81. Backward Differentiation Formulas - Scholarpedia Jul 16, 2009 These are numerical integration methods based on Backward differentiation Formulas (BDFs). They are particularly useful for stiff http://www.scholarpedia.org/article/Backward_differentiation_formulas

Backward differentiation formulas From Scholarpedia Bill Gear (2007), Scholarpedia, 2(8):3162. doi:10.4249/scholarpedia.3162 revision #64891 [ link to/cite this article Hosting and maintenance of this article is sponsored by Brain Corporation Curator: Dr. Bill Gear, Chemical Engineering, Princeton University, NJ Contents Backward Differentiation Methods References External links See Also ... edit Backward Differentiation Methods These are numerical integration methods based on Backward Differentiation Formulas (BDFs). They are particularly useful for stiff differential equations and Differential-Algebraic Equations (DAEs). BDFs are formulas that give an approximation to a derivative of a variable at a time in terms of its function values at and earlier times (hence the "backward" in the name). They are derived by forming the -th degree interpolating polynomial approximating the function using , differentiating it, and evaluating it at For example, the linear interpolating polynomial through and is so the approximation to the derivative is the familiar If this is used to obtain a numerical approximation to the ordinary differential equation by replacing the derivative on the left hand side of equation ( ), one obtains the Backward Euler method

82. Derivative -- From Wolfram MathWorld Oct 11, 2010 Performing numerical differentiation is in many ways more . Griewank, A. Principles and Techniques of Algorithmic differentiation. http://mathworld.wolfram.com/Derivative.html

83. NAGC - Differentiation: Hot Topics Therefore, differentiation of curriculum and instruction is one strategy that educators can use to respect and celebrate the variation found in their http://www.nagc.org/index2.aspx?id=978

84. Maths Tutor You use differentiation. Tutorials in differentiating logs and exponentials, sines and cosines, and 3 key rules explained, providing excellent reference http://www.mathtutor.ac.uk/differentiation

swfobject.registerObject("myFlashContent", "9.0.0"); mathtutor home How do you find a rate of change, in any context, and express it mathematically? You use differentiation. Tutorials in differentiating logs and exponentials, sines and cosines, and 3 key rules explained, providing excellent reference material for undergraduate study. Home About Titles Contact ... Integration

85. Mentoring - Austega Curriculum differentiation as an educational provision for gifted students. http://www.austega.com/gifted/provisions/curdifferent.htm

Jump to... Austega Home Gifted Resources Where to start Australian groups ... Other Diversions Curriculum Differentiation An overview of the research into the curriculum differentiation educational strategy CURRICULUM DIFFERENTIATION is a broad term referring to the need to tailor teaching environments and practices to create appropriately different learning experiences for different students. Keirouz (1993) suggests typical procedures in the case of gifted and talented students include: deleting already mastered material from existing curriculum, adding new content, process, or product expectations to existing curriculum, extending existing curriculum to provide enrichment activities, providing course work for able students at an earlier age than usual, and writing new units or courses that meet the needs of gifted students. Maker's model of differentiated curriculum (Maker 1982a, 1982b, 1986) suggests that curriculum needs to be differentiated in terms of: 1. Learning environment:

86. Logarithmic Differentiation Nov 26, 2007 Use the method of logarithmic differentiation to find the derivative of complicated functions. http://www.analyzemath.com/calculus/Differentiation/logarithm_differentiation.ht

Logarithmic Differentiation The method of logarithmic differentiation ,in calculus, uses the properties of logarithmic functions to differentiate complicated functions and functions where the usual formulas of Differentiation do not apply. Several examples with detailed solutions are presented. Web www.analyzemath.com Example 1: Use the method of taking logarithms to find the derivative y ', if y is given by y = x sin x Solution to Example 1 We first note that there is no formula that can be used to differentiate directly this function. The first derivative may be calculated by first taking the natural logarithm of both sides of y = x sin x ln y = ln [ x sin x Use logarithm properties to rewrite the above equation as follows ln y = sin x ln x We now differentiate both sides with respect to x, using the chain rule on the left side and the product rule formula for differentiation on the right side. y ' / y = cos x ln x + sin x (1/x) Multiply both sides by y to obtain y ' = [ cos x ln x + (1/x) sin x ] y y ' = [ cos x ln x + (1/x) sin x ] x sin x Example 2: Find the derivative y ' of function y defined by y = x e (-x Solution to Example 2 We take the logarithms of both sides ln y = ln x + ln e (-x Simplify the term ln e (-x ln y = ln x - x Differentiate both sides with respect to x.

