---

In its new edition, this book offers an all-new chapter on Fourier integrals and Fourier transforms, plus numerous updates to existing material, 30 new problems with solutions and a substantial update to the contents of the online interactive study guide.

---

This textbook offers an accessible approach to the subject of mathematics which divides the topic into smaller units, guiding students through questions, exercises and problems designed to slowly increase student confidence and experience. The sequence of studies is individualised according to performance and can be regarded as full tutorial course.

The study guide satisfies two objectives simultaneously: firstly it enables students to make effective use of the textbook and secondly it offers advice on the improvement of study skills. Empirical studies have shown that the student´s competence for using written information has improved significantly by using this study guide.

The new edition includes a new chapter on Fourier integrals and Fourier transforms, numerous sections had been updated, 30 new problems with solutions had been added. The interactive study guide has seen a substantial update.

---

Preface.- 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; Determinants.- Eigenvalues and Eigenvectors of Real Matrices.- Vector Analysis: Surface Integrals, Divergence, Curl and Potential.- Fourier Series; Harmonic Analysis.- Probability Calculus.- Probability Distributions.- Theory of Errors.- Fourier Transforms and Fourier Integrals.- Solutions.- Index.

---

From the book reviews:
"In this mathematics textbook, you´ll find possibly all the mathematics you´d need for first years of an undergraduate physics course - algebra, geometry, calculus and statistics. ... With the book there is also an online study guide designed to help the student advance quite quickly. ... If taken alone, the textbook is as any other mathematics textbook for physicists, together with the study guide it is an excellent combination, especially if you prefer to study alone ... ." (Kadri Tinn, AstroMadness.com, February, 2015)

---

Prof. Dr. Klaus Weltner is based at the University of Frankfurt, Germany.


Sebastian John teaches at Cambridge University, UK.


Dr. Wolfgang J. Webern is based in the University of Frankfurt, Germany.


Dr. Peter Schuster teaches at the University of Leeds, UK.


Professor Jean Grosjean is based in the School of Engineering at the University of Bath, UK.

---