https://mklab.gr/ Sat, 17 Oct 2026 21:00:37 +0000 MyBB https://mklab.gr/showthread.php?tid=2219 Mon, 28 Sep 2026 19:27:01 +0300 mklabgr]]> https://mklab.gr/showthread.php?tid=2219 Mathematical Modeling: Process and Presentation
By Eric Marland, Amanda Beecher, Kayla Blyman and Jessica Libertini
Summary
1. Introduction to mathematical modeling
Mathematical Modeling: Process and Presentation is an introductory textbook that teaches students how to translate real-world problems into mathematical models. Rather than focusing exclusively on mathematical techniques, the book emphasizes the entire modeling process, beginning with identifying a problem and formulating questions. It encourages students to make assumptions, simplify complex situations and select appropriate mathematical tools. The central idea is that mathematical modeling is not simply about solving equations but about understanding real-world phenomena through mathematics.

2. From real-world problems to mathematical models
The book introduces different approaches to modeling through practical examples, including estimating the effort required to fill a balloon and developing mathematical criteria for matching college roommates. Students learn to represent problems using diagrams, graphs, probability and algebraic relationships. They explore how assumptions influence the resulting models and how mathematical formulations can simplify otherwise complicated situations. The book also covers optimization, linear programming, proportional dynamics and stochastic processes, demonstrating how different mathematical methods can address different types of problems.

3. Exploring different types of mathematical models
The textbook covers a broad range of modeling techniques, including probability, randomness, dynamics, control theory, geometry and scaling. It examines how mathematical models can describe changing systems, analyze uncertainty and support decision-making. Importantly, the authors revisit certain modeling problems in later chapters, allowing students to refine their initial approaches and explore more sophisticated solutions. This iterative approach illustrates that mathematical modeling is rarely a straightforward process: models can be modified, improved and adapted as new information becomes available.

4. Evaluation, communication and presentation
An important aspect of the book is the emphasis on interpreting and communicating mathematical results. Students are encouraged to reflect on their assumptions, evaluate the limitations of their models and consider whether their results adequately address the original questions. The final chapter focuses on dissemination, highlighting the importance of presenting mathematical findings clearly to others. Designed primarily for advanced undergraduate and early graduate students, the book uses questions and exercises to encourage independent thinking, exploration and the practical application of mathematics.

Key takeaways

• Modeling is a process: Identifying the problem, making assumptions, constructing a model, solving it and evaluating the results are all essential steps.
  
• Real-world applications: Mathematical concepts can be used to investigate problems involving probability, optimization, dynamics and decision-making.
  
• Assumptions matter: Simplifying a problem makes it mathematically manageable, but assumptions can affect the accuracy of the results.
  
• Multiple approaches: The same real-world problem may be modeled using different mathematical techniques.
  
• Iterative improvement: Models can be revisited and refined as understanding improves.
  
• Critical thinking: Students must assess whether a model is appropriate and recognize its limitations.
  
• Communication: Explaining the model, its assumptions and its conclusions is an essential part of mathematical work.
  
• Practical learning: Exercises and open-ended questions encourage students to develop their own models rather than merely apply predefined formulas.
  

Source: BOOK
.]]> Mathematical Modeling: Process and Presentation
By Eric Marland, Amanda Beecher, Kayla Blyman and Jessica Libertini
Summary
1. Introduction to mathematical modeling
Mathematical Modeling: Process and Presentation is an introductory textbook that teaches students how to translate real-world problems into mathematical models. Rather than focusing exclusively on mathematical techniques, the book emphasizes the entire modeling process, beginning with identifying a problem and formulating questions. It encourages students to make assumptions, simplify complex situations and select appropriate mathematical tools. The central idea is that mathematical modeling is not simply about solving equations but about understanding real-world phenomena through mathematics.

2. From real-world problems to mathematical models
The book introduces different approaches to modeling through practical examples, including estimating the effort required to fill a balloon and developing mathematical criteria for matching college roommates. Students learn to represent problems using diagrams, graphs, probability and algebraic relationships. They explore how assumptions influence the resulting models and how mathematical formulations can simplify otherwise complicated situations. The book also covers optimization, linear programming, proportional dynamics and stochastic processes, demonstrating how different mathematical methods can address different types of problems.

