Free Online College Courses Mathematics Archives Calculus Resources On-Line Welcome to the Calculus Resources On-line area of the Mathematics Archives. This area contains information and links to numerous Internet resources, which could be used for teaching and learning of calculus. If you would like to suggest adding information to this area, or have comments or questions, please contact Przemyslaw Bogacki, the calculus moderator. Initiatives, Projects and Programs These are alphabetized by institution's name (pilot sites are listed under the original developer institution). Appalachian State University, Business Calculus A new Business Calculus course has been developed with the focus on business problems which can be efficiently resolved by the appropriate use of mathematics and technology working hand-in-hand. Carleton University This web site, maintained by the Carleton University Math & Stat Department, features interactive tests for first-year calculus students. Cornell University Duke University Pilot Sites Five Colleges, Calculus in Context Pilot Site Wiley
Calculating the Distance to the Horizon For Any Game Home Up Site Map Assumptions | Method 1 | Method 2 Method 1 | Method 2 This is all based on the assumption that the horizon is the point on the world's surface at which the line of sight of the viewer, whatever their height, becomes parallel (tangential) to the surface of the world, and meets the surface of the world (so that the viewer cannot see any further than it). Note that I do not mention units in any of the equations on this page. Assumptions | Method 2 For a right-angled triangle: Where: R is the longest side (the hypotenuse), x and y are the other two sides. Using this equation on the triangle in the figure above, the longest side is the radius of the planet plus the height of the observer (r + h) , and the other two sides are d and r . Or, re-arranged: Or: So the total distance to the horizon is given by: This equation will work for any size world, and any height of observer. Assumptions | Method 1 Back to My Roleplaying Page .
PlanetMath matematika.ba Math on the Web: Mathematics by Classifications Mathematical Awareness Month Math in the Media [Monthly magazine from the AMS] AMS Feature Column [Monthly essay from the AMS] MAA Online Columns Collection [Peterson, Devlin, Colm, Bressoud, Adams and Narayan, Sandifer, Morgan, Bogomolny, Peterson, Pegg] Frequently Asked Questions (FAQ) about Mathematics (The Sci.Math FAQ Team) Favorite Mathematical Constants , by Steven Finch; An online book and extensive collection of the author's "favorite" special numbers. Simon Plouffe's Tables of Mathematical Constants to millions of decimal places. The Erdos Component Page at Oakland U (Rochester, MI USA) - Information on the graph of collaboration in mathematics (J. John Baez's "This week's finds in mathematical physics" Math for Poets, Understanding Mathematics, and Gödel, Escher, Bach (J. International Congress of Mathematicians -- ICM 2002 Beijing Announcements International Congress of Mathematicians -- ICM 1998 Berlin Proceedings International Congress of Mathematicians -- ICM 1994 Zürich Abstracts
Mu-Ency -- The Encyclopedia of the Mandelbrot Set at MROB A second-order embedded Julia set This is a picture from the Mandelbrot Set, one of the most well-known fractal images in the world. (Click it for a larger version). Here are some entries from Mu-Ency: Mandelbrot Set: The mathematical definition. More Pictures: Some entries with pictures of parts of the Mandelbrot Set are: R2, Cusp, Embedded Julia set, 2-fold Embedded Julia set, 4-fold Embedded Julia set, Paramecia, R2.C(0), R2.C(1/3), R2.1/2.C(1/2), R2t series, Seahorse Valley, Delta Hausdorff Dimension, Exponential Map, Reverse Bifurcation. You can also look up specific terms in the index. Coordinates of the image above: Center: -1.769 110 375 463 767 385 + 0.009 020 388 228 023 440 i Width (and height): 0.000 000 000 000 000 160 Algorithm: distance estimator Iterations: 10000 An ASCII art Mandelbrot set: vL , '*m-` -m/**\a, ... _,/#, ]),., ., '#F-.F~*^' '`'*~*eae/: . -__/* '`_* )_. ic,_ ./- T\a 7F*-~~*a, /` dL \_,\F^ '\` .*` .,___\____._/*^* R2a .m~ ` ' :*r(, .
Encyclopedia of Mathemaics Matematička takmičenja u Srbiji www.divulgamat.net Quaternion Graphical representation of quaternion units product as 90°-rotation in 4D-space, ij = k, ji = −k, ij = −ji History[edit] Quaternion plaque on Brougham (Broom) Bridge, Dublin, which says: Here as he walked by on the 16th of October 1843 Sir William Rowan Hamilton in a flash of genius discovered the fundamental formula for quaternion multiplicationi2 = j2 = k2 = ijk = −1 & cut it on a stone of this bridge Quaternion algebra was introduced by Hamilton in 1843.[7] Important precursors to this work included Euler's four-square identity (1748) and Olinde Rodrigues' parameterization of general rotations by four parameters (1840), but neither of these writers treated the four-parameter rotations as an algebra.[8][9] Carl Friedrich Gauss had also discovered quaternions in 1819, but this work was not published until 1900.[10][11] i2 = j2 = k2 = ijk = −1, into the stone of Brougham Bridge as he paused on it. On the following day, Hamilton wrote a letter to his friend and fellow mathematician, John T.
Interactive Mathematics Diferencijalne jednacine prvog reda | Milan Milošević | Svet nauke Kratak pregled metoda resavanja najpoznatijih tipova obicnih diferencijalnih jednacina prvog reda 1.1 Razdvojene promenljive U opštem slučaju: 1.2 Homogena diferencijalna jednačina Smenom: polazna jednačina postaje: tj. diferencijalna jednačina oblika Primedba: diferencijalna jednačina oblika: gde je a, b, c, A, B, C = const, može se svesti na jednačinu oblika . 1o) Ako je smenom: jednačina postaje: Sistem jednačina: ima rešenje po a i bpa jednačina postaje: a to je jednačina oblika . 20) Neka je , tj. gde je k konstanta. , gde je u nova nepoznata f-ja promenljive x. odnosno jednačina oblika . 1.3 Linearna diferencijalna jednačina Ako je jednačina se naziva homogena linearna diferencijalna jednačina. 1o) Homogena jednačina: za postaje: tj. jednačina oblika čije je rešenje: Može se uzeti kao rešenje jednačine . 2o) Da bi rešili pretpostavimo ako se jn-e i zamene u dobija se: odnosno: pa je opšte rešenje jednačine : U eksplicitnom obliku opšte rešenje jednačine dato je kao: 1.4 Bernulijeva jednačina Gde je , za Za Smenom