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Euler's identity is the equality e^1 = -1, where e is Euler's number and i is the imaginary unit. It is a special case of Euler's formula and a famous example of mathematical beauty, as it connects five fundamental constants and shows profound symmetry.
Learn how to use matrices and vectors to collect partial derivatives of multivariable functions. Compare different notational conventions and layouts for scalar-by-vector, vector-by-scalar, vector-by-vector, and scalar-by-matrix derivatives.
This web page contains formulae for finite and infinite sums of various functions, including exponential, trigonometric, and harmonic series. It also provides links to related topics such as integrals, binomial theorem, and polygamma functions.
Calculus is the mathematical study of continuous change, developed by Isaac Newton and Gottfried Wilhelm Leibniz in the 17th century. The article traces the origins and precursors of calculus in ancient Egypt, Greece, China, India, and medieval Europe.
Euler's formula is a mathematical formula that relates the trigonometric functions and the complex exponential function. It has many applications in complex analysis, physics, chemistry, and engineering, and can be proved using different methods such as differentiation, power series, or polar coordinates.
Vector calculus is a branch of mathematics that deals with differentiation and integration of vector fields in three-dimensional space. It has applications in physics, engineering, geometry, and differential equations. Learn about vector fields, vector algebra, vector operators, and integral theorems.
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