Euler's formula

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Related lectures (29)

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Complex Exponential: De Moivre's Formula

Covers De Moivre's formula for finding roots of complex numbers and the concept of complex exponential.

Inverse Element for Multiplication

Covers the inverse element for multiplication and introduces the Euler and Moivre formulas in complex numbers.

Wave Equations: Vibrating String

Explores the wave equation for a vibrating string and its numerical solution using finite difference formulas and the Newmark scheme in MATLAB/GNU Octave.

Introduction to Complex Numbers

Introduces complex numbers, their representations, formulas, and algebraic equations.

Eigenstate Thermalization Hypothesis

Explores the Eigenstate Thermalization Hypothesis in quantum systems, emphasizing the random matrix theory and the behavior of observables in thermal equilibrium.

Interpretation of Taylor's Formula: An Example

Covers the interpretation of Taylor's formula through an example, focusing on developing limited series for sin(x) around a=0.

Gradient and Taylor Formula

Introduces gradient, Laplacian, Taylor formula, polynomial approximations, extrema, and Taylor series expansions in multiple variables.

Complex Numbers: Algebraic Structure

Explores the algebraic structure and properties of complex numbers, including Euler's and Moivre's formulas.

Complex Numbers: Polar Form

Explores complex numbers in polar form, Euler's formula, and coordinate transformation.

Derivatives and Convexity

Explores derivatives, local extrema, and convexity in functions, including Taylor's formula and function compositions.