lesson Assem Deif
Lesson n. 30: Basic functions
   Power function
   Exponential function
   Trigonometric functions
   Trigonometric identities
   Hyperbolic identities 		Go to this lesson Assem Deif
Lesson n. 31: Composite functions
   Composite functions in engineering
   Method of constructing fog 		Go to this lesson Assem Deif
Lesson n. 32: Inverse functions
   Steps to obtain f
   Logarithmic Function
   Solving the equation
   Theorem 		Go to this lesson Assem Deif
Lesson n. 33: Limits
   Limit of a sequence
   Limit of a Function
   One?sided limit 		Go to this lesson Assem Deif
Lesson n. 34: Limit theorem
   Basic theorems
   Squeeze Theorem 		Go to this lesson Assem Deif
Lesson n. 35: Continuity
   Definition of Continuity
   Continuity Theorems
   Continuity on an Interval
   The Extreme Value Theorem 		Go to this lesson Assem Deif
Lesson n. 36: Differentiation
   Definition of the Derivative
   Differentiability on an Interval
   Differentiation Laws
   Derivatives of Basic Functions 		Go to this lesson Assem Deif
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 		Go to this lesson Assem Deif
Lesson n. 38: Applications to the derivative
   Mean Value Theorem and Taylor Formula
   Approximations 		Go to this lesson Assem Deif
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 		Go to this lesson Assem Deif
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 		Go to this lesson Assem Deif
Lesson n. 41: Curve sketching
   Mechanical techniques for drawing graphs
   Graphical Properties 		Go to this lesson Assem Deif
Lesson 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 Assem Deif
Lesson n. 43: Integration by substitution
   Theorem
   By Completing the Square 		Go to this lesson Assem Deif
Lesson n. 44: Integration by parts
   Theorem
   Reduction Formula 		Go to this lesson Assem Deif
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 		Go to this lesson Assem Deif
Lesson n. 46: Trigonometric and hyperbolic substitutions
   Types of substitutions
   By using a reduction formula
   A second method 		Go to this lesson Assem Deif
Lesson n. 47: Integration by partial fractions
   Partial fractions representation
   Some Integrals 		Go to this lesson Assem Deif
Lesson n. 48: The definite integral
   The Definite Integral as a Limit to Riemann Sum
   Riemann Sum
   Theorem 		Go to this lesson Assem Deif
Lesson n. 49: Properties of the definite integral
   Properties of integrable functions
   Useful theorems on parity
   Integral Mean value theorem 		Go to this lesson Assem Deif
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 		Go to this lesson Assem Deif