3. Exploring different types of mathematical models
The textbook covers a broad range of modeling techniques, including probability, randomness, dynamics, control theory, geometry and scaling. It examines how mathematical models can describe changing systems, analyze uncertainty and support decision-making. Importantly, the authors revisit certain modeling problems in later chapters, allowing students to refine their initial approaches and explore more sophisticated solutions. This iterative approach illustrates that mathematical modeling is rarely a straightforward process: models can be modified, improved and adapted as new information becomes available.

4. Evaluation, communication and presentation
An important aspect of the book is the emphasis on interpreting and communicating mathematical results. Students are encouraged to reflect on their assumptions, evaluate the limitations of their models and consider whether their results adequately address the original questions. The final chapter focuses on dissemination, highlighting the importance of presenting mathematical findings clearly to others. Designed primarily for advanced undergraduate and early graduate students, the book uses questions and exercises to encourage independent thinking, exploration and the practical application of mathematics.

Key takeaways

• Modeling is a process: Identifying the problem, making assumptions, constructing a model, solving it and evaluating the results are all essential steps.
  
• Real-world applications: Mathematical concepts can be used to investigate problems involving probability, optimization, dynamics and decision-making.
  
• Assumptions matter: Simplifying a problem makes it mathematically manageable, but assumptions can affect the accuracy of the results.
  
• Multiple approaches: The same real-world problem may be modeled using different mathematical techniques.
  
• Iterative improvement: Models can be revisited and refined as understanding improves.
  
• Critical thinking: Students must assess whether a model is appropriate and recognize its limitations.
  
• Communication: Explaining the model, its assumptions and its conclusions is an essential part of mathematical work.
  
• Practical learning: Exercises and open-ended questions encourage students to develop their own models rather than merely apply predefined formulas.
  

Source: BOOK
.]]> https://mklab.gr/showthread.php?tid=2130 Wed, 23 Sep 2026 23:51:15 +0300 mklabgr]]> https://mklab.gr/showthread.php?tid=2130 Mathematical Models and Their Analysis by Frederic Y. M. Wan is a textbook on how mathematics can be used to formulate, analyze, and interpret models of real-world phenomena. Rather than treating mathematical techniques in isolation, it introduces them through concrete problems from physics, engineering, traffic, environmental management, economics, and resource allocation. The book develops tools including dimensional analysis, ordinary and partial differential equations, perturbation methods, stability analysis, eigenvalue problems, calculus of variations, optimization, and optimal control.

A central theme is that mathematical modeling is an iterative process: begin with a simplified but meaningful model, analyze its behavior, compare its predictions with observations, and refine it when necessary. The applications range from Kepler's planetary laws, Mercury's orbital precession, elastic buckling, traffic flow, shallow-water waves, and heat conduction to fishing limits, urban development, economic growth, renewable resources, and forest harvesting. The final appendix introduces controllability of linear systems, extending the book toward control theory. 

Overall, it emphasizes how the same mathematical structures—especially differential equations and optimization—can illuminate very different real-world problems.

BOOK]]> Mathematical Models and Their Analysis by Frederic Y. M. Wan is a textbook on how mathematics can be used to formulate, analyze, and interpret models of real-world phenomena. Rather than treating mathematical techniques in isolation, it introduces them through concrete problems from physics, engineering, traffic, environmental management, economics, and resource allocation. The book develops tools including dimensional analysis, ordinary and partial differential equations, perturbation methods, stability analysis, eigenvalue problems, calculus of variations, optimization, and optimal control.

A central theme is that mathematical modeling is an iterative process: begin with a simplified but meaningful model, analyze its behavior, compare its predictions with observations, and refine it when necessary. The applications range from Kepler's planetary laws, Mercury's orbital precession, elastic buckling, traffic flow, shallow-water waves, and heat conduction to fishing limits, urban development, economic growth, renewable resources, and forest harvesting. The final appendix introduces controllability of linear systems, extending the book toward control theory. 

Overall, it emphasizes how the same mathematical structures—especially differential equations and optimization—can illuminate very different real-world problems.

