Engineering Analysis

Preface Calculus Linear Algebra Professional This book is about the topic of mathematical analysis, particularly in the field of engineering. It attempts to be a companion piece to high-level engineering texts that will rely on a certain fundamental mathematical background among readers. This will build on topics covered in Probability, Algebra, Linear Algebra, Calculus, and Ordinary Differential Equations. Readers of this book are expected to have background knowledge in all those topics. Topics covered will be inter-disciplinary engineering topics, and will be highly mathematical. However, overlap between this book and other mathematics books, except where necessary, will be minimized. This book is intended to accompany a graduate course of study in engineering analysis. Table of Contents Linear Algebra Vector Spaces Vector Basics Linear Independence and Basis Linear Transformations Minimization Projections Linear Spaces Matrices Matrix Forms Quadratic Forms Eigenvalues and Eigenvectors Diagonalization Spectral Decomposition Error Estimation Matrix Calculus Matrix Functions Cayley-Hamilton Theorem Matrix Exponentials Lyapunov Equation Function Spaces L2 Space Banach and Hilbert Spaces Fourier Series Arbitrary Basis Expansion Bessel Equation and Parseval Theorem Multi-Dimensional Fourier Series Algorithms Design And Analysis Wavelets /Wavelet Transforms/ Stochastic Processes Random Variables Probability Functions Distributions Expectation and Entropy SISO Transformations MISO Transformations Correlation Random Vectors Analysis Leibnitz' Rule /Differential Operator Theory/ /Linear Operators/ /Complex Analysis/ Optimization and Minimization Optimization /Unconstrained Optimizations/ /Constrained Optimizations/ Appendices /Resources/ E Applied mathematics general engineering 50%