Quadratic equations Derives the equation for the roots of a general quadratic equation.
Complex Functions [latex][/latex]All our arithmetic functions gracefully extend from the one-dimensional number line into the 2-dimensional \(\mathbb{C}\)-plane. We will introduce the functions that operate on complex arguments.
Complex Numbers Instead of projecting the future merits of complex numbers, we will introduce them in an intuitive way. We draw a parallel to negative numbers that have been universally accepted around the same time.
Laurent Series Named after Pierre Alphonse Laurent, a French mathematician and Military Officer, published in the series 1843. The Laurent series is a representation of a complex function f(z) as a series. Unlike the Taylor series which expresses \(f(z)\) as a series of terms with non-negative powers of \(z\), a Laurent series includes terms with negative powers. …
Partial Fraction Expansion Oliver Heaviside (1850-1925), was an English electrical engineer, mathematician and physicist who among many things adapted complex numbers to the study of electrical circuits. He introduced a method to decompose rational function of polynomials as they occur when using the Laplace transform to solve differential equations. Whenever the denominator of a rational function can be …
Complex Arithmetic Formulas Complex arithmetic formulas written in LaTex used in the HP-41 program. Includes everything from power to trigonometric functions.
Euler’s formula Proofs Euler's formula using the MacLaurin series for sine and cosine. Introduces Euler's identify and Cartesian and Polar coordinates.