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  Mathematics Archives - Topics in Mathematics - Differential Geometry
Differential Geometry and Quantum Physics, SFB 288, TU Berlin
GRTensor II Calculation of tensor components on curved spacetimes specified in terms of a metric or set of basis vectors.
Lecture notes for the course in Differential Geometry
archives.math.utk.edu /topics/differentialGeom.html   (318 words)

  Differential equation - Wikipedia, the free encyclopedia
In mathematics, a differential equation is an equation in which the derivatives of a function appear as variables.
Differential equations have many applications in physics and chemistry, and are widespread in mathematical models explaining biological, social, and economic phenomena.
The study of differential equations is a wide field in both pure and applied mathematics.
en.wikipedia.org /wiki/Differential_equation   (239 words)

 Differential geometry and topology - Open Encyclopedia   (Site not responding. Last check: 2007-10-20)
Differential geometry is the study of geometry using calculus.
Initially and up to the middle of the nineteenth century, differential geometry was studied from the extrinsic point of view: curves, surfaces were considered as lying in a Euclidean space of higher dimension (for example a surface in an ambient space of three dimensions).
A vector field is a function from a manifold to the disjoint union of its tangent spaces (this union is itself a manifold known as the tangent bundle), such that at each point, the value is an element of the tangent space at that point.
open-encyclopedia.com /Differential_geometry   (982 words)

 Encyclopedia: Differential (mathematics)   (Site not responding. Last check: 2007-10-20)
Also in differential topology, the differential of a map between manifolds is another name for the pushforward of that map.
Mathematical disambiguation For other uses of the term calculus see calculus (disambiguation) Calculus is a central branch of mathematics, developed from algebra and geometry, and built on two major complementary ideas.
In mathematics, a function is a relation, such that each element of a set (the domain) is associated with a unique element of another (possibly the same) set (the codomain, not to be confused with the range).
www.nationmaster.com /encyclopedia/Differential-(mathematics)   (584 words)

 AllRefer.com - differential geometry (Mathematics) - Encyclopedia
differential geometry, branch of geometry in which the concepts of the calculus are applied to curves, surfaces, and other geometric entities.
The approach in classical differential geometry involves the use of coordinate geometry (see analytic geometry; Cartesian coordinates), although in the 20th cent.
the methods of differential geometry have been applied in other areas of geometry, e.g., in projective geometry.
reference.allrefer.com /encyclopedia/D/differn-ge.html   (161 words)

 Mathematics   (Site not responding. Last check: 2007-10-20)
Mathematics is the language in which, for the past four thousand years, people have been communicating and recording their thoughts and findings about the world.
Mathematics is the gateway to understanding many and varied fields: space and time, money and commerce, growth and decay, motion and change.
The Department of Mathematics is a leader among universities in the integrated use of technology to facilitate learning.
www.ju.edu /academics/undergrad_mathematics.asp   (744 words)

 HERS Output
Mathematics 23 is a theoretical version of Mathematics 21 which treats multivariable calculus and linear algebra in a rigorous, proof oriented way.
Mathematics 25 and 55 are theory courses that should be elected only by those students who have a particular interest in, and commitment to, mathematics.
Prerequisite: Mathematics 1b or equivalent, or an A or A- in Mathematics 1a, or a 5 on the AB or a 3 or higher on the BC Advanced Placement Examinations in Mathematics.
www.registrar.fas.harvard.edu /Courses/Mathematics.html   (4762 words)

Mathematics majors can use their training as the foundation for advanced professional study, leading to research and teaching in universities or research in industrial research laboratories; they can use it also in secondary school teaching.
The minor in mathematics is available for those students who want their formal university records to emphasize a serious amount of upper-division work in mathematics.
In addition, transferred mathematics courses are automatically evaluated by title for applicability to the entry skill in mathematics requirement and the D.E.C. category C requirement; this evaluation does not depend on the result of the placement examination.
naples.cc.sunysb.edu /CAS/ubdepts0305.nsf/pages/mat   (2564 words)

