Euler's formula

Formal sciences
Mathematics
Analysis
Complex analysis

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Complex Numbers: Introduction and Operations

Introduces complex numbers and their forms, including Cartesian, polar, and exponential forms, and explains how to find the argument of a complex number.

Taylor's Formula in Two Variables

Explores Taylor's formula in two variables, emphasizing its application and importance for functions of a single variable.

Harmonic Motion: Static Displacement

Explores harmonic motion, displacement, amplitude, velocity, and frequency behavior in mechanical systems.

Complex Numbers: Polar Form

Explains the polar form of complex numbers and Euler's formula in the complex plane.

Polar Coordinates: Jacobian Matrix and Examples

Covers polar coordinates, the Jacobian matrix, and examples of calculating areas in polar coordinates.

Single-Phase Sinusoidal Circuits: Complex Numbers

Explains complex numbers in single-phase sinusoidal circuits and their geometric representation, Euler's formula, and complex exponential functions.

Absolute Value and Complex Numbers

Covers the absolute value function, complex numbers, Euler's formula, and trigonometry applications.

Set Union: Basics and Properties

Introduces set union, its properties, and examples with Euler course contest participants.

Nth Derivative

Explores obtaining n-th derivatives through a recursive process and the regularity of functions defined by power series.