Synopsis
Modern analysis, a core mathematical branch, evolves from classical analysis with profound conceptual and methodological innovations. While classical analysis focuses on local function properties and changes, modern analysis emphasizes holistic perspectives on spaces, structures, and functionals, bridging pure/applied mathematics and natural sciences. This textbook guides aspiring mathematicians to build a solid foundation, grasp disciplinary landscapes, and explore independently. It integrates linear and nonlinear functional analysis—often taught separately—to reveal their intrinsic logical continuity. The content progresses from elementary to profound, covering metric/normed linear/inner product spaces, bounded linear operators, convex analysis, abstract analysis, and nonlinear functional analysis. Structurally, it follows cognitive progression from concrete to abstract and linear to nonlinear. Three key features define the book: rigorous proofs with clear motivation and logical development; organic connection between linear and nonlinear theories; and integration of theory with applications through examples. Since the last century, mathematics has expanded nonlinearly, globally, and stochastically, with functional analysis permeating PDEs, differential geometry, optimization, control theory, and mathematical economics. This book provides a unified framework to navigate these developments, emphasizing both theoretical depth and practical relevance.
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Paperback. Condition: new. Paperback. Modern analysis, a core mathematical branch, evolves from classical analysis with profound conceptual and methodological innovations. While classical analysis focuses on local function properties and changes, modern analysis emphasizes holistic perspectives on spaces, structures, and functionals, bridging pure/applied mathematics and natural sciences. This textbook guides aspiring mathematicians to build a solid foundation, grasp disciplinary landscapes, and explore independently. It integrates linear and nonlinear functional analysis-often taught separately-to reveal their intrinsic logical continuity. The content progresses from elementary to profound, covering metric/normed linear/inner product spaces, bounded linear operators, convex analysis, abstract analysis, and nonlinear functional analysis. Structurally, it follows cognitive progression from concrete to abstract and linear to nonlinear. Three key features define the book: rigorous proofs with clear motivation and logical development; organic connection between linear and nonlinear theories; and integration of theory with applications through examples. Since the last century, mathematics has expanded nonlinearly, globally, and stochastically, with functional analysis permeating PDEs, differential geometry, optimization, control theory, and mathematical economics. This book provides a unified framework to navigate these developments, emphasizing both theoretical depth and practical relevance. This item is printed on demand. Shipping may be from multiple locations in the US or from the UK, depending on stock availability. Seller Inventory # 9789999337823
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Modern Analysis: From Linear Functional to Nonlinear Functional Analysis
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Paperback. Condition: new. Paperback. Modern analysis, a core mathematical branch, evolves from classical analysis with profound conceptual and methodological innovations. While classical analysis focuses on local function properties and changes, modern analysis emphasizes holistic perspectives on spaces, structures, and functionals, bridging pure/applied mathematics and natural sciences. This textbook guides aspiring mathematicians to build a solid foundation, grasp disciplinary landscapes, and explore independently. It integrates linear and nonlinear functional analysis-often taught separately-to reveal their intrinsic logical continuity. The content progresses from elementary to profound, covering metric/normed linear/inner product spaces, bounded linear operators, convex analysis, abstract analysis, and nonlinear functional analysis. Structurally, it follows cognitive progression from concrete to abstract and linear to nonlinear. Three key features define the book: rigorous proofs with clear motivation and logical development; organic connection between linear and nonlinear theories; and integration of theory with applications through examples. Since the last century, mathematics has expanded nonlinearly, globally, and stochastically, with functional analysis permeating PDEs, differential geometry, optimization, control theory, and mathematical economics. This book provides a unified framework to navigate these developments, emphasizing both theoretical depth and practical relevance. This item is printed on demand. Shipping may be from our Sydney, NSW warehouse or from our UK or US warehouse, depending on stock availability. Seller Inventory # 9789999337823
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Paperback. Condition: new. Paperback. Modern analysis, a core mathematical branch, evolves from classical analysis with profound conceptual and methodological innovations. While classical analysis focuses on local function properties and changes, modern analysis emphasizes holistic perspectives on spaces, structures, and functionals, bridging pure/applied mathematics and natural sciences. This textbook guides aspiring mathematicians to build a solid foundation, grasp disciplinary landscapes, and explore independently. It integrates linear and nonlinear functional analysis-often taught separately-to reveal their intrinsic logical continuity. The content progresses from elementary to profound, covering metric/normed linear/inner product spaces, bounded linear operators, convex analysis, abstract analysis, and nonlinear functional analysis. Structurally, it follows cognitive progression from concrete to abstract and linear to nonlinear. Three key features define the book: rigorous proofs with clear motivation and logical development; organic connection between linear and nonlinear theories; and integration of theory with applications through examples. Since the last century, mathematics has expanded nonlinearly, globally, and stochastically, with functional analysis permeating PDEs, differential geometry, optimization, control theory, and mathematical economics. This book provides a unified framework to navigate these developments, emphasizing both theoretical depth and practical relevance. This item is printed on demand. Shipping may be from our UK warehouse or from our Australian or US warehouses, depending on stock availability. Seller Inventory # 9789999337823
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