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Thornton & Marion, Classical Dynamics (5th Edition) Chapter 1. Matrices, Vectors, and Vector Calculus Problem 21. Triple scalar product and Levi-Civita symbol The problem asks you to show The relation between the triple scalar product and Levi-Civita Symbol You should know about Vector and scalar product Triple scalar product (Problem 1-11) Definition of Levi-Civita symbol…
Thornton & Marion, Classical Dynamics (5th Edition) Chapter 1. Matrices, Vectors, and Vector Calculus Problem 20. Kronecker delta & Levi-Civita Symbol The problem asks you to prove Some properties of Kronecker delta and Levi-Civita Symbol You should know about Definition of Kronecker delta symbol (Equation 1.14) Definition of Levi-Civita symbol (Equation 1.67) Solution References https://en.wikipedia.org/wiki/Kronecker_delta…
Thornton & Marion, Classical Dynamics (5th Edition) Chapter 1. Matrices, Vectors, and Vector Calculus Problem 19. Vector Algebra The problem asks you to derive Angle transformation formulae using vector algebra. You should know about Basic concept of a vector algebra Law of cosines Pythagorean trigonometric identity Solution References https://en.wikipedia.org/wiki/Law_of_cosines https://en.wikipedia.org/wiki/Pythagorean_trigonometric_identity
Rybicki & Lightman, Revised Edition Chapter 1. Fundamentals of Radiative Transfer Problem 07. The Einstein coefficients Solution Acknowledgment Thank you, Mateus, for asking this question.
Rybicki & Lightman, Revised Edition Chapter 1. Fundamentals of Radiative Transfer Problem 01. Definition of the flux and solid angle Solution
In this page, I will post solutions of the problems in the Radiative Processes in Astrophysics (Revised Edition), written by Rybicki & Lightman. You can buy the book via https://www.amazon.com/Radiative-Processes-Astrophysics-George-Rybicki/dp/0471827592
Griffiths, Introduction to Electrodynamics, 3rd Edition Chapter 01. Vector Analysis 1.1 Vector Algebra 1.1.5 How Vectors Transform Problem 1.9 Rotation matrix Solution
Griffiths, Introduction to Electrodynamics, 3rd Edition Chapter 01. Vector Analysis 1.1 Vector Algebra 1.1.5 How Vectors Transform Problem 1.8 Matrix and tensor transformation Solution
Thornton & Marion, Classical Dynamics, Fifth Edition Chapter 1. Matrices, Vectors, and Vector Calculus Problem 18. Geometrical interpretation of the vector product Solution
Thornton & Marion, Classical Dynamics, Fifth Edition Chapter 1. Matrices, Vectors, and Vector Calculus Problem 17. Geometrical interpretation of the scalar product Solution