87. WebHome < Projects/CompAD < TWiki The project, developed at the RWTH Aachen University, Germany, aims to put automatic differentiation into the commercial NAGWare Fortran compiler. The AD compiler is available upon request from the author. http://wiki.stce.rwth-aachen.de/bin/view/Projects/CompAD/

@import url('/twiki/pub/TWiki/TWikiTemplates/base.css'); @import url('/twiki/pub/TWiki/PatternSkin/layout.css'); @import url('/twiki/pub/TWiki/PatternSkin/style.css'); @import url('/twiki/pub/TWiki/PatternSkin/colors.css'); @import url("/twiki/pub/TWiki/PatternSkin/print.css"); @import url("/twiki/pub/TWiki/TagMePlugin/tagme.css"); TWiki Projects/CompAD Web WebHome (2009-12-08, Main.gendler) E dit A ttach Tags: create new tag view all tags Compiler-based Automatic Differentiation ( CompAD GOTO: Motivation Overview CompAD-I CompAD-II ... CompAD-III Motivation Automatic differentiation has been proven extremely useful in the context of numerous applications of computational science and engineering requiring numerical methods that are based on derivative information. Refer to for details. Integration of AD into an industrial-strength compiler has the potential of making this technology more robust and efficient as well as user-friendly. The automatic generation of adjoint code is of particular interest to scientists and engineers aiming at a transition from the pure numerical simulation to optimization of the underlying models and/or their parameters. ClickHere for an illustration of the power of adjoint codes.

88. Marketing Strategy- Differentiation: Making A Business Stand Out From Its Compet Aug 9, 2009 One of the most important aspects of an entrepreneurs marketing strategy is differentiation. Learn what it is and how to do it, here. http://www.suite101.com/content/marketing-strategy-differentiation-a136498

89. Web Server Of The TROPICS Team With focus on Parallelization and differentiation of scientific software, Tapenade is an online Automatic differentiation Engine for Fortran programs developed by the TROPICS team at INRIA, France. Along with extensive documentation, description and references, the tool can be downloaded or used online for non-commercial applications. http://www-sop.inria.fr/tropics/

90. TAPENADE An automatic differentiation engine which processes FORTRAN 77, Fortran 95, and C code and generates forward (tangent) and reverse (adjoint) differentiated programs. http://tapenade.inria.fr:8080/

TAPENADE TAPENADE

91. Hoagies' Gifted: Differentiation Of Instruction Feb 24, 2010 Which differentiation techniques do and/or do not work for gifted children in schools? Find research, methods, and examples here http://www.hoagiesgifted.org/differentiation.htm

Click Shop Hoagies' and our affiliate links before you shop... Thanks! Search Hoagies Web Reading lists and links! Support Hoagies' Page Support Hoagies' Page! Click on Shop Hoagies' Page before you shop your favorite on-line stores, year-round and especially at the holidays. Thanks for your support! Donations Your donations also help keep Hoagies' Gifted Education Page on-line. Support Hoagies' Page! Resources! Hoagies' Gifted Education Page is the "All Things Gifted" resource for parents, educators, administrators, counselors, psychologists, and even gifted kids and teens themselves! Differentiation of Instruction "1. Gifted learners must be given stimulating educational experiences appropriate to their level of ability if they are to realize their potential. 2. Each person has the right to learn and to be provided challenges for learning at the most appropriate level where growth proceeds most effectively." National Association for Gifted Children, "Why Should Gifted Education Be Supported?" NAGC

92. Differentiation - Elsevier differentiation of eukaryotes at the molecular level, and the use of transgenic and targeted mutagenesis approaches to problems of differentiation are of particular interest to the journal. Journal of the International Society of differentiation. http://www.elsevier.com/wps/find/journaldescription.cws_home/717204/description#

93. Differentiation In A Reader S Workshop Scholastic.com Third grade teacher Marissa Ochoa shares ideas on meeting students individual needs. New and first year teachers will learn how to challenge their students http://www2.scholastic.com/browse/article.jsp?id=3747938

94. Magmatic Differentiation Any process that causes magma composition to change is called magmatic differentiation. Over the years, various process have been suggested to explain the http://www.tulane.edu/~sanelson/geol212/magmadiff.htm

Geology 212 Petrology Prof. Stephen A. Nelson Magmatic Differentiation Chemical Variation in Rock Suites Soon after geologists began doing chemical analyses of igneous rocks they realized that rocks emplaced in any given restricted area during a short amount of geologic time were likely related to the same magmatic event. Evidence for some kind of relationship between the rocks, and therefore between the magmas that cooled to form the rocks came from plotting variation diagrams. A variation diagram is a plot showing how each oxide component in a rock varies with some other oxide component. Because SiO usually shows the most variation in any given suite of rocks, most variation diagrams plot the other oxides against SiO as shown in the diagram here, although any other oxide could be chosen for plotting on the x-axis. Plots that show relatively smooth trends of variation of the components suggested that the rocks might be related to one another through some process. Of course, in order for the magmas to be related to one another, they must also have been intruded or erupted within a reasonable range of time. Plotting rocks of Precambrian age along with those of Tertiary age may show smooth variation, but it is unlikely that the magmas were related to one another. If magmas are related to each other by some processes, that process would have to be one that causes magma composition to change. Any process that causes magma composition to change is called

