# Mathematics applied to deterministic problems in the natural sciences

@inproceedings{Lin1995MathematicsAT, title={Mathematics applied to deterministic problems in the natural sciences}, author={Chia-chiao Lin and Lee A. Segel and G. H. Handelman}, booktitle={Classics in applied mathematics}, year={1995} }

A. An Overview of the Interaction of Mathematics and Natural Science: 1. What is applied mathematics? 2. Deterministic systems and ordinary differential equations 3. Random processes and ial differential equations 4. Superposition, heat flow, and Fourier analysis 5. Further developments in Fourier analysis B. Some Fundamental Procedures Illustrated on Ordinary Differential Equations: 6. Simplification, dimensional analysis, and scaling 7. Regular perturbation theory 8. Illustration of…

## 453 Citations

On the Application of the Fixed Point Theory to the Solution of Systems of Linear Differential Equations to Biological and Physical Problems

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In this study, I worked on how to solve the biological and physical problems using systems of linear differential equations. A differential equation is an equation involving an unknown function and…

Numerical analysis

- Computer ScienceScholarpedia
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This area is concerned with using the most powerful tools of numerical analysis, computer graphics, symbolic mathematical computations, and graphical user interfaces to make it easier for a user to set up, solve, and interpret complicated mathematical models of the real world.

Partial Differential Equations in Action: From Modelling to Theory

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The book is intended as an advanced undergraduate or first-year graduate course for students from various disciplines, including applied mathematics, physics and engineering. It has evolved from…

Lin & Segel's Standing Gradient Problem Revisited: A Lesson in Mathematical Modeling and Asymptotics

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- 2011

This work revisits a physiological standing gradient problem of Lin and Segel with a view to giving it an up-to-date perspective and shows that the problem can be analyzed using the tools of singular perturbation theory and matched asymptotic expansions.

Introduction to Computation and Modeling for Differential Equations

- Computer Science
- 2008

This book successfully introduces readers to the subject through a unique "Five-M" approach: Modeling, Mathematics, Methods, MATLAB, and Multiphysics, which facilitates a thorough understanding of how models are created and preprocessed mathematically with scaling, classification, and approximation.

Kinematics in Regular and Irregular Waves based on a Lagrangian Formulation

- Physics
- 2000

Kinematics in two-dimensional regular and irregular swface waves is described based on the Lagrangian form of the equations of motion, with particular emphasis 011 the conditions in the so-called…

Dynamical Systems Methods Applied to the Michaelis-Menten and Lindemann Mechanisms

- Mathematics
- 2009

In the first part of this thesis, we will explore an iterative procedure to determine the detailed asymptotic behaviour of solutions of a certain class of nonlinear vector differential equations…

Hyperbolic differential-operator equations on a whole axis

- Mathematics
- 2004

We give an abstract interpretation of initial boundary value problems for hyperbolic equations such that a part of initial boundary value conditions contains also a differentiation on the time t of…

The Method of Matched Asymptotic Expansions and Its Generalizations

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Milton Van Dyke’s Perturbation Methods in Fluid Mechanics [490] was effectively both the earliest and the most influential book specifically about applied singular perturbations. (Some credit might…

An analytical approach to bifurcations and stability in simplified mathematical models of nuclear reactors

- MathematicsProgress in Nuclear Energy
- 2019