An advanced mathematics course offered by EPFLx
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.
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.
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
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!