- Mathematical Activities with Computer Algebra:
a photocopiable resource book
Etchells T, Hunter M, Monaghan J, Pozzi S, Rothery A
This photocopiable resource book is the first of a new generation of
support materials for the educational use of computer algebra. Designed to
be used with any computer algebra system, the authors go beyond mere button
pressing and show how to harness the power of computer algebra systems for
educational purposes.
Concepts are illustrated, techniques and methods presented, and modelling
and applications are explained. Appendices give overviews of
DERIVE, Maple, Mathematica, Theorist (MathPlus) and the new TI-92 calculator.
Activity Worksheets, Help Sheets and Teaching Notes cover a wide range of
mathematical topics at school and college level.
Topics covered include; functions and graphs, differentiation, integration,
sequences and series, vectors and matrices, mechanics, trigonometry,
numerical methods.
Activities include: Multiplying factors; Equation of a tangent; Taxing
functions; The tile factory; Function and derivative - visualisation; The
approximate derivative function; Sketching graphs; Pollution and
population; Max cone; Optimising transport costs; Area under a curve;
Enclosed areas; A function whose derivative is itself; Wine glass design;
The limit of a sequence; Visualising Taylor approximations; Visualising
matrix transformations; Blood groups; Circular motion; Swing safety; No
turning back; Modelling the sine function; Solving equations with tangents.
20 Pounds, 96 pp, 1996, ISBN 0-86238-405-2
- MATHEMATICS ON THE PC: Introduction to Derive
A book for teachers and students Kutzler, Bernhard
This is the most up-to-date book on how to use Derive for teaching and
learning mathematics (the only book covering version 3). It leads you
through several mathematical topics demonstrating the major features and
techniques of Derive. The examples also provide ideas for using Derive
during teaching. Since it aims to be a gentle manual with a wide range of
educational examples, it can be used with Derive at a wide range of
educational levels.
14.50 Pounds, 1995, 162 pages
- Improving Mathematics Teaching with DERIVE
A guide for teachers
Kutzler, Bernhard
One of the most important recent books on the subject of teaching
mathematics. The world's leading expert on teaching mathematics with the
popular DERIVE computer algebra system (also available on the Texas
Instruments TI-92 calculator) shows how to use it in the classroom.
Alternative implementation strategies are offered to suit different topics
and situations. He also advises, convincingly, on how this new technology
will change curricula and and teaching methods. The book is full of clearly
presented practical examples and is a must for every mathematics teacher.
CONTENTS: Introduction;
Chapter 1: What DERIVE can do
Chapter 2: DERIVE in Traditional Mathematics Teaching
The House of Mathematics
- Example 1: Solving equations
- Example 2: Applied trigonometry problems
How do we teach, and how do we learn?
Building a house with DERIVE
Scaffolding
A different view: DERIVE as mathematical spectacles
Chapter 3: The Future of Mathematics Teaching
What is Mathematics?
Cleaning out
Concentration upon critical points of education
- rational and irrational numbers
- variables
- representations
- functions
- limits
New subjects
New teaching methods
What must a mathematician be capable of? New old educational goals
- Understanding
- Description
- Argumentation
- To be critical
- Understanding numbers, percentages and
orders of magnitude
- Abstraction
- Induction and deduction
Chapter 4: Examples for Teaching
- Example 1 Curve fitting
- Example 2 Simulating two dice
- Example 3 From physics: a line of curvature
- Example 4 Introduction to Taylor Series
- Example 5 Introduction to limits
- Example 6 Introduction to integration
Chapter 5: Tips and Tricks
Input of expressions
Expression manipulation
Vectors and matrices
Function evaluation
Solving equations
Plotting graphs
Loading and saving
Chapter 6: You Own System: User-defined menus
Chapter 7: How Does a Computer Algebra System Work?
Arbitrarily long numbers
Working with formulae
Symbolic differentiation
Multiplying longer numbers
Symbolic integration
Simplification
Chapter 8: DERIVE and 250 Years of History - Quo Vadis?
Index
14.50 Pounds, ISBN 0-86238-422-2, 185 pages
- A Tutorial Introduction to Derive Ellis, Wade Jr. and Lodi, Ed:
A friendly and popular introduction to Derive.
It includes examples and
exercises covering equation solving, function definitions, 2 and 3D
plotting, calculus and linear algebra.
12.95 Pounds, 60 pages, 1991
- Learning Mathematics through DERIVE
Berry J, Graham E, Watkins A J
This book develops foundation mathematics for scientists and engineers
through the use of DERIVE. It emphasises the role of DERIVE 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. 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. Readership: Post-16
mathematics through to undergraduate level.