 Mathematics > Geometry > Differential
A comprehensive approach to qualitative problems in intrinsic differential geometry, this text for upper-level undergraduates and graduate students emphasizes cases in which geodesics possess only local uniqueness properties--and consequently, the relations to the foundations of geometry are decidedly less relevant, and Finsler spaces become the...
Introduction to Differential Geometry with applications to Navier-Stokes Dynamics is an invaluable manuscript for anyone who wants to understand and use exterior calculus and differential geometry, the modern approach to calculus and geometry.
In "Exterior Differential Systems, the authors present the results of their ongoing development of a theory of the geometry of differential equations, focusing especially on Lagrangians and Poincar� 9-Cartan forms.
www.libreriauniversitaria.it /BUS/r_MAT01203/p_1/Differential.htm   (500 words)

 Differential equations (from mathematics, history of) --¬† Encyclop√¶dia Britannica   (Site not responding. Last check: 2007-10-20)
Differential equations are very common in science and engineering, other fields of quantitative study.
branch of mathematics that studies the geometry of curves, surfaces, and manifolds (the higher-dimensional analogs of surfaces).
Mathematics is often defined as the study of quantity, magnitude, and relations of numbers or symbols.
www.britannica.com /eb/article-66026   (876 words)

 Differential (mathematics) - Wikipedia, the free encyclopedia
In differential topology, which is a generalization of calculus to manifolds, the differential of a function on a manifold becomes a one-form.
In this setting the differential generalizes to exterior derivative operator on differential forms
are often called differentials because the exterior derivative plays this role in the de Rham cohomology.
en.wikipedia.org /wiki/Differential_(mathematics)   (158 words)

 Guide to math needed to study physics
Differential geometry begins with the study of differentiable manifolds, coordinate systems, vectors and tensors.
The mathematics of differential forms, developed by Elie Cartan at the beginning of the 20th century, has been powerful technology for understanding Hamiltonian dynamics, relativity and gauge field theory.
Cohomology is the study of the relationship between closed and exact differential forms defined on some manifold M. Students explore the generalization of Stokes' theorem, de Rham cohomology, the de Rahm complex, de Rahm's theorem and cohomology groups.
superstringtheory.com /math/math2.html   (724 words)

 Interactive Learning in Calculus and Differential Equations with Applications
The Mathematics Department at Indiana University of Pennsylvania (IUP) established a computerized learning environment, consisting of a classroom with 31 Macintosh Centris 650s and a laboratory with 12 Macintosh LCs, all equipped with Mathematica.
The Mathematics Department is fully implementing this curriculum in all sections of its science calculus sequence and in the two-semester differential equations sequence.
Mathematics and Applied Mathematics majors are required to take Differential Equations, and Mathematics Education majors have a unit devoted to the project in the teacher preparation course, Computers and Calculators in Secondary Mathematics.
www.ma.iup.edu /projects/CalcDEMma/Summary.html   (389 words)

 Mathematics Partial Differential Equations
Our understanding of the fundamental processes of the natural word is based to a large extent on partial differential equations (PDE).
The dynamics of fluids and elastic solids are governed by partial differential equations that go back to Euler and Cauchy.
For example, the study of the equation thermal diffusion lead to the discovery of Fourier series and ultimately the field of Fourier analysis.
www.math.ucsb.edu /department/pde.php   (284 words)

 Mathematics Guide to Research - Georgetown University Library
The Mathematical MacTutor History of Mathematics Archive at the School of Mathematical and Computational Sciences of the University of St. Andrews includes more than 1000 biographies with major mathematicians listed alphabetically and chronologically, an index of topics, and a birthplace map.
Scholars have contributed chapters on the whole range of mathematical topics including the history of mathematics, number systems, linear algebra, analytical geometry, analysis, sequences and series, theory of functions, ordinary differential equations, special functions, vector analysis, partial differential equations, numerical analysis, the Laplace transform, probability and statistics.
This is a collection of short articles designed to provide an introduction to the areas of modern mathematics and pointers to further information, as well as answers to some common (or not!) questions.
www.library.georgetown.edu /guides/math   (1706 words)