BOOK]]> https://mklab.gr/showthread.php?tid=1959 Mon, 14 Sep 2026 01:06:24 +0300 mklabgr]]> https://mklab.gr/showthread.php?tid=1959 Authors: Nan Chen & Charlotte Moser
Publisher: CRC Press / Chapman & Hall, Taylor & Francis
Publication: forthcoming, 2026
ISBN: 978-1-041-23824-9

Summary
Applied Mathematics Toolkit is designed as a modern, integrated introduction to the mathematical machinery needed to study complex scientific and engineering systems. Its central idea is that modeling, statistics, machine learning, dynamical systems, stochastic methods, and computation should not be learned as disconnected subjects. Real problems typically involve several simultaneously: a mathematical model may be incomplete, observations noisy, dynamics nonlinear, the state high-dimensional, and important quantities only partially observable. The book therefore develops these techniques as parts of a single problem-solving framework connecting models + data + algorithms.
The scope is unusually broad. 

After an introduction, the book develops separate toolkits for statistics, machine learning, dynamical systems, applied analysis, and stochastic mathematics. It then moves toward subjects that connect these areas: data assimilation, information theory and uncertainty quantification, causal inference, and reduced-order modeling. The latter topics are especially important for modern scientific computing because they address questions such as how to combine imperfect models with observations, quantify uncertainty in predictions, infer possible causal relationships from data, and replace extremely high-dimensional systems with computationally manageable approximations.
 
A major pedagogical feature is that the authors emphasize not merely formulas but why a method works, what assumptions it makes, when it should be used, and where it can fail. Concepts are introduced through relatively simple examples before moving to more complicated applications. Example code supports computational experimentation, while short companion “one concept–one example” videos of roughly 5–10 minutes are intended to build intuition and facilitate review. This makes the book suitable both as a university text and for self-study by scientists or engineers who want a working mathematical toolkit rather than a purely theoretical survey.
 
Contents at a glance

1. Introduction
   
2. Statistical Toolkit
   
3. Machine Learning Toolkit
   
4. Dynamical Toolkit
   
5. Applied Analysis Toolkit
   
6. Stochastic Toolkit
   
7. Data Meets Models: An Introduction to Data Assimilation
   
8. Information Theory and Uncertainty Quantification
   
9. Causal Inference
   
10. Reduced-Order Models
    

BOOK]]> Authors: Nan Chen & Charlotte Moser
Publisher: CRC Press / Chapman & Hall, Taylor & Francis
Publication: forthcoming, 2026
ISBN: 978-1-041-23824-9

Summary
Applied Mathematics Toolkit is designed as a modern, integrated introduction to the mathematical machinery needed to study complex scientific and engineering systems. Its central idea is that modeling, statistics, machine learning, dynamical systems, stochastic methods, and computation should not be learned as disconnected subjects. Real problems typically involve several simultaneously: a mathematical model may be incomplete, observations noisy, dynamics nonlinear, the state high-dimensional, and important quantities only partially observable. The book therefore develops these techniques as parts of a single problem-solving framework connecting models + data + algorithms.
The scope is unusually broad. 

After an introduction, the book develops separate toolkits for statistics, machine learning, dynamical systems, applied analysis, and stochastic mathematics. It then moves toward subjects that connect these areas: data assimilation, information theory and uncertainty quantification, causal inference, and reduced-order modeling. The latter topics are especially important for modern scientific computing because they address questions such as how to combine imperfect models with observations, quantify uncertainty in predictions, infer possible causal relationships from data, and replace extremely high-dimensional systems with computationally manageable approximations.
 
A major pedagogical feature is that the authors emphasize not merely formulas but why a method works, what assumptions it makes, when it should be used, and where it can fail. Concepts are introduced through relatively simple examples before moving to more complicated applications. Example code supports computational experimentation, while short companion “one concept–one example” videos of roughly 5–10 minutes are intended to build intuition and facilitate review. This makes the book suitable both as a university text and for self-study by scientists or engineers who want a working mathematical toolkit rather than a purely theoretical survey.
 