15.95 Pounds, 1994, 370 pages
- DERIVE-Based Investiga-tions for Post-16 Core Mathematics
Watkins A J
Tony Watkins of the Centre for Teaching Mathematics, University of
Plymouth, has produced these excellent practical exercises which show how
to use Derive to discover mathematical concepts faster, have more fun in
the process and achieve a deeper understanding. Developed over a 5 year
period and extensively trialled, the investigations can be used by a wide
range of students; from those with only high school mathematics to
university undergraduates. The author's wide experience of using
DERIVE as
a highly effective teaching tool will provide stimulating and proven
techniques for your own classroom.
9.95 Pounds, ISBN 0-86238-312-9, 102 pages, 2nd edition
- DERIVE in Education:Opportunities & Strategies
Heugl, H., Kutzler, B
The main contributions from the 1993 Krems conference on
DERIVE didactics
are beautifully presented here. Experts from 14 countries examine a wide
range of educational issues, offering suggestions and experiences at
school, college and university level. This book will help you to teach and
use maths in a faster, more efficient and more comprehensive way using
DERIVE and looks at how maths teaching should be changed to take advantage
of it.
19.95 Pounds, ISBN 0-86238-351-X, 1994, 302 pages
- Teaching Mathematics with DERIVE Ed. Josef Bohm
This illustrated guide is packed full of sound advice and teaching
materials. Top European educationalists show how to use computer algebra
systems to teach mathematics (particularly to 12-18 year olds). It is full
of helpful suggestions for teachers and shows the impact on different parts
of the curriculum. If you are teaching mathematics, at school, college, or
university, these papers from the 1992 Krems conference will be useful and
thought-provoking.
13.95 Pounds, ISBN 0-86238-319-6, 298 pages
- Numerical Analysis Via Derive Schonefeld, Steven
This new book shows how to use Derive to implement
numerical methods for
solving a wide range of problems. It may be used as a primary textbook for
an introductory, undergraduate course in numerical analysis. For
convenience, an accompanying disk contains all the Derive procedures in the
book.
The book is quite similar to many standard numerical analysis texts, yet
Derive is integrated throughout. Written as an introductory course in
numerical analysis, it may be used as the main text for a one or two
semester course at college freshman+ level. Many topics are within the
grasp of a mature college freshman. If you do not want to cover the
solutions to differential equations, Calculus may be the only prerequisite.
The book differs from many numerical analysis texts in that it does not
require the reader to be proficient in any programming language. You don't
need a second language to use this book. However if you enjoy programming,
some of the advanced exercises may challenge your skills. Most of the
sections are largely self-contained, allowing the book to be used in a
flexible way.
29.95 Pounds, 529 pages, 1994
- College Algebra Laboratories using Derive
DeMarois, Phil:
These 19 lab experiences use Derive to remove
computational barriers so
students can concentrate on discovering and applying key concepts.
Students are presented with a series of guided experimental activities that
result in intuitive discovery. The book helps students to realise the
connections between real world problems and various areas of mathematics.
Mathematics is made theirs through active engagement in the construction of
key ideas. It broadens students' ability to visualise mathematical ideas.
Most of the sessions may be assigned with no previous background expected
of the students.
13.95 Pounds, 125 pages, 1992
- Elementary Linear Algebra with Derive
an integrated text Hill R. J., Keagy T. A.
A modern approach to linear algebra that blends an emphasis on
elegant theoretical structure and a rich supply of applications.
Uses almost 600 statements from Derive to illustrate how to
simplify tedious calculations which could otherwise distract and discourage
students. Up-to-date with DERIVE VERSION 3.
Allows for rapid coverage of the elementary properties of matrices,
vector spaces, linear transformations, and determinants without the burden
of time consuming hand calculations.
Emphasises eigenvalues, eigenvectors, matrix analysis, and
applications in diverse areas such as least squares approximations, Markof
processes, difference equations, and linear systems of differential
equations with constant coefficients.
Includes more than 180 example problems worked in detail.
Provides more than 600 exercises, most with solutions.
CONTENTS: Derive and Matrices: Introduction to Derive, Matrices and the
Algebra of Matrices, Multiplication of Matrices, Inverse of a Square
Matrice, Elementary Matrices, Linear Systems of Equations, Row Echelon
Form, Vector Spaces: Vector Spaces, Subspaces, Linear Independence and
Dependence, Spanning Sets of Vectors, Basis and Dimension, Linear
Transformations: Linear Transformations, Properties of Linear
Transformations, Coordinates, Matrix of a Linear Transformation,
Composition of Linear Transformations, Similarity, Determinants: Definition
and Computation of Determinants, The Adjoint Matrix, Cramer's Rule and
Systems of Equations, Eigenvalues and Eigenvectors: Eigenvalues and
Eigenvectors, The Cayley Hamilton Theorem, Special Types of Matrices,
Bounds for Eigenvalues, Jordan Canonical Form, Matrix Analysis: Vector and
Matrix Norms, Limits of Matrices and Vectors, Functions of Matrices,
Functions of Matrices - An Algorithm, Applications: Least Squares
Approximations, Markof Processes, Difference Equations, Linear Systems of
Difference Equations with Constant Coefficients, Answers to Selected
Exercises, Symbols, Index.
