Real Quaternionic Calculus Handbook

Real Quaternion Analysis Is A Multi-faceted Subject. Created To Describe Phenomena In Special Relativity, Electrodynamics, Spin Etc., It Has Developed Into A Body Of Material That Interacts With Many Branches Of Mathematics, Such As Complex Analysis, Harmonic Analysis, Differential Geometry, And Differential Equations. It Is Also A Ubiquitous Factor In The Description And Elucidation Of Problems In Mathematical Physics. In The Meantime Real Quaternion Analysis Has Become A Well Established Branch In Mathematics And Has Been Greatly Successful In Many Different Directions. This Book Is Based On Concrete Examples And Exercises Rather Than General Theorems, Thus Making It Suitable For An Introductory One- Or Two-semester Undergraduate Course On Some Of The Major Aspects Of Real Quaternion Analysis In Exercises. Alternatively, It May Be Used For Beginning Graduate Level Courses And As A Reference Work. With Exercises At The End Of Each Chapter And Its Straightforward Writing Style The Book Addresses Readers Who Have No Prior Knowledge On This Subject But Have A Basic Background In Graduate Mathematics Courses, Such As Real And Complex Analysis, Ordinary Differential Equations, Partial Differential Equations, And Theory Of Distributions. 1. An Introduction To Quaternions -- 2. Quaternions And Spatial Rotation -- 3. Quaternion Sequences -- 4. Quaternion Series And Infinite Products -- 5. Exponents And Logarithms --6. Trigonometric Functions -- 7. Hyperbolic Functions -- 8. Inverse Hyperbolic And Trigonometric Functions -- 9. Quaternion Matrices -- 10. Monomials, Polynomials And Binomials -- 11. Solutions. João Pedro Morais, Svetlin Georgiev, Wolfgang Sprössig. Includes Bibliographical References And Index. Front Matter....Pages i-xii An Introduction to Quaternions....Pages 1-34 Quaternions and Spatial Rotation....Pages 35-51 Quaternion Sequences....Pages 53-67 Quaternion Series and Infinite Products....Pages 69-85 Exponents and Logarithms....Pages 87-105 Trigonometric Functions....Pages 107-116 Hyperbolic Functions....Pages 117-124 Inverse Hyperbolic and Trigonometric Functions....Pages 125-132 Quaternion Matrices....Pages 133-147 Monomials, Polynomials and Binomials....Pages 149-164 Solutions....Pages 165-209 Back Matter....Pages 211-216