Maxwell's formulation - differential forms on euclidean spacegreentask
One of the greatest advances in theoretical physics of the nineteenth
century was Maxwell’s formulation of the the equations of electromag-
netism. This article uses differential forms to solve a problem related
to Maxwell’s formulation. The notion of differential form encompasses
such ideas as elements of surface area and volume elements, the work
exerted by a force, the flow of a fluid, and the curvature of a surface,
space or hyperspace. An important operation on differential forms is
exterior differentiation, which generalizes the operators div, grad, curl
of vector calculus. the study of differential forms, which was initiated
by E.Cartan in the years around 1900, is often termed the exterior
differential calculus.However, Maxwells equations have many very im-
portant implications in the life of a modern person, so much so that
people use devices that function off the principles in Maxwells equa-
tions every day without even knowing it
Published by:
Wang Jing
School of Physical and Mathematical Sciences
Nanyang Technological University
jwang14@e.ntu.edu.sg
Numerical methods by Jeffrey R. Chasnovankushnathe
This document contains lecture notes for an introduction to numerical methods course. It covers several topics:
- IEEE floating point arithmetic and number representations in computers. Different number formats like single and double precision are discussed.
- Root finding methods like bisection, Newton's and secant methods. Their convergence properties are analyzed.
- Solving systems of linear and nonlinear equations using Gaussian elimination and Newton's method.
- Numerical integration techniques like the midpoint, trapezoidal and Simpson's rules for evaluating integrals. Adaptive integration methods are introduced.
- Numerical solutions to ordinary differential equations using Euler, Runge-Kutta and shooting methods to solve initial and boundary value problems.
The document provides an overview of key concepts in algebra including:
1) Real numbers which are made up of rational and irrational numbers. Real numbers have properties like closure under addition and multiplication.
2) Exponents and radicals including laws involving integral, zero, fractional exponents and radicals.
3) Polynomials which are algebraic expressions made up of variables and coefficients, and can be added or subtracted by combining like terms.
Maxwell's formulation - differential forms on euclidean spacegreentask
One of the greatest advances in theoretical physics of the nineteenth
century was Maxwell’s formulation of the the equations of electromag-
netism. This article uses differential forms to solve a problem related
to Maxwell’s formulation. The notion of differential form encompasses
such ideas as elements of surface area and volume elements, the work
exerted by a force, the flow of a fluid, and the curvature of a surface,
space or hyperspace. An important operation on differential forms is
exterior differentiation, which generalizes the operators div, grad, curl
of vector calculus. the study of differential forms, which was initiated
by E.Cartan in the years around 1900, is often termed the exterior
differential calculus.However, Maxwells equations have many very im-
portant implications in the life of a modern person, so much so that
people use devices that function off the principles in Maxwells equa-
tions every day without even knowing it
Published by:
Wang Jing
School of Physical and Mathematical Sciences
Nanyang Technological University
jwang14@e.ntu.edu.sg
Numerical methods by Jeffrey R. Chasnovankushnathe
This document contains lecture notes for an introduction to numerical methods course. It covers several topics:
- IEEE floating point arithmetic and number representations in computers. Different number formats like single and double precision are discussed.
- Root finding methods like bisection, Newton's and secant methods. Their convergence properties are analyzed.
- Solving systems of linear and nonlinear equations using Gaussian elimination and Newton's method.
- Numerical integration techniques like the midpoint, trapezoidal and Simpson's rules for evaluating integrals. Adaptive integration methods are introduced.
- Numerical solutions to ordinary differential equations using Euler, Runge-Kutta and shooting methods to solve initial and boundary value problems.
The document provides an overview of key concepts in algebra including:
1) Real numbers which are made up of rational and irrational numbers. Real numbers have properties like closure under addition and multiplication.
2) Exponents and radicals including laws involving integral, zero, fractional exponents and radicals.
3) Polynomials which are algebraic expressions made up of variables and coefficients, and can be added or subtracted by combining like terms.
Delaunay triangulation from 2-d delaunay to 3-d delaunaygreentask
The document discusses Delaunay triangulation in 2D and 3D. It covers several key topics:
1. Computing the circumcenter of a triangle and using it to find cavities when inserting a new point.
2. Improving the algorithm to find which edges can form new balls/triangles by recording edges as cavities are found.
3. The complexity of finding cavities and balls, and how finding balls can be optimized.
4. Extending the 2D Delaunay triangulation concepts like cavity detection to 3D meshes. This involves operations to recover missing geometry and merge the cavity mesh.