14.95 Pounds, 370 pages, 1995
- Learning Linear Algebra through DERIVE Denton B
Contents: Introduction to Matrices. Vectors with Applications to Geometry.
Systems of Linear Equations. Vech spaces. Linear Transformation.
Eigenvectors and eigenvalues. Conclusions. Solutions.
16.95 Pounds, 296 pages, 1995
- Linear Algebra with Derive Evans B, Johnson J
An enrichment supplement to a traditional introductory linear algebra
course. No prior knowledge of Derive is required. Appendix 1 summarizes
important commands and helps novice users get started. The exercises
progress from the simple to more challenging problems. Numerous
applications are provided including optimization, Markov chains, systems of
differential equations, the Gauss-Seidel method, generalized inverses;
curve fitting, rotation of axes, and cryptography. The LU and QR
factorisations are presented. Optional code for automating some precedures
is provided.
Contents: Systems of equations; Augmented matrices and elementary row
operations; The algebra of matrices; Inverses of matrices; Determinants,
adjoints, and Cramer's rule; Application - matrix algebra and modular
arithmetic; Vector products, lines and planes; Vector spaces and subspaces;
Independence, basis and dimension; Row space, column space, null space;
Inner product spaces; Orthonormal bases and the Gram-Schmidt process;
Change of basis and orthogonal matrices; Eigenvalues and Eigenvectors;
Diagonalization and orthogonal diagonalization; Matrices and linear
transformations from Rn to Rm; Matrices of general linear transformations -
similarity; Applications and numerical methods.
16.50 Pounds, 280 pages, 1994
- Linear Algebra Experiments Using the Derive Program
Salter M, Gilligan L,
13.95 Pounds, 122 pages, 1992
- Pre-calculus Investigations Using Derive Mathews, David M
Exciting alternative to traditional lecture and listen pre-calculus and
algebra and trigonometry courses. Twelve carefully structured interactive
learning environments for your students.
Contents: Introduction to Derive; Polynomial functions and their graphs;
Applications of polynomial functions; Rational functions and their graphs;
Applications of rational functions; Exponential and logarithmic functions;
Applications of exponential functions; Applications of logarithmic
functions; Trigonometric functions and their graphs; The simple harmonic
model; Solving trigonometric equations; Solving systems of equations.
12.95 Pounds, 1994
- Discovering Calculus with Derive Johnson J, Evans B
Supplements an otherwise traditional course. Explore calculus beyond the
level of rote calculations and superficial exercises. Each chapter has
four parts: Introduction, Solved Problems, Laboratory Exercises, and
Exploration and Discovery.
Contents: Coordinates, graphs, lines; Functions and limits;
Differentiation; Applications of differentiation; Integration; Applications
of the definite integral; Logarithm and exponential functions; Inverse
trigonometric and hyperbolic functions; Techniques of integration; Improper
integrals and L'Hopital's Rule; Infinite series; Topics in analytic
geometry; Polar coordinates and parametric equations; Three dimensional
space and vectors; Vector-valued functions; Partial derivatives; Multiple
integrals; Topics in vector calculus; Second-order differential equations.
18.50 Pounds, 193 pages, 1992
- Calculus Laboratories Using Derive Leinbach, L. Carl:
This book consists of 21 Derive laboratory exercises
for use in a first
year calculus course. Each lab is designed so that the student may
concentrate on the process or concept, while Derive does the tedious
algebraic work. The goal is "to lead students to some deep and interesting
mathematics and applications of mathematics".
21.50 Pounds, 147 pages, 1991
- Calculus and the Derive Program: Gilligan, L G., Marquardt, JF
A brief introduction to Derive followed by twenty-two calculus experiments
using software. It provides enough material for a two semester calculus
course. Each experiment includes a list of objectives, background
information, a step-by-step procedure, and a data sheet with questions and
space for answers.
13.95 Pounds, 2nd Edition, 151 pages, 1991
- Exploring Calculus with Derive Arney, David C:
Intended for use in a laboratory setting, a wide range of calculus concepts
are developed and investigated through a series of exploratory activities.
David Arney teaches at the United States Military Academy at Westpoint.
Contents: Preface; Notation and technical information; Getting started,
Examples; Exercises; Other reading; Index.
