Learning Differential Equations through DERIVE

Av Brian Lowe, John Berry

240 kr (exkl. moms och frakt)

Learning Differential Equations through DERIVE develops the standard theory of first and second order differential equations, with applications to the physical and environmental sciences, supported by the use of the computer algebra package, DERIVE for Windows. The authors emphasise the role of DERIVE as a tool to help in the solution phase of solving real problems from the physical world and as an investigative tool to help students understand the basic concepts of differential equations.

The book is written for students of mathematics, engineering and the physical sciences who have not studied the theory and solution of differential equations before. It develops the theory from first principles ensuring that students are given the opportunity to solve the equations by hand as well as with the support of DERIVE.

Many differential equations arise from the study of physical situations where the problem is modelled using mathematics. The book begins with a chapter on mathematical modelling and examples of differential equations as models of real world situations. These models are then revisited during the book.

What makes Learning Differential Equations through DERIVE different from the many other texts available at this level is its mixture of applications, theory and solution of differential equations using DERIVE. The experience of the authors in teaching differential equations at Glamorgan and Plymouth shows that DERIVE can give the understanding and confidence to succeed in learning differential equations, and applying their techniques to real problems.

Contents
Preface
Series Preface

Chapter 1: A Modelling Approach to Differential Equations
1.1 Mathematical Modelling
1.2 Some Mathematical Models
1.3 Classification of Differential Equations

Chapter 2: Analytical Solution of First Order Differential Equations
2.1 Direction Fields
2.2 Analytical Solutions
2.3 Equations Solved by Direct Integration
2.4 Separation of Variables
2.5 First Order Linear Equations
2.6 Bernoulli Equations
2.7 Homogeneous Equations
2.8 Exact Equations
2.9 Miscellaneous Substitutions

Chapter 3: Numerical Solution of First Order Differential Equations
3.1 Introduction
3.2 Numerical Methods for Solving First Order Differential Equations
3.3 The Analysis of Numerical Methods
3.4 Stability
3.5 Systems of Linear First Order Equations

Chapter 4: Applications of First Order Differential Equations
4.1 Emptying the Bath
4.2 Heating and Cooling
4.3 Population Models
4.4 Mechanics

Chapter 5: Analytical Solution of Second Order Differential Equations
5.1 Classification of Second Order Differential Equations
5.2 Homogeneous Linear Equations with Constant Coefficients
5.3 Non-Homogenous Linear Equations with Constant Coefficients
5.4 Other Linear Differential Equations With Constant Coefficients
5.5 Linear Second Order Equations in General
5.6 Systems of Linear Differential Equations
5.7 Numerical Solution of Second Order Differential Equations

Chapter 6: Applications of Second Order and Simultaneous First Order Differential Equations
6.1 Oscillations and Vibrations
6.2 Mixing Problems
6.3 Projectile Motion in Two Dimensions

Appendix 1 Glossary of DERIVE FOR WINDOWS Commands
Appendix 2 Functions and Utility Commands
Answers to Exercises