MOOC Massive Open Online Courses (Academic Year 2018/2019)

Mathematics I

Enseignant vidéo: Abdelilah Dahlane - Université Cadi Ayyad (Marrakech - Morocco)

Leçon n. 1: Introduction Differential and Integral Calculus Limit Squaring of the parabola		Assem Deif
Leçon n. 2: Real Numbers Sets and relations The set R Algebraic and order properties Inequalities Neighborhood Cartesian product		Assem Deif
Leçon n. 3: Real Functions The Function as a Concept Characteristics of f Domain and range of a function		Assem Deif
Leçon n. 4: Classifications of functions The Function Even Function Odd Function Monotonically increasing Periodic Function New Equation		Assem Deif
Leçon n. 5: Basic functions Power function Exponential function Trigonometric functions Trigonometric identities Hyperbolic identities		Assem Deif
Leçon n. 6: Composite functions Composite functions in engineering Method of constructing fog		Assem Deif
Leçon n. 7: Inverse functions Steps to obtain f Logarithmic Function Solving the equation Theorem		Assem Deif
Leçon n. 8: Limits Limit of a sequence Limit of a Function One?sided limit		Assem Deif
Leçon n. 9: Limit theorem Basic theorems Squeeze Theorem		Assem Deif
Leçon n. 10: Continuity Definition of Continuity Continuity Theorems Continuity on an Interval The Extreme Value Theorem		Assem Deif
Leçon n. 11: Differentiation Definition of the Derivative Differentiability on an Interval Differentiation Laws Derivatives of Basic Functions		Assem Deif
Leçon n. 12: 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		Assem Deif
Leçon n. 13: Applications to the derivative Mean Value Theorem and Taylor Formula Approximations		Assem Deif
Leçon n. 14: Indeterminate forms and l'hospital rule Indeterminate quantities Cauchy mean value theorem L?Hospital Rule Convexity, Concavity and Extrema Convexity and Concavity		Assem Deif
Leçon n. 15: 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		Assem Deif
Leçon n. 16: Curve sketching Mechanical techniques for drawing graphs Graphical Properties		Assem Deif
Leçon n. 17: Antiderivative or the indefinite integral Notion of the Indefinite integral Remarks about the Antiderivative Properties of the indefinite integral		Assem Deif
Leçon n. 18: Integration by substitution Theorem By Completing the Square		Assem Deif
Leçon n. 19: Integration by parts Theorem Reduction Formula		Assem Deif
Leçon n. 20: Trigonometric and hyperbolic integrals The equivalence of trigonometric and hyperbolic integrals Rules for even and odd powers When do the rules fail		Assem Deif
Leçon n. 21: Trigonometric and hyperbolic substitutions Types of substitutions By using a reduction formula A second method		Assem Deif
Leçon n. 22: Integration by partial fractions Partial fractions representation Some Integrals		Assem Deif
Leçon n. 23: The definite integral The Definite Integral as a Limit to Riemann Sum Riemann Sum Theorem		Assem Deif
Leçon n. 24: Properties of the definite integral Properties of integrable functions Useful theorems on parity Integral Mean value theorem		Assem Deif
Leçon n. 25: 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		Assem Deif

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MOOC Massive Open Online Courses (Academic Year 2018/2019)

Mathematics I

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MOOC Massive Open Online Courses (Academic Year 2018/2019)

Mathematics I

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