Introduction to mathematical techniques used in GIS / by Peter Dale.

Format:

Book

Author/Creator:

Dale, Peter.

Contributor:

Hazel M. Hussong Fund.

Language:

English

Subjects (All):

Geography--Mathematics.

Geography.

Geographic information systems.

Physical Description:

xv, 202 pages : illustrations ; 25 cm

Place of Publication:

Boca Raton : CRC Press, [2005]

Contents:

Chapter 1 Characteristics of Geographic Information 1

1.1 Geographic Information and Data 1

1.2 Categories of Data 2

1.3 Spatial Referencing 4

1.4 Lines and Shapes 7

Chapter 2 Numbers and Numerical Analysis 9

2.1 The Rules of Arithmetic 9

2.2 The Binary System 13

2.3 Square Roots 15

2.4 Indices and Logarithms 17

Chapter 3 Algebra - Treating Numbers as Symbols 23

3.1 The Theorem of Pythagoras 23

3.2 The Equations for Intersecting Lines 25

3.3 Points in Polygons 30

3.4 The Equation for a Plane 31

3.5 Further Algebraic Equations 31

3.6 Functions and Graphs 36

3.7 Interpolating Intermediate Values 38

Chapter 4 The Geometry of Common Shapes 43

4.1 Triangles and Circles 43

4.2 Areas of Triangles 46

4.3 Centers of a Triangle 49

4.4 Polygons 51

4.5 The Sphere and the Ellipse 53

4.6 Sections of a Cone 55

Chapter 5 Plane and Spherical Trigonometry 59

5.1 Basic Trigonometric Functions 59

5.2 Obtuse Angles 63

5.3 Combined Angles 65

5.4 Bearings and Distances 67

5.5 Angles on a Sphere 72

Chapter 6 Differential and Integral Calculus 77

6.1 The Basis of Differentiation 77

6.2 Differentiating Trigonometric Functions 81

6.3 Polynomial Functions 83

6.4 Basic Integration 85

6.5 Areas and Volumes 87

Chapter 7 Matrices, Determinants, and Vectors 91

7.1 Basic Matrix Operations 91

7.3 Related Matrices 95

7.4 Applying Matrices 98

7.5 Rotations and Translations 99

7.6 Simplifying Matrices 105

Chapter 8 Curves and Surfaces 115

8.1 Parametric Forms 115

8.2 The Ellipse 119

8.3 The Radius of Curvature 121

8.4 Fitting Curves to Points 122

8.5 The Bezier Curve 128

Chapter 9 Transformations 131

9.1 Homogeneous Coordinates 131

9.2 Rotating an Object 132

9.3 Hidden Lines and Surfaces 139

9.4 Map Projections 140

9.5 Cylindrical Projections 142

9.6 Azimuthal Projections 145

9.7 Conical Projections 147

Chapter 10 Basic Statistics 153

10.1 Probabilities 153

10.2 Measures of Central Tendency 156

10.3 The Normal Distribution 160

10.4 Levels of Significance 163

10.5 The t-Test 165

10.6 Analysis of Variance 166

10.7 The Chi-Squared Test 169

10.8 The Poisson Distribution 170

Chapter 11 Best-Fit Solutions 173

11.1 Correlation 173

11.2 Regression 176

11.3 Weights 180

11.4 Linearization 182

11.5 Least-Square Solutions 184.

Notes:

Includes bibliographical references (page 197) and index.

Local Notes:

Acquired for the Penn Libraries with assistance from the Hazel M. Hussong Fund.

ISBN:

0415334144

OCLC:

55587662