Experiments In Mathematics Using Maple / Edition 1

by Christopher T.J. Dodson, Elizabeth A. Gonzalez

Overview

The book is designed for use in school computer labs or with home computers running the computer algebra system Maple.

Product Details

ISBN-13:	9783540592846
Publisher:	Springer Berlin Heidelberg
Publication date:	11/22/1995
Edition description:	Softcover reprint of the original 1st ed. 1995
Pages:	465
Product dimensions:	6.10(w) x 9.25(h) x 0.05(d)

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.