Contents at a glance

1. Introduction
   
2. Statistical Toolkit
   
3. Machine Learning Toolkit
   
4. Dynamical Toolkit
   
5. Applied Analysis Toolkit
   
6. Stochastic Toolkit
   
7. Data Meets Models: An Introduction to Data Assimilation
   
8. Information Theory and Uncertainty Quantification
   
9. Causal Inference
   
10. Reduced-Order Models
    

BOOK]]> https://mklab.gr/showthread.php?tid=1668 Mon, 17 Aug 2026 19:37:07 +0300 mklabgr]]> https://mklab.gr/showthread.php?tid=1668 Author: Mark H. Holmes
Publication date: 2009
Publisher: Springer New York
Series:Texts in Applied Mathematics, Vol. 56

Introduction to the Foundations of Applied Mathematics is a substantial introduction to the central ideas and techniques of applied mathematics, aimed primarily at advanced undergraduate and beginning graduate students. Rather than presenting applied mathematics as a collection of unrelated applications, Mark H. Holmes develops a systematic approach to constructing, analyzing, and interpreting mathematical models. The book grew out of the long-running Foundations of Applied Mathematics (FOAM) course at Rensselaer Polytechnic Institute and continues the tradition of integrating mathematical reasoning with physical intuition. 

The book begins with dimensional analysis, showing how units, scaling, and nondimensionalization can reveal the essential structure of a physical problem before detailed calculations begin. It then introduces perturbation methods, which provide approximations when an exact solution is unavailable or impractical. From there Holmes develops increasingly sophisticated models involving kinetics, diffusion and traffic flow, illustrating how differential equations and conservation principles emerge naturally from physical assumptions. 

The later chapters move into continuum mechanics, first in one spatial dimension and then in three dimensions. Elastic and viscoelastic materials and fluid mechanics provide major applications in which concepts such as stress, strain, conservation of mass, momentum and constitutive laws are developed mathematically. The progression is particularly valuable because the mathematics is introduced together with the modeling assumptions that produce it: the reader learns not merely how to solve equations, but why those equations are appropriate models in the first place. Supplementary material covers topics including Taylor's theorem, Fourier analysis and stochastic differential equations. 

One of the book's strengths is therefore its balance between mathematical rigor, physical reasoning and modeling practice. It assumes a solid background in calculus and differential equations, so it is not an elementary introduction, but for mathematically mature students it provides a bridge between pure mathematical techniques and their use in science and engineering. Reviews have particularly praised this integration of theory and application and the large collection of exercises. 

Key takeaways

• Applied mathematics is fundamentally about modeling: deriving equations from assumptions about real systems is as important as solving them.
  
• Scaling and approximation are essential tools: dimensional analysis and perturbation methods often reveal useful information without requiring exact solutions.
  
• A small collection of mathematical principles has remarkably broad applications, from chemical kinetics and diffusion to traffic, elasticity and fluid mechanics.
  
• The book is especially useful for advanced undergraduate or beginning graduate students who want to understand the mathematical foundations behind models used in physics, engineering and applied science. 
  

Springer — Introduction to the Foundations of Applied Mathematics]]> Author: Mark H. Holmes
Publication date: 2009
Publisher: Springer New York
Series:Texts in Applied Mathematics, Vol. 56

Introduction to the Foundations of Applied Mathematics is a substantial introduction to the central ideas and techniques of applied mathematics, aimed primarily at advanced undergraduate and beginning graduate students. Rather than presenting applied mathematics as a collection of unrelated applications, Mark H. Holmes develops a systematic approach to constructing, analyzing, and interpreting mathematical models. The book grew out of the long-running Foundations of Applied Mathematics (FOAM) course at Rensselaer Polytechnic Institute and continues the tradition of integrating mathematical reasoning with physical intuition. 

The book begins with dimensional analysis, showing how units, scaling, and nondimensionalization can reveal the essential structure of a physical problem before detailed calculations begin. It then introduces perturbation methods, which provide approximations when an exact solution is unavailable or impractical. From there Holmes develops increasingly sophisticated models involving kinetics, diffusion and traffic flow, illustrating how differential equations and conservation principles emerge naturally from physical assumptions. 

