Heat Equation from Partial Differential Equations An Introduction (Strauss) These notes were written based on a number of courses I taught over the years in the U.S.‚ Greece and the U.K. They form the core material for an undergraduate course on Markov chains in discrete time. There are‚ of course‚ dozens of good books on the topic. The only new thing here is that I give emphasis to probabilistic methods as soon as possible. Also‚ I introduce stationarity before even talking about state classification
Premium Partial differential equation Probability theory
Band broadening theory (Van Deemter equation) It is well recognized now that column band broadening originates from three main sources: 1. multiple path of an analyte through the column packing; 2. molecular diffusion; 3. effect of mass transfer between phases. In 1956 J.J. Van Deemter introduced the equation which combined all three sources and represented them as the dependence of the theoretical plate height (HETP) on the mobile phase linear velocity. Originally‚ it was introduced for gas
Premium Chromatography Gas chromatography Analytical chemistry
------------------------------------------------- Equations and Problem-Solving * An airplane accelerates down a runway at 3.20 m/s2 for 32.8 s until is finally lifts off the ground. Determine the distance travelled before take-off. ------------------------------------------------- Solutions Given: a = +3.2 m/s2 | t = 32.8 s | vi = 0 m/s | | Find:d = ?? | d = VI*t + 0.5*a*t2 d = (0 m/s)*(32.8 s) + 0.5*(3.20 m/s2)*(32.8 s)2 d = 1720 m ------------------------------------------------- Equations and Problem-Solving
Premium Acceleration Kinematics
27 4 d e (2) 3 (b) If the length of the rectangle is x m‚ and the area is A m2‚ express A in terms of x only. (1) (c) What are the length and width of the rectangle if the area is to be a maximum? (3) (Total 6 marks) 5. (a) Solve the equation x2 – 5x + 6 = 0. (b) Find the coordinates of the points where the graph of y = x2 – 5x + 6 intersects the x-axis. Working: Answers: (a) ………………………………………….. (b) .................................................................. (Total 4 marks)
Premium Dimension René Descartes Cartesian coordinate system
breaking of chemical bonds. There are several different types of chemical reactions and more than one way of classifying them. Here are some common reaction types. However‚ if you are asked to name the main 4‚ 5 or 6 types of chemical reactions‚ here is how they are categorized. Direct Combination or Synthesis Reaction In a synthesis reaction two or more chemical species combine to form a more complex product. A + B ? AB The combination of iron and sulfur to form iron (II) sulfide is an example of a
Premium Chemical reaction Hydrogen Chemistry
Mirror and Magnification Equations The mirror equation expresses the quantitative relationship between the object distance (do)‚ the image distance (di)‚ and the focal length (f). The equation is stated as follows: [pic] The magnification equation relates the ratio of the image distance and object distance to the ratio of the image height (hi) and object height (ho). The magnification equation is stated as follows: [pic] These two equations can be combined to yield information about the
Premium Optics Length
quadratic equation is an equation that has a second-degree term and no higher terms. A second-degree term is a variable raised to the second power‚ like x2. When you graph a quadratic equation‚ you get a parabola‚ and the solutions to the quadratic equation represent where the parabola crosses the x-axis. A quadratic equation can be written in the form: quadratic equation‚ where a‚ b‚ and c are numbers (a ≠0)‚ and x is the variable. x is a solution (or a root) if it satisfies the equation ax2 +
Premium Quadratic equation Real number
Chemical Reactions and Equations Chemical Reaction: The transformation of chemical substance into another chemical substance is known as Chemical Reaction. For example: rusting of iron‚ setting of milk into curd‚ digestion of food‚ respiration‚ etc. In chemical reaction new substance is formed which is completely different in properties from the original substance‚ so in a chemical reaction chemical change takes place. Following are the signs of chemical reaction: (a) Change of state of substance
Premium Chemical reaction Iron Hydrogen
Geo Test #1eCalculators PermittedName________________________ Time: 70 minutes100 points 1) Solve the system of simultaneous linear equations . 2)Find the equation of the line that is perpendicular to the line with equation and that passes through the point with coordinates (2‚ 1). What is the perpendicular distance from the origin to the line with equation ? 3) Solve the inequality 2 4)Consider the vectors a = i − j + k‚ b = i + 2 j + 4k and c = 2i − 5 j − k. (a)Given that c = ma
Premium Analytic geometry Line Euclidean geometry
Archie Unleashed examines several data sets and techniques for handling these data and defines a simple spreadsheet to do the calculations. Section 1. The Archie Equation -water saturation as a decimal fraction. -Resistivity of the 100% water saturated rock. -Resistivity of the rock-fluid system. Equation 1.1 was empirically derived by G. E. Archie while working for Shell. This work was reported in in his famous 1942 paper. He plotted SW versus the ratio Rt/Ro (the
Premium Density