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Vector Calculus
Published in Khalid Khan, Tony Lee Graham, Engineering Mathematics with Applications to Fire Engineering, 2018
Vector calculus deals with the differentiation and integration of vector fields in two- and three-dimensional space. In this chapter important concepts such as the different types of line integrals are first considered and then how closed line integrals can be equivalent to double integrals over a region known as Green’s theorem. Further important ideas on the gradient and curl of vector fields are developed leading to surface integrals and their applications to describe fluid flow and many different force fields that occur naturally in the world.
Vector Calculus
Published in Abul Hasan Siddiqi, Mohamed Al-Lawati, Messaoud Boulbrachene, Modern Engineering Mathematics, 2017
Abul Hasan Siddiqi, Mohamed Al-Lawati, Messaoud Boulbrachene
Vector calculus now serves as a basic mathematical tool in all areas of science and engineering where mechanical, electromagnetic and thermodynamics forces determine the behaviours of solids, fluids, electric conductors, semiconductors and magnetic materials. Many ideas of this chapter are based on references [7, 8]: 7 is out of print.
Foundation of Electromagnetic Theory
Published in Bahman Zohuri, Patrick J. McDaniel, Electrical Brain Stimulation for the Treatment of Neurological Disorders, 2019
Bahman Zohuri, Patrick J. McDaniel
Now that we have covered basic vector algebra, we pay our attention to vector calculus, which extends to vector gradient, integration, vector curl and differentiation of vectors. The simplest of these is the relation of a particular vector field to the derivative of a scalar field.
Students’ ability to use geometry knowledge in solving problems of geometrical optics
Published in International Journal of Mathematical Education in Science and Technology, 2023
Aneta Gacovska Barandovska, Boce Mitrevski, Lambe Barandovski
The need for geometry in physics is not only focused on geometrical optics. Besides geometrical optics and astronomy, a thorough geometrical approach, especially vector calculus is essential for learning Electromagnetic field theory and problem-solving, at all levels. At Colorado State University, this approach is proposed for junior-level undergraduate electromagnetic education. Notaros states the importance of vector calculus and analysis for reading and translating the geometrical approach into equations, to visualize the structures (Notaros, 2013). According to the author, this is the most challenging component even for university students in the Electrical Engineering curriculum. The geometrical approach is far more intuitive and visual than the formal algebraic approach to vector analysis in electromagnetism. Students at Colorado State University have confirmed these findings through preliminary testing and assessment of the success and satisfaction in the courses of Electromagnetic fields, I and II.
Method for detecting damage in carbon-fibre reinforced plastic-steel structures based on eddy current pulsed thermography
Published in Nondestructive Testing and Evaluation, 2018
Xuan Li, Zhiping Liu, Xiaoli Jiang, Gabrol Lodewijks
where ki is a scalar term. The divergence characterizes the diffusion (or convergence) rate of the fluid volume of an object. In vector calculus, divergence is a vector operator that measures the magnitude of a vector field’s source or sink at a given point. For example,