 Differential Equations
Differential equations provide the medium for the interaction between mathematics (especially calculus) and various branches of science and engineering.
Differential equations come in all levels of complexity and even today there is active mathematical research in differential equations.
In general, a differential equation gives a relationship between (among) a function (or functions) and its (their) derivatives (of various orders).
dept.physics.upenn.edu /courses/gladney/mathphys/java/sect2/subsubsection2_1_1_4.html   (673 words)

 Amazon.com: Books: Partial Differential Equations (Graduate Studies in Mathematics, V. 19) GSM/19 (Graduate Studies in ...   (Site not responding. Last check: 2007-10-20)
Differential Forms in Algebraic Topology (Graduate Texts in Mathematics) by Raoul Bott
Evans succeded in writing a text on partial differential equations which can serve a broad spectrum of users: from pure mathematicians interested in hard theorems about the properties of solutions to various types of PDEs to sophisticated practitioners interested in solving specific problems leading to PDEs.
This is a textbook for a first-year graduate course in PDE (for mathematics students).
www.amazon.com /exec/obidos/tg/detail/-/0821807722?v=glance   (1348 words)

 Differential - Wikipedia, the free encyclopedia
A differential can mean one of several things:
Differential signaling is used to carry high speed digital signals.
This is a disambiguation page, a list of pages that otherwise might share the same title.
en.wikipedia.org /wiki/Differential   (83 words)

 Powell's Books - Graduate Texts in Mathematics #0160: Differential and Riemannian Manifolds by Serge Lang   (Site not responding. Last check: 2007-10-20)
This is the third version of a book on Differential Manifolds; in this latest expansion three chapters have been added on Riemannian and pseudo-Riemannian geometry, and the section on sprays and Stokes' theorem have been rewritten.This text provides an introduction to basic concepts in differential topology, differential geometry and differential equations.
In differential topology one studies classes of maps and the possibility of finding differentiable maps in them, and one uses differentiable structures on manifolds to determine their topological structure.
In differential equations one studies vector fields and their integral curves, singular points, stable and unstable manifolds, and the like.
www.powells.com /biblio?isbn=0387943382   (351 words)

 Mathematics > Differential Equations
Beginning with the structure of the solution space and the stability and periodic properties of linear ordinary and Volterra differential equations, the text proceeds to an...
Engineering Mathematics a worldwide bestseller, this book can be used in the classroom or as an in-depth self-study guide.
This is a unique book that presents rigorous mathematical results on Fermi-Pasta-Ulam lattices, a field of great interest in nonlinear analysis, nonlinear science, mathematical physics, etc. It considers travelling waves and time periodic oscillations in infinite Fermi-Pasta-Ulam lattices, which are not necessarily spatially homogenous.
www.libreriauniversitaria.it /BUS/r_MAT00700/p_1/Differential_Equations.htm   (499 words)

 Mathematics and Statistics - MATH 113 Differential Equations   (Site not responding. Last check: 2007-10-20)
To solve a number of differential equations which model physical phenomena, such as bacterial population growth, tumour expansion and oscillating systems subject to forcing and friction.
A vast number of naturally occurring phenomena are modelled by differential equations, for which solutions are required to explain these phenomena.
After we explore the nature of differential equations and their solutions, and how they arise, a number of elementary types of first-order differential equations are solved.
www.maths.lancs.ac.uk /department/study/years/first/modules/math113   (379 words)

 35: Partial differential equations
Like ordinary differential equations, partial differential equations are equations to be solved in which the unknown element is a function, but in PDEs the function is one of several variables, and so of course the known information relates the function and its partial derivatives with respect to the several variables.
Linear differential equations occur perhaps most frequently in applications (in settings in which a superposition principle is appropriate.) When these differential equations are first-order, they share many features with ordinary differential equations.
For example, integral techniques (solving a differential equation by computing a convolution, say) lead to integral operators (transforms on functions spaces); these and differential operators lead in turn to general pseudodifferential operators on function spaces.
www.math.niu.edu /~rusin/known-math/index/35-XX.html   (1097 words)

