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Analysis I

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Lectures in this MOOC (216)

Inflection Points MOOC: Analysis I MOOC: Analysis I (part 6) : Study of functions, limited developments

Explores inflection points in functions, emphasizing the role of the second derivative.

Integration of Rational Functions MOOC: Analysis I MOOC: Analysis I (part 7) : Indefinite and definite integrals, integration (selected chapters)

Covers the integration of rational functions, decomposition into irreducible factors, and step-by-step integration examples.

Integration Techniques MOOC: Analysis I MOOC: Analysis I (part 7) : Indefinite and definite integrals, integration (selected chapters)

Covers the development of integration techniques and the application of generalized integrals.

Integrals of Type 1 MOOC: Analysis I MOOC: Analysis I (part 7) : Indefinite and definite integrals, integration (selected chapters)

Covers the definition of integrals of type 1 and the importance of continuity.

General Case MOOC: Analysis I MOOC: Analysis I (part 6) : Study of functions, limited developments

Explores determining local maximums, minimums, and inflection points of functions.

Immediate Consequences MOOC: Analysis I MOOC: Analysis I (part 5): Continuous and derivable functions, the derivative function

Explores the immediate consequences of f' = 0 and monotonicity on intervals.

Limit Calculations Applications MOOC: Analysis I MOOC: Analysis I (part 6) : Study of functions, limited developments

Demonstrates efficient limit calculations using Taylor expansions and basic algebraic operations.

Counterexample to Induction Theorem MOOC: Analysis I (part 1): Prelude, basic concepts, real numbers MOOC: Analysis I

Explores a counterexample to the induction principle, demonstrating a property of natural numbers.

Discussion of Function f MOOC: Analysis I MOOC: Analysis I (part 6) : Study of functions, limited developments

Covers the discussion of the function f(x) = |2x-1| -x²+1 on a given domain and its continuity, zeros, and derivatives.

Preparation: Polynomial Integration MOOC: Analysis I MOOC: Analysis I (part 7) : Indefinite and definite integrals, integration (selected chapters)

Covers the preparation for polynomial integration with examples and emphasis on polynomial division.

Implications of the Mean Value Theorem MOOC: Analysis I MOOC: Analysis I (part 5): Continuous and derivable functions, the derivative function

Explores the implications of the mean value theorem and how to predict function values using derivatives.

Developing Cosine Composition MOOC: Analysis I MOOC: Analysis I (part 6) : Study of functions, limited developments

Explores the composition of Taylor expansions through an example, simplifying complex compositions to identify essential terms.

Developing Taylor's Theorem MOOC: Analysis I MOOC: Analysis I (part 6) : Study of functions, limited developments

Covers Taylor's theorem, power series, and representing functions by their Taylor series.

Basic Notions MOOC: Analysis I (part 1): Prelude, basic concepts, real numbers MOOC: Analysis I

Covers the basic concepts of sets, functions, and number systems.

Derivability and Extrema Analysis MOOC: Analysis I MOOC: Analysis I (part 6) : Study of functions, limited developments

Explores derivability at specific points and the analysis of local extrema.

Prelude: Linking Mathematics and Course Content MOOC: Warm-up for EPFL MOOC: Analysis I (part 1): Prelude, basic concepts, real numbers MOOC: Analysis I

Introduces the course content by linking familiar mathematics with upcoming topics.

Real Number Sequences: Introduction MOOC: Analysis I MOOC: Analysis I (part 3) : Real number sequences I and II

Introduces real number sequences, limits, and their properties.

Convexity and Concavity MOOC: Analysis I MOOC: Analysis I (part 6) : Study of functions, limited developments

Covers the definitions of convexity, concavity, stationary points, and inflection points.

Integrals: Indefinite and Definite MOOC: Analysis I MOOC: Analysis I (part 7) : Indefinite and definite integrals, integration (selected chapters)

Discusses indefinite and definite integrals, their connection, and integration methods.

Untitled MOOC: Analysis I MOOC: Analysis I (part 3) : Real number sequences I and II

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