Overview

This guide is designed to be used in school computer labs or with home computers, running the computer algebra system Maple, or its student version. It supports the interactive Maple worksheets, which the authors have developed and which are available free of charge via anonymous ftp (ftp.utirc.utoronto.ca(/pub/ednet/maths/maple)), or the University of Toronto Instructional and Research Computing World Wide Web home page over the Internet. The book aims to address readers who are learning calculus at a pre-university level.

Full Product Details

Author:   Christopher T.J. Dodson ,  Elizabeth A. Gonzalez
Publisher:   Springer-Verlag Berlin and Heidelberg GmbH & Co. KG
Imprint:   Springer-Verlag Berlin and Heidelberg GmbH & Co. K
Edition:   Softcover reprint of the original 1st ed. 1995
Dimensions:   Width: 15.50cm , Height: 2.50cm , Length: 23.50cm
Weight:   0.770kg
ISBN:  

9783540592846

ISBN 10:   3540592849
Pages:   465
Publication Date:   08 November 1995
Audience:   College/higher education ,  Undergraduate
Format:   Paperback
Publisher's Status:   Active
Availability:   Out of stock  
The supplier is temporarily out of stock of this item. It will be ordered for you on backorder and shipped when it becomes available.

Table of Contents

I Pre-Calculus Mathematics.- 1 Introduction to Maple.- 1.1 Documentation.- 1.2 First Maple Session.- 1.2.1 Basic Operations.- 1.2.2 Solving Equations.- 1.3 More Commands.- 1.3.1 Calling Function Packages.- 1.3.2 Isolating Variables.- 1.3.3 Variable Names.- 1.3.4 Syntax.- 1.3.5 Assigning Variables.- 1.3.6 Ditto.- 1.3.7 Notation of Mathematical Expressions.- 1.3.8 Commonly Used Commands.- 1.4 Plots.- 1.4.1 Options.- 1.4.2 Text.- 1.4.3 Implicit Plots.- 1.4.4 3D Plots.- 1.4.5 Animations.- 1.5 Preparing Worksheets for Printing.- 2 Functions.- 2.1 Relations and Functions.- 2.2 Multiplication by a Real Number.- 2.3 Addition and Subtraction of Functions.- 2.4 Multiplication and Division of Functions.- 2.5 Composition of Functions.- 2.6 Inverse Functions.- 3 Quadratic Functions.- 3.1 Quadratic Functions.- 3.2 Parabola.- 3.3 Vertex.- 3.4 Maximum and Minimum Values.- 3.5 Applications of Quadratic Functions.- 4 Solving Quadratic Equations.- 4.1 Roots of Quadratic Equations.- 4.2 Nature of Roots of Quadratic Equations.- 4.3 Quadratic Equations in Other Variables.- 4.4 Linear-Quadratic Systems.- 4.5 Slope of a Tangent to a Parabola.- 5 Polynomial Functions.- 5.1 Polynomial Functions.- 5.2 Division of Polynomials.- 5.3 Product and Sum of Roots.- 5.4 Related Roots.- 5.5 Roots of Higher Order Polynomials.- 6 Exponential Functions.- 6.1 Properties of Exponentials.- 6.2 Scientific Notation.- 6.3 Table of Values.- 6.4 Exponential Growth and Decay.- 7 Logarithmic Functions.- 7.1 Properties of Logarithms.- 7.3 pH Scale.- 7.4 Simple Interest.- 7.5 Compound Interest.- 7.6 Equivalent Rates.- 8 Circular Functions.- 8.1 Primary Trigonometric Functions.- 8.2 Reciprocal Trigonometric Functions.- 8.3 Inverse Circular Functions.- 8.4 Transformations.- 8.5 Addition of Circular Functions.- 8.6 Simple Harmonic Motion.- 9 Trigonometry.- 9.1 Basic Trigonometry.- 9.2 Trigonometric Identities.- 9.3 Trigonometric Equations.- 9.4 Power Series Expansions.- 9.5 Right-Angled Triangles.- 9.6 Law of Sines.- 9.7 Law of Cosines.- 9.8 Vectors.- 9.8.1 Dot Product.- 9.9 Bisector of a Triangle.- 10 Similar Figures.- 10.1 Similar Figures.- 10.1.1 Similar Triangles.- 10.2 Length of a Perpendicular.- 10.3 Areas of Similar Triangles.- 10.4 Dilatations and Similar Figures.- 11 Circles and Spheres.- 11.1 Circle.- 11.1.1 Intersection of a Line and a Circle.- 11.1.2 Tangent to a Circle.- 11.1.3 Arc Length.- 11.1.4 Area Bounded by a Circle.- 11.2 Sphere.- 11.2.1 Intersection of a Plane and a Sphere.- 11.2.2 Volume and Surface Area.- 12 Loci.- 12.1 Locus.- 12.2 Equations and Inequations of a Locus.