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Workbook on Aspects of Dynamical Meteorology a Self Discovery Mathematical Journey for Inquisitive Minds

By Gertenbach, Jan D.

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Book Id: WPLBN0000659239
Format Type: PDF eBook
File Size: 460.16 KB.
Reproduction Date: 2005
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Title: Workbook on Aspects of Dynamical Meteorology a Self Discovery Mathematical Journey for Inquisitive Minds  
Author: Gertenbach, Jan D.
Volume:
Language: English
Subject: Science., Physics, Physics--Research
Collections: Physics Literature
Historic
Publication Date:
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APA MLA Chicago

Gertenbach, J. D. (n.d.). Workbook on Aspects of Dynamical Meteorology a Self Discovery Mathematical Journey for Inquisitive Minds. Retrieved from http://www.worldebooklibrary.org/


Description
Physics Literature

Table of Contents
Contents 1. Fundamental Mathematical Aspects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1.1. Vector algebra . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 1.1.1. Vector space . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 1.1.2. Basis and co-ordinate system . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 1.1.3. Scalar product . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 1.1.4. Vector product . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 1.1.5. Orthogonal vectors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 1.2. Functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 1.3. Differentiation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 1.3.1. Scalar valued functions of one variable . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 1.3.2. Vector valued functions of one variable . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 1.3.3. Scalar valued functions of several variables . . . . . . . . . . . . . . . . . . . . . . . . . 7 1.3.4. Partial derivatives . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 1.3.5. The total derivative and temperature advection . . . . . . . . . . . . . . . . . . . . 9 1.3.6. Vector valued functions of several variables . . . . . . . . . . . . . . . . . . . . . . . 11 1.3.7. Integration of knowledge . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12 1.4. Integration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12 1.4.1. Fundamental theorems of the Calculus . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12 1.4.2. Transformation of integrals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13 1.4.3. Interchanging total differentiation and integration . . . . . . . . . . . . . . . . . 14 1.5. More examples with meteorological applications . . . . . . . . . . . . . . . . . . . . . . 16 1.5.1. Motion of a particle in a circle . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16 1.5.2. Circulation and vorticity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18 1.5.3. Divergence and convergence . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20 1.5.4. Advection and the material derivative . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21 1.5.5. Integration of knowledge . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22 1.6. Further vector algebra . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22 1.6.1. Vector product (in R3) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22 1.6.2. The scalar triple product . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23 1.6.3. The vector triple product . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23 1.6.4. Integration of knowledge . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24 2. The momentum equation in rotating spherical co-ordinates . . . . . . 25 2.1. The inertial reference frame . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25 2.1.1. Spherical co-ordinates . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26 2.2. The rotating frame of reference . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26 2.2.1. Spherical co-ordinates in the rotating frame of reference . . . . . . . . . . . 26 2.2.2. The motion of a particle (parcel of air) in the rotating frame . . . . . . 27 2.3. Differentiation of an arbitrary vector A . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27 2.3.1. Notation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29 2.4. Velocity and acceleration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29 2.4.1. The velocity vector . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29 2.4.2. The acceleration vector . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30 3. Balance laws in physics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33

 

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