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Modelling with Ordinary Differential Equations - T.P. Dreyer

Modelling with Ordinary Differential Equations

Paperback Published: 28th June 1993
ISBN: 9780849386367
Number Of Pages: 304

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Modelling with Ordinary Differential Equations integrates standard material from an elementary course on ordinary differential equations with the skills of mathematical modeling in a number of diverse real-world situations. Each situation highlights a different aspect of the theory or modeling. Carefully selected exercises and projects present excellent opportunities for tutorial sessions and self-study.
This text/reference addresses common types of first order ordinary differential equations and the basic theory of linear second order equations with constant coefficients. It also explores the elementary theory of systems of differential equations, Laplace transforms, and numerical solutions. Theorems on the existence and uniqueness of solutions are a central feature. Topics such as curve fitting, time-delay equations, and phase plane diagrams are introduced. The book includes algorithms for computer programs as an integral part of the answer-finding process. Professionals and students in the social and biological sciences, as well as those in physics and mathematics will find this text/reference indispensable for self-study.

Preface
Introductionp. 1
Mathematical Modellingp. 1
Boundary Value Problemsp. 3
Direction Fieldsp. 7
Finding Zerosp. 13
First Order Differential Equationsp. 23
Population Growth: Malthus Modelp. 29
Least Squares Method of Curve Fittingp. 33
Population Growth: Logistic Modelp. 37
Harvestingp. 45
Optimization of Profitp. 50
Epidemicsp. 54
Potato Blightp. 56
Free Fall with Air Resistancep. 60
Powerp. 67
Rocketsp. 70
Numerical Methodsp. 99
Existence Theoremp. 100
Euler Algorithmp. 102
Error Analysisp. 105
Runge-Kutta Algorithmp. 112
Fruitfliesp. 116
Laplace Transformsp. 133
Linear Transformsp. 133
Some Properties of Laplace Transformsp. 136
Solving Differential Equations with Laplace Transformsp. 141
Table of Laplace Transformsp. 148
Simultaneous Linear First Order Differential Equationsp. 165
Projectile Trajectories with Air Resistancep. 168
Romantic Relationshipsp. 171
Neutron Flowp. 176
Electrical Networksp. 180
Marriagep. 187
Residential Segregationp. 188
Second Order Linear Differential Equationsp. 205
Mechanical Vibrationsp. 205
Electrical Networksp. 221
The Ignition of An automobilep. 223
Simultaneous Equationsp. 228
Second Order Nonlinear Differential Equationsp. 237
The Pendulum without Dampingp. 239
The Pendulum with Dampingp. 248
Population of Interacting Speciesp. 252
Table of Integralsp. 263
Answersp. 267
Referencesp. 277
Indexp. 282
Table of Contents provided by Blackwell. All Rights Reserved.

ISBN: 9780849386367
ISBN-10: 0849386365
Audience: Professional
Format: Paperback
Language: English
Number Of Pages: 304
Published: 28th June 1993
Publisher: CRC PR INC
Country of Publication: US
Dimensions (cm): 23.5 x 15.88  x 1.91
Weight (kg): 0.43
Edition Number: 1

Earn 249 Qantas Points
on this Book