LEARNING THROUGH COMPUTER ALGEBRA SERIES
Series editor John Berry, University of Plymouth
Learning Mathematics through DERIVE J. S. Berry, E. Graham, A. J. P. Watkins
This book develops foundation mathematics for scientists and engineers through the use of DERIVE. It is a standalone textbook, for post-16 through to undergraduate level, with DERIVE integrated as an investigative tool. DERIVE is used to introduce and help students to understand basic concepts in mathematics and as a problem-solving tool for solving real problems from the world of science and engineering.
Written primarily for students who have not studied maths at A-level or equivalent, or who are entering a science or engineering degree at the foundation level. However, the book will also provide an introduction to the use of DERIVE to those students who are already familiar with scientific functions and calculus.
CONTENTS: Introductory functions; Exponential and logarithmic functions; Trigonometric functions; Sequences and series; Simple numerical methods for solving equations, Differentiation; Integration; Numerical methods; Differential equations; Complex numbers; Matrices.
370 pages, 1996, 15.95 Pounds Sterling
Cover of "Learning Mathematics through DERIVE"
Learning Numerical Analysis through DERIVE Terence Etchells, John Berry
This book covers the major numerical methods, and their analysis, for first courses at college and undergraduate level. The relative merits of each method are covered both analytically, providing a thorough grounding in the algebraic approach, and practically, through the tried and tested computer lab-based activities.
DERIVE provides a platform on which to quickly and accurately perform many complicated numerical calculations. Also, DERIVE's ability to algebraically manipulate expressions and perform calculus operations, enhances the investigation of the convergence of numerical methods.
Each chapter includes the development and algebraic analysis of the methods, lab-based activities, ideas for coursework, case studies, exercises and solutions. Free supporting utility files are available from Terence Etchells' website.
Chapter 1 introduces the basic tool of numerical methods, which is recurrence relations, their solution and ill-conditioning problems. In chapter 2 we use recurrence relations methods that are used in solving equations. Chapter 3 deals with the approximation of functions by polynomials, and in particular the Taylor Polynomial, which is then used extensively in chapter 4 to analyse the errors associated with numerical methods.
Chapters 5 and 6 deal with numerical approaches to the calculus of differentiation and integration. In chapter 7 we introduce and analyse numerical methods of solving differential equations.
239 Pages, 1997, 15.95 Pounds Sterling
Cover of "Learning Numerical Analysis through DERIVE"
Learning Linear Algebra through DERIVE Brian Denton
The book covers a two-semester course. It assumes no prior knowledge of matrices and vectors and therefore is suitable for 6th formers or undergraduates. The book can be used without teacher assistance. The applications touch on: networks, steady-state and Markov processes, economics, coding, quadratic forms and conic sections and differential equations.
Answers to all the exercises, and solutions to all the consolidation exercises, are included. There is also a full index of definitions as well as a comprehensive Bibliography for Further Reading and sources for more exercises. The book finishes with a five page index. CONTENTS: Introduction to matrices; Determinants; Vectors with applications to geometry; More matrices; Systems of linear equations; Vector spaces and linear transformations, Eigenvectors and eigenvalues; Orthogonal matrices; Some applications; Conclusions; Solutions.
296 pages, 1995, 16.95 Pounds Sterling
Cover of "Learning Linear Algebra through DERIVE"
NEW
Learning Modelling with DERIVE Stewart Townend, David Pountney
Develops undergraduate mathematical modelling skills with the support of DERIVE. The book provides students with the opportunity to develop both their problem-solving and IT skills through the fully integrated use of DERIVE. The authors' experience of teaching modelling at Liverpool John Moores University shows that the use of DERIVE enhances the students' modelling expertise.
- Gently guides the reader through the problem formulating, solution and revision stages of modelling.
- Provides a wide range assortment of case studies, some of which are developed fully while others have only hints provided. A wide-ranging set of modelling problems is also provided.
CONTENTS: Introduction; Geometric and trigonometric models; Algebraic models; Optimisation-based models; Statistical and simulations models; The techniques of dimensional analysis.
256 pages, 1995, 15.95 Pounds Sterling
Cover of "Learning Modelling with DERIVE"
Learning Mathematics through the TI-92 J. S. Berry, E. Graham, A. J. P. Watkins
Cover of "Learning Mathematics through the TI-92" Learning Mathematics through the TI-92 develops the foundation mathematics needed by scientists and engineers through the use of the Texas Instruments TI-92. The authors emphasise its use as an investigative tool to introduce, and help students to understand, basic concepts in mathematics, and as a problem solving tool for solving real problems from the world of science and engineering.
The book is written primarily for students who have not studied mathematics in depth at school, and will prepare them for a foundation course in science or engineering. However, the book also provides an introduction to the use of the TI-92 for those students who are already familiar with scientific functions and calculus.
Learning Mathematics through the TI-92 provides an exciting and unique opportunity for students to learn and use mathematics in a refreshing way. The experience of the authors in teaching engineering students at Plymouth shows how their approach provides the understanding and confidence to succeed in learning mathematics.
367 pages, 1997, 15.95 Pounds Sterling
Learning Differential Equations through DERIVE Brian Lowe, John Berry
Cover of "Learning Differential Equations through DERIVE" 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
1998, approx 15.95 Pounds Sterling
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