Lectures related to Master of Financial Engineering: Program Overview

Complex Numbers: Introduction and Operations

Covers the introduction and operations of complex numbers in physics and engineering applications.

Computational Science and Engineering: Master Program Overview

Outlines the Master in Computational Science and Engineering program at EPFL, detailing its structure, projects, and career opportunities for graduates.

Integration by Substitution

Explores integration by substitution with proofs and examples on anti-derivatives and function equivalence.

Implicit Functions Theorem

Covers the Implicit Functions Theorem, explaining how equations can define functions implicitly.

Advanced Analysis II: Derivatives and Functions

Covers the review of derivatives and functions, including the concept of chain rule and graphical representation.

Derivatives and Continuity in Mathematics

Covers derivatives, continuity, Rolle's Theorem, function examples, and extrema.

Implicit Functions and Taylor Polynomials

Covers implicit functions, Taylor polynomials, and tangent equations.

Applications of Theorems

Demonstrates the practical application of theorems in calculus through two clever examples.

Bernoulli's Hospital Rule

Covers the statement of the Bernoulli's Hospital Rule and its application.

Calculus: Derivatives and Integrals

Covers the fundamentals of calculus, focusing on derivatives and integrals.

Introduction to Mathematics for Engineers

Introduces the purpose of mastering mathematics and calculation tools for engineers, emphasizing the need to think methodically and rigorously.

Hyperbolic Functions: Tangent and Cotangent

Covers the definitions and examples of hyperbolic tangent and cotangent functions.

Differential Equations: Implicit Solutions

Explores implicit solutions for differential equations and their applications in different scenarios.

Partial Derivatives and Derivability

Explains partial and directional derivatives, and functions' derivability.

Laplacian in Polar and Spherical Coordinates: Derivatives

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

Partial Derivatives: Definitions and Applications

Explores the definitions and applications of partial derivatives in functions of several variables, emphasizing the importance of specifying the choice of variables.

Implicit Differentiation: Basics

Covers the basics of implicit differentiation, focusing on techniques and applications.

General Mathematics I: Derivatives and Tangents

Explores derivatives, tangents, and elementary function rules in general mathematics.

Taylor Polynomial: Order 2

Presents the solution to finding the second-order Taylor polynomial of a function.

Limits and Derivatives in Multivariable Functions

Covers limits and derivatives in multivariable functions, focusing on continuity, partial derivatives, and the gradient.