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A First Course in Applied Mathematics

Jorge Rebaza (Autor)

Software / Digital Media

464 Seiten

2012
John Wiley & Sons Inc (Hersteller)
978-1-118-27718-8 (ISBN)

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This book details how applied mathematics involves predictions, interpretations, analysis, and mathematical modeling to solve real-world problems. Written at a level that is accessible to readers from a wide range of scientific and engineering fields, the book masterfully blends standard topics with modern areas of application and provides the needed foundation for transitioning to more advanced subjects. Utilizing MATLAB to showcase the presented theory and illustrate interesting real-world applications, this valuable reference helps practitioners working with mathematical modeling, computational methods, and the applications of mathematics in their everyday work.

JORGE REBAZA, PhD, is Associate Professor in the Department of Mathematics at Missouri State University. Dr. Rebaza has published numerous journal articles in his areas of research interest, which include numerical analysis, dynamical systems, matrix computations, and applied mathematics.

Preface xi 1. Basics of Linear Algebra 1 1.1 Notation and Terminology 1 1.2 Vector and Matrix Norms 4 1.3 Dot Product and Orthogonality 8 1.4 Special Matrices 9 1.5 Vector Spaces 21 1.6 Linear Independence and Basis 24 1.7 Orthogonalization and Direct Sums 30 1.8 Column Space, Row Space and Null Space 34 1.9 Orthogonal Projections 43 1.10 Eigenvalues and Eigenvectors 47 1.11 Similarity 56 1.12 Bezier Curves Postscripts Fonts 59 1.13 Final Remarks and Further Reading 68 2. Ranking Web Pages 79 2.1 The Power Method 80 2.2 Stochastic, Irreducible and Primitive Matrices 84 2.3 Google's PageRank Algorithm 92 2.4 Alternatives to Power Method 106 2.5 Final Remarks and Further Reading 120 3. Matrix Factorizations 131 3.1 LU Factorization 132 3.2 QR Factorization 142 3.3 Singular Value Decomposition (SVD) 155 3.4 Schur Factorization 166 3.5 Information Retrieval 186 3.6 Partition of Simple Substitution Cryptograms 194 3.7 Final Remarks and Further Reading 203 4. Least Squares 215 4.1 Projections and Normal Equations 215 4.2 Least Squares and QR Factorization 224 4.3 Lagrange Multipliers 228 4.4 Final Remarks and Further Reading 231 5. Image Compression 235 5.1 Compressing with Discrete Cosine Transform 236 5.2 Huffman Coding 260 5.3 Compression with SVD 267 5.4 Final Remarks and Further Reading 271 6. Ordinary Differential Equations 277 6.1 One-Dimensional Differential Equations 278 6.2 Linear Systems of Differential Equations 307 6.3 Solutions via Eigenvalues and Eigenvectors 308 6.4 Fundamentals Matrix Solution 312 6.5 Final Remarks and Further Reading 316 7. Dynamical Systems 325 7.1 Linear Dynamical Systems 326 7.2 Nonlinear Dynamical Systems 340 7.3 Predator-Prey Models with Harvesting 374 7.4 Final Remarks and Further Reading 385 8. Mathematical Models 395 8.1 Optimization of a Waste Management System 396 8.2 Grouping Problem in Networks 404 8.3 American Cutaneous Leishmaniasis 410 8.4 Variable Population Interactions 420 References 431 Index 435

Erscheint lt. Verlag	27.4.2012
Verlagsort	New York
Sprache	englisch
Maße	150 x 250 mm
Gewicht	666 g
Themenwelt	Mathematik / Informatik ► Mathematik ► Algebra
Themenwelt	Mathematik / Informatik ► Mathematik ► Angewandte Mathematik
ISBN-10	1-118-27718-X / 111827718X
ISBN-13	978-1-118-27718-8 / 9781118277188
Zustand	Neuware