17.95 Pounds, 1992, 166 pages
- Exploring Math from Algebra to Calculus with Derive A Mathematical
Assistant Glynn, Jerry,
Using illustrated examples and keystroke guides, this entertaining and
enlightening book poses a mathematical question, walks you through its
solution, and then encourages you to extend the problem and charge off in
your own direction. Subjects include plotting, factoring, equation solving,
complex numbers, trigonometry, calculus and how to teach maths using
Derive.
13.95 Pounds
- Differential Equations with Derive Arney, David C:
Opening with a general explanation of the basic capabilities and
limitations of Derive, subsequent chapters contain examples and exercises
similar to those found in differential equations textbooks. Examples show
how to use Derive to perform some of the manipulations, plotting and
analysis to solve the problem. Some problems involve differential equation
models from other applications. Other problems deal directly with the
mathematical concepts of topics in the course. Laboratory exercises
require you to use Derive to solve, explore, and analyse problems - through
which you are led step-by-step.
Contents: Preface; Notation and technical information; Getting started;
Basic tools; First-order differential equations; Numerical methods and
difference equations; Second- and higher-order equations; Matrix algebra
and systems of equations; Partial differential equations; Other reading;
Index.
19.95 Pounds, 1993, 284 pages
- Derive Laboratory Manual for Differential Equations
Arney, David C.
This book is a set of examples and exercises showing how
to use Derive to solve differential equations.
It is meant as a companion
manual for any differential equation textbook. Since the manual is
designed for undergraduates, only elementary techniques are discussed.
15.95 Pounds, 189 pages, 1991
- Learning Modelling with DERIVE Townend S., Pountney D.
Teaches mathematical modelling using the algebraic software package,
DERIVE. Mathematical modelling is very much the fashion as the maths
syllabus develops towards applications and problem solving.
Gently guides the reader through the problem formulating and
solutions stages of modelling.
Provides a wide range assortment of case studies to illustrate issues.
Contents: Introduction. Geometric and Trigonometric Models. Algebraic
Models. Optimisation-based Models. Calculus-based Models. Discrete Models.
Differential Equations-based Models. Statistical & Simulations Models. The
Techniques of Dimensional Analysis.
15.95 Pounds, 256 pages, 1995
- Backstrom, G.
Practical Mathematics using MATLAB
This book is a guided tour of first year undergraduate mathematics,
intended to parallel conventional courses. Most of the applications are
numeric and also illustrate elementary principles of programming. Students
may work through the examples and the problems on a personal computer,
either individually or in groups under supervision. The sofware
MATLAB is
available for PC compatibles, Apple Macintosh, and various workstations.
MATLAB originally arose from an endeavour to simplify matrix arithmetic. It
requires neither types nor dimensions and saves much time in calculations
where vectors and matrices play a dominant role. MATLAB is an extremely
practical software package, allowing exponentiation, complex numbers, and
graph plotting.
Contents: PRELIMINARIES: Introduction; MATLAB as a calculator; Vectors.
FUNCTIONS: Plotting functions of one variable; Roots; Interpolation.
CALCULUS: Limits, Derivatives; Sums Integrals. DATA ANALYSIS: Systems of
linear equations; Statistics; Fitting functions to data. DIFFERENTIAL
EQUATIONS: First-order differential equations; Second-order differential
equations; Smarter than Euler; Eigenvalues and eigenvectors. COMPLEX
NUMBERS: Functions of a complex variable. SYMBOLIC OPERATIONS: Symbolic
algebra; Symbolic calculus; Symbolic ODEs. OVERVIEW: Basic MATLAB
commands; Index.
14.95 Pounds, 1995, ISBN 0-86238-403-6, 241 pp
- Backstrom, G.
Fields of Physics on the PC by Finite Element Analysis
Shows how to exploit finite element analysis (FEA) as an educational tool.
Numerous examples illustrate how to use this convenient technique to solve
partial differential equations (PDEs) occurring in various fields of
classical physics, e.g., gravity, electricity and magnetism, heat
conduction, elastic deformation and liquid flow.
Any reader who is able to express a problem in terms of PDEs will benefit.
The examples refer to PDEase software, but it is not necessary to have it
to learn the power of FEA, and to gain insight into the many interesting
phenomena connected with fields.
The work also suggests how to use numerical techniques to introduce
functions of two variables and to illuminate the concepts of vector
calculus for the benefit of beginners.
Undergraduate students of physics or engineering may use this book as a
companion to ordinary textbooks, which present the theory of the various
fields in detail. They may work through the examples and problems on a PC,
either individually or in a group under supervision.
19.95 Pounds, 312 pp, 1994, ISBN 0-86238-382-X
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