{"product_id":"a-first-course-in-applied-mathematics-9781118229620","title":"A First Course in Applied Mathematics","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003eThis book details how applied mathematics involves predictions, interpretations, analysis, and mathematical modeling to solve real-world problems.\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\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","brand":"John Wiley \u0026 Sons Inc","offers":[{"title":"Default Title","offer_id":49406842208599,"sku":"9781118229620","price":102.56,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9781118229620.jpg?v=1730497307","url":"https:\/\/bookcurl.com\/products\/a-first-course-in-applied-mathematics-9781118229620","provider":"Book Curl","version":"1.0","type":"link"}