Acta EruditorumActa Eruditorum (from Latin: Acts of the Erudite) was the first scientific journal of the German-speaking lands of Europe, published from 1682 to 1782. Acta Eruditorum was founded in 1682 in Leipzig by Otto Mencke, who became its first editor, with support from Gottfried Leibniz in Hanover, who contributed 13 articles over the journal's first four years. It was published by Johann Friedrich Gleditsch, with sponsorship from the Duke of Saxony, and was patterned after the French Journal des savants and the Italian Giornale de'letterati.
Stationary pointIn mathematics, particularly in calculus, a stationary point of a differentiable function of one variable is a point on the graph of the function where the function's derivative is zero. Informally, it is a point where the function "stops" increasing or decreasing (hence the name). For a differentiable function of several real variables, a stationary point is a point on the surface of the graph where all its partial derivatives are zero (equivalently, the gradient is zero).
Saddle pointIn mathematics, a saddle point or minimax point is a point on the surface of the graph of a function where the slopes (derivatives) in orthogonal directions are all zero (a critical point), but which is not a local extremum of the function. An example of a saddle point is when there is a critical point with a relative minimum along one axial direction (between peaks) and at a relative maximum along the crossing axis. However, a saddle point need not be in this form.
Secant lineIn geometry, a secant is a line that intersects a curve at a minimum of two distinct points. The word secant comes from the Latin word secare, meaning to cut. In the case of a circle, a secant intersects the circle at exactly two points. A chord is the line segment determined by the two points, that is, the interval on the secant whose ends are the two points. A straight line can intersect a circle at zero, one, or two points. A line with intersections at two points is called a secant line, at one point a tangent line and at no points an exterior line.
Mathematics educationIn contemporary education, mathematics education—known in Europe as the didactics or pedagogy of mathematics—is the practice of teaching, learning, and carrying out scholarly research into the transfer of mathematical knowledge. Although research into mathematics education is primarily concerned with the tools, methods, and approaches that facilitate practice or the study of practice, it also covers an extensive field of study encompassing a variety of different concepts, theories and methods.
Derivative testIn calculus, a derivative test uses the derivatives of a function to locate the critical points of a function and determine whether each point is a local maximum, a local minimum, or a saddle point. Derivative tests can also give information about the concavity of a function. The usefulness of derivatives to find extrema is proved mathematically by Fermat's theorem of stationary points. The first-derivative test examines a function's monotonic properties (where the function is increasing or decreasing), focusing on a particular point in its domain.
Guillaume de l'HôpitalGuillaume François Antoine, Marquis de l'Hôpital (ɡijom fʁɑ̃swa ɑ̃twan maʁki də lopital; sometimes spelled L'Hospital; 1661 – 2 February 1704), also known as Guillaume-François-Antoine Marquis de l'Hôpital, Marquis de Sainte-Mesme, Comte d'Entremont, and Seigneur d'Ouques-la-Chaise, was a French mathematician. His name is firmly associated with l'Hôpital's rule for calculating limits involving indeterminate forms 0/0 and ∞/∞.
Linear approximationIn mathematics, a linear approximation is an approximation of a general function using a linear function (more precisely, an affine function). They are widely used in the method of finite differences to produce first order methods for solving or approximating solutions to equations. Given a twice continuously differentiable function of one real variable, Taylor's theorem for the case states that where is the remainder term.