 MA113 Differential Equations A   (Site not responding. Last check: 2007-10-20)
The basic theory of ordinary differential equations (ODEs) as covered in these modules (Differential Equations A & B) is the cornerstone of all applied mathematics.
Indeed, modern applied mathematics essentially began when Newton developed the calculus in order to solve (and to state precisely) the differential equations that followed from his laws of motion.
Objectives: You should be able to solve various simple differential equations (first order and linear second order) and to interpret their qualitative behaviour; and to do the same for simple difference equations.
www.maths.warwick.ac.uk /pydc/blue/blue-MA113.html   (461 words)

 Wiley::Partial Differential Equations of Applied Mathematics, 2nd Edition   (Site not responding. Last check: 2007-10-20)
Zauderer develops mathematical models that give rise to partial differential equations and describes classical and modern solution techniques.
It continues in a less statistical vein to cover an exceptionally broad range of topics, including stabilities, singularities, transform methods, the use of Green's functions, and perturbation and asymptotic treatments.
Partial Differential Equations of Applied Mathematics, Second Edition is a superior advanced-undergraduate to graduate-level text for students in engineering, the sciences, and applied mathematics.
www.wiley.com /remtitle.cgi?isbn=0471315168   (390 words)

 Mathematics   (Site not responding. Last check: 2007-10-20)
The mathematics courses aim to afford students the opportunity to acquire a sound mathematical foundation and to develop powers of applying mathematical concepts and procedures, and an analytical problem-solving approach.
Because the mathematics program emphasises conceptual thinking, accuracy and competence in problem solving, it is an excellent educational tool for preparing junior officers for future command positions.
Formal understanding of mathematical methods and techniques forms the foundation for the acquisition of technological knowledge and competence in the military field.
academic.sun.ac.za /mil/mil_maths   (126 words)

 math224 Applied Mathematics: Ordinary Differential Equations (Department of Mathematics, Bowdoin)
A study of some of the ordinary differential equations that model a variety of systems in the natural and social sciences.
Classical methods for solving differential equations with an emphasis on modern, qualitative techniques for studying the behavior of solutions to differential equations.
Prerequisite: Mathematics 181 or permission of the instructor.
academic.bowdoin.edu /courses/f04/math224   (136 words)

 math264 Applied Mathematics: Partial Differential Equations (Department of Mathematics, Bowdoin)
A study of some of the partial differential equations that model a variety of systems in the natural and social sciences.
Classical methods for solving partial differential equations, with an emphasis where appropriate on modern, qualitative techniques for studying the behavior of solutions.
Mathematics 264 Reserve List (no items currently on reserve).
academic.bowdoin.edu /courses/s04/math264   (129 words)

 Wiley::Elementary Differential Equations and Boundary Value Problems, 7th Edition   (Site not responding. Last check: 2007-10-20)
Written primarily for undergraduate students of mathematics, science, or engineering, who typically take a course on differential equations during their first or second year.
The environment in which instructors teach, and students learn differential equations has changed enormously in the past few years and continues to evolve at a rapid pace.
Like its predecessors, this edition is written from the viewpoint of the applied mathematician, focusing both on the theory and the practical applications of differential equations as they apply to engineering and the sciences.
www.wiley.com /cda/product/0,,0471319996,00.html   (397 words)

 Differential Mathematics Term Papers, Essay Research Paper Help, Essays on Differential Mathematics
We are available to write Differential Mathematics term papers for research—24 hours a day, 7 days a week—on topics at every level of education.
Equipped with proper research tools and primary / secondary sources, we write essays on Differential Mathematics that are accurate and up-to-date.
In addition to regular libraries, our professional Differential Mathematics researchers have access to online, member-only libraries that contain millions of books, journals, periodicals, magazines, and vast information on every conceivable Differential Mathematicssubject.
www.essaytown.com /topics/differential_mathematics_essays_papers.html   (803 words)

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