Functional Analysis In Modern Applied Mathematics By Ruth F Curtain
- Publisher: MATHEMATICS
- Availability: In Stock
- SKU: 49250
- Number of Pages: 174
Rs.720.00
Rs.1,050.00
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Functional Analysis in Modern Applied Mathematics
Author: Ruth F. Curtain
Binding: Paperback
Paper Quality: White Paper
Category: Functional Analysis, Applied Mathematics, Advanced Mathematics
Recommended For:
BS (Hons) / MSc Mathematics, Applied Mathematics, Engineering, and Physics students, especially those pursuing research, MPhil, or Ph.D. with applications in control theory, differential equations, and functional spaces.
Key Points:
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Introduction to Functional Analysis Functional analysis serves as a foundational tool in modern applied mathematics, focusing on the study of vector spaces equipped with topological structures and linear operators.
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Applications in Partial Differential Equations (PDEs) Functional analysis techniques are crucial in studying and solving complex partial differential equations arising in physics, engineering, and finance.
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Optimization and Control Theory The book explores how functional analysis contributes to optimization problems and control theory, enabling efficient algorithms and robust control strategies.
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Harmonic Analysis and Signal Processing Functional analysis methods play a vital role in harmonic analysis, signal processing, and image reconstruction, enhancing the understanding and manipulation of signals and images.
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Numerical Analysis and Approximation Theory Techniques from functional analysis are employed in numerical analysis and approximation theory to develop accurate computational methods and algorithms.
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Probability Theory and Stochastic Processes The application of functional analysis in probability theory and stochastic processes helps in modeling random phenomena and analyzing their statistical properties.
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Operator Theory and Quantum Mechanics Functional analysis provides the theoretical framework for operator theory, essential in understanding quantum mechanics and its mathematical formulations.
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Data Analysis and Machine Learning The book discusses how functional analysis concepts are adapted for data analysis tasks and machine learning algorithms, enhancing predictive modeling and pattern recognition.
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Nonlinear Analysis and Dynamical Systems Functional analysis tools are essential in studying nonlinear phenomena and dynamical systems, offering insights into stability, bifurcations, and chaos theory.
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Interdisciplinary Applications Finally, the interdisciplinary nature of functional analysis allows its application in diverse fields such as biology, economics, and geophysics, addressing complex problems with mathematical rigor.
Conclusion: "Functional Analysis in Modern Applied Mathematics" serves as a vital resource for researchers, academics, and practitioners seeking to apply advanced mathematical techniques to real-world problems. It bridges theoretical insights with practical applications across various domains, highlighting the versatility and power of functional analysis in modern mathematics.
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Writer ✤ Ruth F Curtain & AJ Pritchard