- 12.3 Circles Associated with a Triangle.- 12.3.1 Circumcircle and Circumcentre.- 12.3.2 Inscribed Circle and Incentre.- 12.3.3 Bisectors of Interior Angles.- 12.3.4 Exscribed Circles and E-Centres.- 12.3.5 Centroid of a Triangle.- 12.3.6 Orthocentre of a Triangle.- 12.4 Equations of Loci After a Transformation.- 12.4.1 Translation.- 12.4.2 Stretch.- 12.4.3 Reflection.- 12.4.4 Dilatation.- 12.5 Simulations.- 13 Sequences and Series.- 13.1 Sequences.- 13.1.1 Arithmetic Sequences.- 13.1.2 Geometric Sequences.- 13.2 Series.- 13.2.1 Arithmetic Series.- 13.2.2 Geometric Series.- 14 Statistics and Probability.- 14.1 Organizing and Presenting Data.- 14.1.1 Plots.- 14.1.2 Mean, Median, Mode, and Standard Deviation.- 14.2 Probability of Events.- 14.2.1 Binomial Theorem.- II Beginning Calculus.- 15 Secants and Tangents.- 15.1 Slope of a Line.- 15.2 Slope of a Secant.- 15.3 Slope of a Tangent.- 15.4 Equation of the Tangent to a Curve.- 16 Sequences and Limits.- 16.1 Sequences.- 16.2 Limit of an Infinite Sequence.- 16.3 Sum of an Infinite Geometric Series.- 16.4 Limit of a Function.- 16.5 Rules for Limits.- 16.5.1 Constants Rule.- 16.5.2 Sum Rule.- 16.5.3 Product Rule.- 16.5.4 Quotient Rule.- 16.5.5 Exponential Rule.- 16.5.6 Inequality Rule.- 16.5.7 Sandwich Rule.- 16.5.8 Squeeze Rule.- 16.6 Continuous Functions.- 16.7 Limits Involving $$\frac{0}{0}$$.- 17 Derivatives of Functions.- 17.1 Derivative.- 17.2 Differentiating from First Principles.- 17.3 Rules of Differentiation.- 17.3.1 Derivative of a Constant.- 17.3.2 Power Rule.- 17.3.3 Derivative of a Sum of Functions.- 17.3.4 Chain Rule.- 17.3.5 Product Rule.- 17.3.6 Quotient Rule.- 17.4 Higher Order Derivatives.- 17.5 Notation.- 17.6 Implicit Differentiation.- 18 Functions and Graphs.- 18.1 Plotting Functions.- 18.2 X- and Y-Intercepts.- 18.3 Asymptotes.- 18.3.1 Vertical Asymptotes.- 18.3.2 Horizontal Asymptotes.- 18.3.3 Oblique Asymptotes.- 18.4 Symmetry.- 18.5 Increasing and Decreasing Functions.- 18.6 Concavity.- 18.7 Relative Maxima and Minima.- 18.8 Inflection Point.- 18.9 Plot of f(x).- 19 Rates.- 19.1 Position, Velocity, and Acceleration.- 19.2 Rate of Change.- 19.3 Related Rates of Change.- 20 Integration.- 20.1 Approximation of the Area Under a Curve.- 20.2 Definite Integral.- 20.3 Indefinite Integral.- 20.4 Fundamental Theorem of Calculus.- 20.5 Rules of Integration.- 20.5.1 Sum of Functions.- 20.5.2 Function Times a Constant.- 20.5.3 Power Rule.- 20.6 Area Between Curves.- 20.7 Differential Equations.- 20.8 Integration by Parts.- 20.9 Partial Fractions.- 20.10 Numerical Integration.- 20.10.1 Trapezoidal Rule.- 20.10.2 Simpson's Rule.- 21 Trigonometry.- 21.1 Compound Angles.- 21.2 Graphs of Trigonometric Functions.- 21.3 Derivative of Sine Function.- 21.4 Derivatives of Trigonometric Functions.- 21.5 Maxima and Minima.- 21.6 Integrals of Trigonometric Functions.- 21.7 Areas Defined by Trigonometric Functions.- 22 Exponents and Logarithms.- 22.1 Base for Natural Logarithm.- 22.2 Exponential Growth and Decay.- 22.3 Derivatives.- 22.4 Integrals.- 23 Polar Coordinates.- 23.1 Converting Coordinates.- 23.2 Circles in Polar Coordinates.- 23.3 Area in Polar Coordinates.- 23.3.1 Sector of a Circle.- 23.3.2 Region Enclosed by a Curve.- Appendices.- A Solutions to Part I Exercises.- A.1 Functions.- A.2 Quadratics.- A.3 Solving Quadratics.- A.4 Polynomials.- A.5 Exponential Functions.- A.6 Logarithmic Functions.- A.8 Trigonometry.- A.9 Similar Figures.- A.10 Circles and Spheres.- A.11 Loci.- A.12 Sequences and Series.- A.13 Statistics and Probability.- B Solutions to Part II Exercises.- B.1 Secants and Tangents.- B.2 Sequences and Limits.- B.3 Derivatives of Functions.- B.4 Functions and Graphs.- B.5 Rates.- B.6 Integration.- B.7 Trigonometry.- B.8 Exponents and Logarithms.- B.9 Polar Coordinates.- C.1 angles.- C.2 showAntiderivative.

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