Mathematics for Physicists and Engineers

Prof. Dr. Klaus Weltner (1927-2020) studied physics at the Technical University Hannover (Germany) and the University of Bristol (England). He graduated in plasma physics and was professor of physics and didactic of physics at the universities Osnabruck, Berlin, Frankfurt and visiting professor of physics at the Federal University of Bahia (Brazil). Prof. Dr. Jean Grosjean was Head of Applied Mechanics at the School of Engineering at the University of Bath (England). Wolfgang J. Weber studied mathematics at the Universities of Frankfurt (Germany), Oxford (England) and Michigan State (USA). He is currently responsible for the training of computer specialists at the computing center at the University of Frankfurt. Dr.-Ing. Peter Schuster was lecturer at the School of Engineering at the University of Bath (England). Different appointments in the chemical industry. Dr. S. T. John completed a Ph.D. in Physics at the University of Cambridge (England) and has been working in probabilistic machine learning research both in industry and academia.

Introduction.- Vector Algebra I: Scalars and Vectors.- Vector Algebra II: Scalar and Vector Products.- Functions.- Exponential, Logarithmic and Hyperbolic Functions.- Differential Calculus.- Integral Calculus.- Applications of Integration.- Taylor Series and Power Series.- Complex Numbers.- Differential Equations.- Laplace Transforms.- Functions of Several Variables; Partial Differentiation; and Total Differentiation.- Multiple Integrals; Coordinate Systems.- Transformation of Coordinates; Matrices.- Sets of Linear Equations; Determinanats.- Eigenvalues and Eigenvectors of Real Matrices.- Vector Analysis: Surface Integrals, Divergence, Curl and Potential.- Fourier Series; Harmonic Analysis.- Fourier Integrals and Fourier Transforms.- Probability Calculus.- Probability Distributions.- Theory of Errors.- Answers.