Engineering Analysis

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Engineering Analysis

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Contents 1 Preface 2 Table of Contents 2.1 Linear Algebra 2.2 Matrix Calculus 2.3 Wavelet Analysis 2.4 Stochastic Processes 2.5 Complex Analysis 2.6 Optimization and Minimization 3 Resources and Licensing

[edit] Preface

This book requires that you first read Calculus.

This book requires that you first read Linear Algebra.

This book is intended for professional readers.

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 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.

[edit] Table of Contents

[edit] Linear Algebra

• Vector Spaces
• Vector Basics
• Linear Independence and Basis
• Linear Transformatins
• Minimization
• Projections
• Linear Spaces
• Matrices
• Matrix Forms
• Quadratic Forms
• Eigenvalues and Eigenvectors
• Diagonalization
• Spectral Decomposition
• Error Estimation

[edit] 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

[edit] Wavelet Analysis

• Wavelets
• Wavelet Transforms

[edit] Stochastic Processes

• Random Variables
• Probability Functions
• Distributions
• Expectation and Entropy
• SISO Transformations
• MISO Transformations
• Correlation
• Random Vectors

[edit] Complex Analysis

• Leibnitz' Rule
• Linear Operators
• Complex Analysis
• Operator Theory

[edit] Optimization and Minimization

• Optimization
• Unconstrained Optimizations
• Constrained Optimizations

[edit] Resources and Licensing

• Resources
• Licensing