{"product_id":"a-first-course-in-applied-mathematics-isbn-9781118229620","title":"A First Course in Applied Mathematics","description":"\u003cp\u003eExplore real-world applications of selected mathematical theory, concepts, and methods\u003c\/p\u003e \u003cp\u003eExploring related methods that can be utilized in various fields of practice from science and engineering to business, A First Course in Applied Mathematics details how applied mathematics involves predictions, interpretations, analysis, and mathematical modeling to solve real-world problems.\u003c\/p\u003e \u003cp\u003eWritten 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. The author utilizes MATLAB® to showcase the presented theory and illustrate interesting real-world applications to Google's web page ranking algorithm, image compression, cryptography, chaos, and waste management systems. Additional topics covered include:\u003c\/p\u003e \u003cul\u003e \u003cli\u003e \u003cp\u003eLinear algebra\u003c\/p\u003e \u003c\/li\u003e \u003cli\u003e \u003cp\u003eRanking web pages\u003c\/p\u003e \u003c\/li\u003e \u003cli\u003e \u003cp\u003eMatrix factorizations\u003c\/p\u003e \u003c\/li\u003e \u003cli\u003e \u003cp\u003eLeast squares\u003c\/p\u003e \u003c\/li\u003e \u003cli\u003e \u003cp\u003eImage compression\u003c\/p\u003e \u003c\/li\u003e \u003cli\u003e \u003cp\u003eOrdinary differential equations\u003c\/p\u003e \u003c\/li\u003e \u003cli\u003e \u003cp\u003eDynamical systems\u003c\/p\u003e \u003c\/li\u003e \u003cli\u003e \u003cp\u003eMathematical models\u003c\/p\u003e \u003c\/li\u003e \u003c\/ul\u003e \u003cp\u003eThroughout the book, theoretical and applications-oriented problems and exercises allow readers to test their comprehension of the presented material. An accompanying website features related MATLAB® code and additional resources.\u003c\/p\u003e \u003cp\u003eA First Course in Applied Mathematics is an ideal book for mathematics, computer science, and engineering courses at the upper-undergraduate level. The book also serves as a valuable reference for practitioners working with mathematical modeling, computational methods, and the applications of mathematics in their everyday work.\u003c\/p\u003e \u003cp\u003ePreface xiii\u003c\/p\u003e \u003cp\u003e\u003cb\u003e1 Basics of Linear Algebra 1\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e1.1 Notation and Terminology 1 \u003c\/p\u003e \u003cp\u003e1.2 Vector and Matrix Norms 4\u003c\/p\u003e \u003cp\u003e1.3 Dot Product and Orthogonality 8 \u003c\/p\u003e \u003cp\u003e1.4 Special Matrices 9\u003c\/p\u003e \u003cp\u003e1.5 Vector Spaces 21\u003c\/p\u003e \u003cp\u003e1.6 Linear Independence and Basis 24\u003c\/p\u003e \u003cp\u003e1.7 Orthogonalization and Direct Sums 30\u003c\/p\u003e \u003cp\u003e1.8 Column Space, Row Space and Null Space 34\u003c\/p\u003e \u003cp\u003e1.9 Orthogonal Projections 43\u003c\/p\u003e \u003cp\u003e1.10 Eigenvalues and Eigenvectors 47\u003c\/p\u003e \u003cp\u003e1.11 Similarity 56\u003c\/p\u003e \u003cp\u003e1.12 Bezier Curves Postscript Fonts 59\u003c\/p\u003e \u003cp\u003e1.13 Final Remarks and Further Reading 68\u003c\/p\u003e \u003cp\u003eExercises 69\u003c\/p\u003e \u003cp\u003e\u003cb\u003e2 Ranking Web Pages 79\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e2.1 The Power Method 80\u003c\/p\u003e \u003cp\u003e2.2 Stochastic, Irreducible and Primitive Matrices 84\u003c\/p\u003e \u003cp\u003e2.3 Google’s PageRank Algorithm 92\u003c\/p\u003e \u003cp\u003e2.4 Alternatives to Power Method 106\u003c\/p\u003e \u003cp\u003e2.5 Final Remarks and Further Reading 120\u003c\/p\u003e \u003cp\u003eExercises 121\u003c\/p\u003e \u003cp\u003e\u003cb\u003e3 Matrix Factorizations 131\u003c\/b\u003e \u003c\/p\u003e \u003cp\u003e3.1 \u003ci\u003eLU\u003c\/i\u003e Factorization 132\u003c\/p\u003e \u003cp\u003e3.2 \u003ci\u003eQR\u003c\/i\u003e Factorization 142\u003c\/p\u003e \u003cp\u003e3.3 Singular Value Decomposition (SVD) 155\u003c\/p\u003e \u003cp\u003e3.4 Schur Factorization 166\u003c\/p\u003e \u003cp\u003e3.5 Information Retrieval 186\u003c\/p\u003e \u003cp\u003e3.6 Partition of Simple Substitution Cryptograms 194\u003c\/p\u003e \u003cp\u003e3.7 Final Remarks and Further Reading 203\u003c\/p\u003e \u003cp\u003eExercises 205\u003c\/p\u003e \u003cp\u003e\u003cb\u003e4 Least Squares 215\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e4.1 Projections and Normal Equations 215\u003c\/p\u003e \u003cp\u003e4.2 Least Squares and \u003ci\u003eQR\u003c\/i\u003e