**Are you an EPFL student looking for a semester project?**

Work with us on data science and visualisation projects, and deploy your project as an app on top of GraphSearch.

Lecture# Analytical Trajectories: Key Ingredients

Description

This lecture delves into the concept of analytical trajectories, focusing on key ingredients such as critical points, inequalities, and analyticity. The instructor explains how to identify critical points, analyze inequalities, and leverage analyticity to understand trajectories. Through a series of examples and derivations, students learn how to apply these concepts in analytical scenarios.

Login to watch the video

Official source

This page is automatically generated and may contain information that is not correct, complete, up-to-date, or relevant to your search query. The same applies to every other page on this website. Please make sure to verify the information with EPFL's official sources.

Instructor

In course

MATH-301: Ordinary differential equations

Le cours donne une introduction à la théorie des EDO, y compris existence de solutions locales/globales, comportement asymptotique, étude de la stabilité de points stationnaires et applications, en pa

Related lectures (4)

Related concepts (69)

Analytical Solutions: EDO

Explores the analytical solutions of ordinary differential equations, emphasizing the identification and solving process for various EDO types.

Measure Spaces: O-Finite and Probability Measures

Explores o-finite and finite measure spaces, probability measures, and inequalities, concluding with LP space completeness.

Harmonic Forms and Riemann Surfaces

Explores harmonic forms on Riemann surfaces, covering uniqueness of solutions and the Riemann bilinear identity.

Harmonic Forms: Main Theorem

Explores harmonic forms on Riemann surfaces and the uniqueness of solutions to harmonic equations.

Mathematics is an area of knowledge that includes the topics of numbers, formulas and related structures, shapes and the spaces in which they are contained, and quantities and their changes. These topics are represented in modern mathematics with the major subdisciplines of number theory, algebra, geometry, and analysis, respectively. There is no general consensus among mathematicians about a common definition for their academic discipline. Most mathematical activity involves the discovery of properties of abstract objects and the use of pure reason to prove them.

In contemporary education, mathematics education—known in Europe as the didactics or pedagogy of mathematics—is the practice of teaching, learning, and carrying out scholarly research into the transfer of mathematical knowledge. Although research into mathematics education is primarily concerned with the tools, methods, and approaches that facilitate practice or the study of practice, it also covers an extensive field of study encompassing a variety of different concepts, theories and methods.

The history of mathematics deals with the origin of discoveries in mathematics and the mathematical methods and notation of the past. Before the modern age and the worldwide spread of knowledge, written examples of new mathematical developments have come to light only in a few locales. From 3000 BC the Mesopotamian states of Sumer, Akkad and Assyria, followed closely by Ancient Egypt and the Levantine state of Ebla began using arithmetic, algebra and geometry for purposes of taxation, commerce, trade and also in the patterns in nature, the field of astronomy and to record time and formulate calendars.

Social inequality occurs when resources in a given society are distributed unevenly, typically through norms of allocation, that engender specific patterns along lines of socially defined categories of persons. It poses and creates a gender gap between individuals that limits the accessibility that women have within society. The differentiation preference of access to social goods in the society is brought about by power, religion, kinship, prestige, race, ethnicity, gender, age, sexual orientation, and class.

The philosophy of mathematics is the branch of philosophy that studies the assumptions, foundations, and implications of mathematics. It aims to understand the nature and methods of mathematics, and find out the place of mathematics in people's lives. The logical and structural nature of mathematics makes this branch of philosophy broad and unique. The philosophy of mathematics has two major themes: mathematical realism and mathematical anti-realism. The origin of mathematics is of arguments and disagreements.