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Integrals of Functions MOOC: Warm-up for EPFL

Covers integrals as the reciprocal function of the derivative and explains displacement integral of velocity and variation of speed and acceleration in rectilinear motion.

Differential Forms Integration

Covers the integration of differential forms on smooth manifolds, including the concepts of closed and exact forms.

Harmonic Forms: Main Theorem

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

Improper Integrals: Convergence and Comparison

Explores improper integrals, convergence criteria, comparison theorems, and solid revolution.

Integration Exercise

Covers the process of calculating new bounds for integration and solving equations involving integrals and derivatives.

Analytic Continuation: Residue Theorem

Covers the concept of analytic continuation and the application of the Residue Theorem to solve for functions.

Definite Integrals: Properties and Interpretation

Covers the calculation of minimum points and the concept of definite integrals.

Cauchy Problem Resolution: Differential Equations Overview

Covers the resolution of a Cauchy problem for a first-order linear differential equation, detailing the construction of its general solution and the determination of initial conditions.

Generalized Integrals: Convergence and Divergence

Explores the convergence and divergence of generalized integrals using comparison methods and variable transformations.

Functions xr, r>0, on 10,1 MOOC: Analysis I MOOC: Analysis I (part 7) : Indefinite and definite integrals, integration (selected chapters)

Covers the properties of functions xr, r>0, on 10,1, including limits and integrals.

Integration Techniques: Change of Variable and Integration by Parts

Explores advanced integration techniques such as change of variable and integration by parts to simplify complex integrals and solve challenging integration problems.

Linear Approximation and Derivative Parametric

Covers linear approximation, parametric derivatives, and differentiability conditions on intervals.

Magnetostatics: Magnetic Field and Force Log in to Mediaspace to watch this video

Covers magnetic fields, Ampère's law, and magnetic dipoles with examples and illustrations.

Mathematical Complements: df or δf Log in to Mediaspace to watch this video

Explores mathematical tools for differentials of functions of multiple variables and their practical applications in thermodynamics and real-life scenarios.

Generalized Integrals: Definition and Applications Log in to Mediaspace to watch this video

Covers the definition and applications of generalized integrals in advanced analysis, including real functions, differential equations, and multiple integrals.

Numerical Integration Methods Log in to Mediaspace to watch this video

Explores numerical integration methods and their application in solving differential equations and simulating physical systems.

Advanced Analysis II: Sequences and Integrals Log in to Mediaspace to watch this video

Explores sequences, integrals, symmetrical functions, differential equations, and the Cauchy problem in advanced analysis.

Advanced Analysis II: Integrals and Functions Log in to Mediaspace to watch this video

Covers advanced topics in analysis, focusing on integrals, functions, and their properties.

Laplacian in Polar and Spherical Coordinates: Derivatives Log in to Mediaspace to watch this video

Covers the Laplacian operator in polar and spherical coordinates, focusing on derivatives and integral calculations.

Functions: Parametric, Integrals, Multi-variable Log in to Mediaspace to watch this video

Covers parametric functions, integrals, and the origin of plasticity in metals.