Back to Results (3d)

EPFLx: Analyse I (partie 7) : Intégrales indéfinies et définies, intégration (chapitres choisis)

by École polytechnique fédérale de Lausanne

Analyse I, partie 7: Intégration

An advanced mathematics course offered by EPFLx

Course Description

Welcome to "Analyse I, partie 7: Intégration," the final installment in the Analyse I series. This course focuses on the crucial concept of integration in calculus. Through comprehensive lectures and exercises, students will delve deep into the world of indefinite and definite integrals, exploring their properties, applications, and various integration techniques.

What Students Will Learn

Indefinite and definite integrals
Properties of definite integrals
The Mean Value Theorem for integrals
The Fundamental Theorem of Calculus
Various integration techniques
Integration of special functions
Generalized (improper) integrals
Integration of rational functions

Prerequisites

Students should have completed the previous parts of the Analyse I MOOC (parts 1-6). A strong foundation in calculus and mathematical reasoning is essential.

Course Coverage

Indefinite and definite integrals
Properties of definite integrals
Mean Value Theorem for integrals
Fundamental Theorem of Calculus
Integration techniques
Integration of trigonometric functions
Applications to numerical series
Integration of Taylor series
Integration of power series
Integration of piecewise continuous functions
Generalized (improper) integrals
Integration of rational functions

Who This Course Is For

Mathematics majors seeking to deepen their understanding of calculus
Science and engineering students who require advanced integration skills
Educators looking to enhance their knowledge of integration techniques
Self-learners passionate about advanced mathematics

Real-World Applications

Physics: Calculating work, energy, and fluid dynamics
Engineering: Analyzing structural loads and electrical circuits
Economics: Computing consumer and producer surplus
Statistics: Working with probability distributions
Computer Graphics: Rendering complex 3D shapes
Finance: Calculating present and future values of investments

Syllabus

Chapter 11: Indefinite and Definite Integrals

11.1 The indefinite integral
11.2 The definite integral
11.3 Properties of definite integrals
11.4 Mean Value Theorem
11.5 Fundamental Theorem of Calculus
11.6 First examples
11.7 Integration methods
11.7.5 Examples

Chapter 12: Integration (selected chapters)

12.1 Integration of Taylor series
12.2 Integration of power series
12.3 Integration of piecewise continuous functions
12.4 Generalized (improper) integrals
12.5 Examples of generalized integrals
12.6 Convergence of numerical series
12.7 Integration of rational functions
12.8 The general case

This course offers a comprehensive exploration of integration, equipping students with powerful mathematical tools applicable across various scientific and professional fields. Don't miss this opportunity to master one of the most fundamental concepts in calculus!

Similar Courses