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Modelling, Analysis and Asymptotics: Unraveling the Complexities of Mathematical Modeling

Blake Kennedy

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Published in Quantum Transport: Modelling Analysis And Asymptotics Lectures Given At The C I M E Summer School Held In Cetraro Italy September 11 16 2006 (Lecture Notes In Mathematics 1946)

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Quantum Transport: Modelling, Analysis and Asymptotics - Lectures given at the C.I.M.E. Summer School held in Cetraro, Italy, September 11–16, 2006 (Lecture Notes in Mathematics Book 1946)

by Tanya Deloatch

4.7 out of 5

Language	:	English
File size	:	8152 KB
Screen Reader	:	Supported
Print length	:	274 pages

In the realm of science and engineering, mathematical modeling plays a pivotal role in understanding and predicting complex phenomena. "Modelling, Analysis and Asymptotics" embarks on an enlightening journey into the intricate world of mathematical modeling, asymptotic techniques, and numerical analysis. This comprehensive guide equips you with the essential knowledge and tools to tackle real-world problems across a wide range of scientific disciplines.

Chapter 1: Mathematical Modeling: The Art of Abstraction

Embark on a captivating exploration of mathematical modeling, the process of transforming real-world phenomena into tractable mathematical representations. Delve into the art of abstraction, learning how to identify key features and relationships, and translate them into mathematical equations. Discover the power of simplifying assumptions, approximations, and idealizations in constructing meaningful models.

Chapter 2: Asymptotic Techniques: Unveiling Hidden Behaviors

Asymptotic techniques unlock the secrets of understanding behaviors as parameters approach limits. Explore the concept of asymptotic expansions, learning how to approximate solutions to differential equations, integrals, and other mathematical expressions as parameters become large or small. Uncover the hidden patterns and behaviors of complex systems using asymptotic analysis, revealing insights inaccessible through conventional methods.

Chapter 3: Numerical Analysis: Harnessing Computational Power

Numerical analysis empowers us to solve complex mathematical problems using computers. Dive into the world of numerical methods, discovering how to approximate solutions to equations, perform simulations, and analyze data. Learn about the finite difference method, finite element method, and other essential techniques for solving partial differential equations and other complex mathematical problems.

Chapter 4: Applications in Engineering and Science

Witness the transformative power of mathematical modeling, asymptotic techniques, and numerical analysis in various scientific disciplines. Explore applications in engineering, physics, biology, and more. Discover how mathematical models and simulations help design efficient aircraft, predict weather patterns, and unravel the mysteries of the human body.

Chapter 5: Case Studies: Real-World Success Stories

Delve into real-world case studies that showcase the successful application of mathematical modeling, asymptotic techniques, and numerical analysis. Learn how these powerful tools have contributed to groundbreaking advancements in fields such as aerodynamics, fluid dynamics, and materials science.

Benefits of "Modelling, Analysis and Asymptotics"

Gain a comprehensive understanding of mathematical modeling, asymptotic techniques, and numerical analysis.
Develop the ability to construct and analyze mathematical models of real-world phenomena.
Master asymptotic techniques for approximating solutions and uncovering hidden behaviors.
Acquire proficiency in numerical methods for solving complex mathematical problems.
Discover applications of mathematical modeling, asymptotic techniques, and numerical analysis in various scientific disciplines.
Enhance your problem-solving skills and critical thinking abilities.

Target Audience

"Modelling, Analysis and Asymptotics" is an invaluable resource for:

Students and researchers in applied mathematics, mathematical modeling, and numerical analysis.
Engineers, scientists, and practitioners in fields such as aerospace, mechanical engineering, physics, and biology.
Anyone seeking to deepen their understanding of mathematical modeling and its applications.

Call to Action

Embark on a transformative learning journey with "Modelling, Analysis and Asymptotics." Free Download your copy today and unlock the power of mathematical modeling, asymptotic techniques, and numerical analysis. Let this comprehensive guide be your companion as you delve into the fascinating world of mathematical modeling and its countless applications.

Modelling, Analysis And Asymptotics: Book Cover Quantum Transport: Modelling Analysis And Asymptotics Lectures Given At The C I M E Summer School Held In Cetraro Italy September 11 16 2006 (Lecture Notes In Mathematics 1946)

About the Authors

The authors of "Modelling, Analysis and Asymptotics" are leading experts in the field of applied mathematics. Their combined decades of experience and research ensure that the book provides an authoritative and up-to-date account of the subject matter.