95. The MAD Project Automatic differentiation addon for the TOMLAB optimization package for Matlab, developed by Cranfield University, UK. Site contains links to related publications and User Guide, however the package is commercially distributed by TOMLAB. http://www.amorg.co.uk/AD/MAD/index.html

The MAD (MATLAB Automatic Differentiation) Project Investigators: Dr Shaun Forth , Cranfield University (Shrivenham Campus), School of Defence Technology, UK Introduction Automatic Differentiation (AD) software tools are available for a range of programming languages (see list at www.autodiff.org ), but progress on developing AD tools for MATLAB has been much slower. Project Aim: In this project we aim to carefully implement the standard (and hopefully not so standard) algorithms of AD by operator overloading in MATLAB. We will pay particular attention to achieving good performance and robustness so that the software can be used on genuine applications and not just carefully coded test cases. Progress: We have implemented the standard forward mode of AD via operator overloading in the fmad class with linear combinations of directional derivatives performed by the optimized derivvec class. Details may be found in An Efficient Implementation of Forward Mode Automatic Differentiation in MATLAB and the User Guide In collaboration with the TOMLAB company , we have integrated MAD into TOMLAB's suite of optimization software for MATLAB.

96. Differential Geometry Of Curves: Information From Answers.com Answers.com encyclopedia entry on differential geometry. http://www.answers.com/topic/differential-geometry-of-curves

var isReferenceAnswers = true; BodyLoad('s'); On this page Library Animal Life Health History, Politics, Society ... Technology Differential geometry of curves Wikipedia: Differential geometry of curves Home Library Miscellaneous Wikipedia This article considers only curves in Euclidean space. Most of the notions presented here have analogues for curves in Riemannian and pseudo-Riemannian manifolds . For a discussion of curves in an arbitrary topological space , see the main article on curves Differential geometry of curves is the branch of geometry that deals with smooth curves in the plane and in the Euclidean space by methods of differential and integral calculus Starting in antiquity, many concrete curves have been thoroughly investigated using the synthetic approach. Differential geometry takes another path: curves are represented in a parametrized form , and their geometric properties and various quantities associated with them, such as the curvature and the arc length , are expressed via derivatives and integrals using vector calculus . One of the most important tools used to analyze a curve is the Frenet frame , a moving frame that provides a coordinate system at each point of the curve that is "best adapted" to the curve near that point.

97. Differential Geometry - Wikipedia, The Free Encyclopedia Wikipedia article on this mathematical discipline that uses the methods of differential and integral calculus, as well as linear and multilinear algebra, to study problems in geometry. http://en.wikipedia.org/wiki/Differential_geometry

Differential geometry From Wikipedia, the free encyclopedia Jump to: navigation search A triangle immersed in a saddle-shape plane (a hyperbolic paraboloid ), as well as two diverging ultraparallel lines. Differential geometry is a mathematical discipline that uses the methods of differential and integral calculus , as well as linear and multilinear algebra , to study problems in geometry . The theory of plane and space curves and of surfaces in the three-dimensional Euclidean space formed the basis for its initial development in the eighteenth and nineteenth century. Since the late nineteenth century, differential geometry has grown into a field concerned more generally with geometric structures on differentiable manifolds . It is closely related to differential topology , and to the geometric aspects of the theory of differential equations Grigori Perelman 's proof of the Poincaré conjecture using the techniques of Ricci flow demonstrated the power of the differential-geometric approach to questions in topology and highlighted the important role played by the analytic methods. Differential geometry of surfaces already captures many of the key ideas and techniques characteristic of the field.

98. Chris Athorne's Home Page The site describes research activities of the differential equations group in the mathematics department at the university of Glasgow, UK, and provides some resources of a general nature. http://www.maths.gla.ac.uk/~ca/

This is not a Still Life Perspective Life 2005 -6 Life 2006 -7 Life 2008-9 ... Winterreise

99. Differential Equations In Banach Algebras Fuchsian Singularities of Linear Ordinary Differential Equations in Banach Algebras. By Gerald Albrecht in Wuppertal. http://www.gwfa.de/math/Fuchs_1996.pdf

100. Analytic Differential Equations Lectures on Analytic Differential Equations by Sergei Yakovenko at the Weizmann Institute. http://www.wisdom.weizmann.ac.il/~yakov/thebook.pdf

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