The later chapters move into continuum mechanics, first in one spatial dimension and then in three dimensions. Elastic and viscoelastic materials and fluid mechanics provide major applications in which concepts such as stress, strain, conservation of mass, momentum and constitutive laws are developed mathematically. The progression is particularly valuable because the mathematics is introduced together with the modeling assumptions that produce it: the reader learns not merely how to solve equations, but why those equations are appropriate models in the first place. Supplementary material covers topics including Taylor's theorem, Fourier analysis and stochastic differential equations. 

One of the book's strengths is therefore its balance between mathematical rigor, physical reasoning and modeling practice. It assumes a solid background in calculus and differential equations, so it is not an elementary introduction, but for mathematically mature students it provides a bridge between pure mathematical techniques and their use in science and engineering. Reviews have particularly praised this integration of theory and application and the large collection of exercises. 

Key takeaways

• Applied mathematics is fundamentally about modeling: deriving equations from assumptions about real systems is as important as solving them.
  
• Scaling and approximation are essential tools: dimensional analysis and perturbation methods often reveal useful information without requiring exact solutions.
  
• A small collection of mathematical principles has remarkably broad applications, from chemical kinetics and diffusion to traffic, elasticity and fluid mechanics.
  
• The book is especially useful for advanced undergraduate or beginning graduate students who want to understand the mathematical foundations behind models used in physics, engineering and applied science. 
  

Springer — Introduction to the Foundations of Applied Mathematics]]> https://mklab.gr/showthread.php?tid=638 Tue, 23 Jun 2026 09:25:41 +0300 mklabgr]]> https://mklab.gr/showthread.php?tid=638 The Princeton Companion to Applied Mathematics

Summary

The Princeton Companion to Applied Mathematics is a comprehensive guide to the world of applied mathematics, showing how mathematical ideas are used to understand and solve real problems in science, engineering, technology, and society. Edited by Nicholas J. Higham with contributions from many leading experts, the book explores the language of applied mathematics, important concepts, equations, algorithms, modeling techniques, and modern research areas such as numerical analysis, dynamical systems, mathematical physics, and computational methods.

 Rather than being a traditional textbook, it feels more like a guided tour through the landscape of applied mathematics, helping readers see how different fields connect and why mathematics is such a powerful tool for describing the world around us. It is a valuable reference for students, researchers, engineers, and anyone curious about how abstract mathematical ideas become practical solutions. 



ARTICLE]]> The Princeton Companion to Applied Mathematics

Summary

The Princeton Companion to Applied Mathematics is a comprehensive guide to the world of applied mathematics, showing how mathematical ideas are used to understand and solve real problems in science, engineering, technology, and society. Edited by Nicholas J. Higham with contributions from many leading experts, the book explores the language of applied mathematics, important concepts, equations, algorithms, modeling techniques, and modern research areas such as numerical analysis, dynamical systems, mathematical physics, and computational methods.

 Rather than being a traditional textbook, it feels more like a guided tour through the landscape of applied mathematics, helping readers see how different fields connect and why mathematics is such a powerful tool for describing the world around us. It is a valuable reference for students, researchers, engineers, and anyone curious about how abstract mathematical ideas become practical solutions. 



ARTICLE]]> https://mklab.gr/showthread.php?tid=101 Fri, 05 Jun 2026 17:26:04 +0300 mklabgr]]> https://mklab.gr/showthread.php?tid=101


Title : Introduction to Experimental Mathematics (Cambridge Mathematical Textbooks) 1st Edition
Author : Søren Eilers, Rune Johansen
Date : 2017

Summary :  Introduction to Experimental Mathematics (by Søren Eilers and Rune Johansen, published by Cambridge University Press) is a highly practical textbook designed to bridge the gap between traditional theoretical mathematics and computational exploration.

BOOK PAGE]]>


Title : Introduction to Experimental Mathematics (Cambridge Mathematical Textbooks) 1st Edition
Author : Søren Eilers, Rune Johansen
Date : 2017

Summary :  Introduction to Experimental Mathematics (by Søren Eilers and Rune Johansen, published by Cambridge University Press) is a highly practical textbook designed to bridge the gap between traditional theoretical mathematics and computational exploration.

BOOK PAGE]]>