Mathematical Techniques: An Introduction for the Engineering, Physical, and Mathematical SciencesUndergraduate students of engineering, science, and mathematics must quickly master a variety of mathematical methods, although many of these students do not have strong mathematics backgrounds. In this well-received book, now in its second edition, the authors use their extensive experience with diverse groups of students to provide an accessible introduction to mathematical techniques. They start at the elementary level and proceed to cover the full range of topics typically encountered by beginning students: BL Analytic geometry, vector algebra, vector fields (div and curl), differentiation, and integration. BL Complex numbers, matrix operations, and linear systems of equations. BL Differential equations and first-order linear systems, functions of more than one variable, double integrals, and line integrals. BL Laplace transforms, Fourier series and Fourier transforms. BL Probability and statistics. Incorporating many suggestions from readers, this new edition has expanded discussions of vectors and new chapters on Fourier series and on probability and statistics. The emphasis throughout is on understanding concepts through well-chosen examples, and the book includes over 500 fully worked problems. As far as is possible chapter topics are self-contained so that a student only needing to master certain techniques can omit others without trouble. The generously illustrated text also includes simple numerical processes which lead to examples and projects for computation (particularly with Mathematica), and contains a large number of exercises (with answers) to reinforce the material. These features combine to make this book an ideal starting point for students entering the sciences |
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a₁ angle antiderivative approximation Argand diagram axes axis b₁ c₁ chain rule circuit coefficients complex numbers components cos² curve derivatives diagonal diagram differential equation direction dr² dx dx dx dy dx/dt dy dx dy/dx eigenvalues eigenvectors elements equal Evaluate Example expression Find formula Fourier series function given grad graph Hence inverse Laplace transform linear matrix notation obtain oscillations parameter particular solution path perpendicular phasor plane polar coordinates polynomial position vector problem r₁ random variable represents result Section Show shown in Fig signed area sin² Sketch slope solve ẞt stationary points straight line Suppose tangent Taylor series theorem trapezium rule unit vector velocity vertices voltage x₁ zero δχ ду дх