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.
Includes a separate study guide with 823 interactive learning tutorials, available online
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.
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.