Factorization 224\u003c\/p\u003e \u003cp\u003e4.3 Lagrange Multipliers 228\u003c\/p\u003e \u003cp\u003e4.4 Final Remarks and Further Reading 231\u003c\/p\u003e \u003cp\u003eExercises 231\u003c\/p\u003e \u003cp\u003e\u003cb\u003e5 Image Compression 235\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e5.1 Compressing with Discrete Cosine Transform 236\u003c\/p\u003e \u003cp\u003e5.2 Huffman Coding 260\u003c\/p\u003e \u003cp\u003e5.3 Compression with \u003ci\u003eSVD\u003c\/i\u003e 267\u003c\/p\u003e \u003cp\u003e5.4 Final Remarks and Further Reading 269\u003c\/p\u003e \u003cp\u003eExercises 271\u003c\/p\u003e \u003cp\u003e\u003cb\u003e6 Ordinary Differential Equations 277\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e6.1 One-Dimensional Differential Equations 278\u003c\/p\u003e \u003cp\u003e6.2 Linear Systems of Differential Equations 307\u003c\/p\u003e \u003cp\u003e6.3 Solutions via Eigenvalues and Eigenvectors 307\u003c\/p\u003e \u003cp\u003e6.4 Fundamentals Matrix Solution 312\u003c\/p\u003e \u003cp\u003e6.5 Final Remarks and Further Reading 316\u003c\/p\u003e \u003cp\u003eExercises 316\u003c\/p\u003e \u003cp\u003e\u003cb\u003e7 Dynamical Systems 325\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e7.1 Linear Dynamical Systems 326\u003c\/p\u003e \u003cp\u003e7.2 Nonlinear Dynamical Systems 340\u003c\/p\u003e \u003cp\u003e7.3 Predator-Prey Models with Harvesting 374\u003c\/p\u003e \u003cp\u003e7.4 Final Remarks and Further Reading 385\u003c\/p\u003e \u003cp\u003eExercises 385\u003c\/p\u003e \u003cp\u003e\u003cb\u003e8 Mathematical Models 395\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e8.1 Optimization of a Waste Management System 396\u003c\/p\u003e \u003cp\u003e8.2 Grouping Problem in Networks 404 \u003c\/p\u003e \u003cp\u003e8.3 American Cutaneous Leishmaniasis 410\u003c\/p\u003e \u003cp\u003e8.4 Variable Population Interactions 420\u003c\/p\u003e \u003cp\u003eReferences 431\u003c\/p\u003e \u003cp\u003eIndex 435\u003c\/p\u003e \u003cp\u003e\u003cb\u003eJORGE REBAZA, PHD,\u003c\/b\u003e 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.\u003c\/p\u003e \u003cp\u003e\u003cb\u003eExplore real-world applications of selected mathematical theory, concepts, and methods\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003eExploring related methods that can be utilized in various fields of practice from science and engineering to business,\u003ci\u003e A First Course in Applied Mathematics\u003c\/i\u003e details how applied mathematics involves predictions, interpretations, analysis, and mathematical modeling to solve real-world problems.\u003c\/p\u003e \u003cp\u003eWritten 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. The author utilizes MATLAB® to showcase the presented theory and illustrate interesting real-world applications to Google's web page ranking algorithm, image compression, cryptography, chaos, and waste management systems. Additional topics covered include:\u003c\/p\u003e \u003cul\u003e \u003cli\u003eLinear algebra\u003c\/li\u003e \u003cli\u003eRanking web pages\u003c\/li\u003e \u003cli\u003eMatrix factorizations\u003c\/li\u003e \u003cli\u003eLeast squares\u003c\/li\u003e \u003cli\u003eImage compression\u003c\/li\u003e \u003cli\u003eOrdinary differential equations\u003c\/li\u003e \u003cli\u003eDynamical systems\u003c\/li\u003e \u003cli\u003eMathematical models\u003c\/li\u003e \u003c\/ul\u003e \u003cp\u003eThroughout the book, theoretical and applications-oriented problems and exercises allow readers to test their comprehension of the presented material. An accompanying website features related MATLAB® code and additional resources.\u003c\/p\u003e \u003cp\u003e\u003ci\u003eA First Course in Applied Mathematics\u003c\/i\u003e is an ideal book for mathematics, computer science, and engineering courses at the upper-undergraduate level. The book also serves as a valuable reference for practitioners working with mathematical modeling, computational methods, and the applications of mathematics in their everyday work.\u003c\/p\u003e","brand":"Wiley","offers":[{"title":"Default Title","offer_id":47988627472613,"sku":"NP9781118229620","price":147.95,"currency_code":"USD","in_stock":false}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/1842\/7735\/files\/9781118229620.jpg?v=1761781031","url":"https:\/\/k12savings.com\/es\/products\/a-first-course-in-applied-mathematics-isbn-9781118229620","provider":"K12savings","version":"1.0","type":"link"}