Mathematical techniques in GIS /
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| Author / Creator: | Dale, Peter, author. |
|---|---|
| Uniform title: | Introduction to mathematical techniques used in GIS |
| Edition: | Second edition. |
| Imprint: | Boca Raton, FL : CRC Press, [2004] |
| Description: | xxvii, 331 pages ; 24 cm |
| Language: | English |
| Subject: | |
| Format: | Print Book |
| URL for this record: | http://pi.lib.uchicago.edu/1001/cat/bib/10075554 |
Table of Contents:
- Preface to Second Edition
- Preface to First Edition
- The Author
- List of Tables
- List of Illustrations
- List of Boxes
- List of Examples
- Chapter 1. Characteristics of Geographic Information
- 1.1. Geographic Information and Data
- 1.2. Categories of Data
- Summary
- Chapter 2. Numbers and Numerical Analysis
- 2.1. The Rules of Arithmetic
- 2.2. The Binary System
- 2.3. Square Roots
- 2.4. Indices and Logarithms
- Summary
- Chapter 3. Algebra: Treating Numbers as Symbols
- 3.1. The Theorem of Pythagoras
- 3.2. The Equations for Intersecting Lines
- 3.3. Points in Polygons
- 3.4. The Equation for a Plane
- 3.5. Further Algebraic Equations
- 3.6. Functions and Graphs
- 3.7. Interpolating Intermediate Values
- Summary
- Chapter 4. The Geometry of Common Shapes
- 4.1. Triangles and Circles
- 4.2. Areas of Triangles
- 4.3. Centers of a Triangle
- 4.4. Polygons
- 4.5. The Sphere and the Ellipse
- 4.6. Sections of a Cone
- Summary
- Chapter 5. Plane and Spherical Trigonometry
- 5.1. Basic Trigonometric Functions
- 5.2. Obtuse Angles
- 5.3. Combined Angles
- 5.4. Bearings and Distances
- 5.5. Angles on a Sphere
- Summary
- Chapter 6. Differential and Integral Calculus
- 6.1. Differentiation
- 6.2. Differentiating Trigonometric Functions
- 6.3. Polynomial Functions
- 6.4. Linearization
- 6.5. Basic Integration
- 6.6. Areas and Volumes
- Summary
- Chapter 7. Matrices and Determinants
- 7.1. Basic Matrix Operations
- 7.2. Determinants
- 7.3. Related Matrices
- 7.4. Applying Matrices
- 7.5. Rotations and Translations
- 7.6. Simplifying Matrices
- Summary
- Chapter 8. Vectors
- 8.1. The Nature of Vectors
- 8.2. Dot and Cross Products
- 8.3. Vectors and Planes
- 8.4. Angles of Incidence
- 8.5. Vectors and Rotations
- Summary
- Chapter 9. Curves and Surfaces
- 9.1. Parametric Forms
- 9.2. The Ellipse
- 9.3. The Radius of Curvature
- 9.4. Fitting Curves to Points
- 9.5. The Bezier Curve
- 9.6. B-Splines
- Summary
- Chapter 10. 2D/3D Transformations
- 10.1. Homogeneous Coordinates
- 10.2. Rotating an Object
- 10.3. Hidden Lines and Surfaces
- 10.4. Photogrammetric Measurements
- Summary
- Chapter 11. Map Projections
- 11.1. Map Projections
- 11.2. Cylindrical Projections
- 11.3. Azimuthal Projections
- 11.4. Conical Projections
- Summary
- Chapter 12. Basic Statistics
- 12.1. Probabilities
- 12.2. Measures of Central Tendency
- 12.3. The Normal Distribution
- 12.4. Levels of Significance
- 12.5. The t-Test
- 12.6. Analysis of Variance
- 12.7. The Chi-Squared Test
- 12.8. The Poisson Distribution
- Summary
- Chapter 13. Correlation and Regression
- 13.1. Correlation
- 13.2. Regression
- 13.3. Weights
- 13.4. Spatial Autocorrelation
- Summary
- Chapter 14. Best-Fit Solutions
- 14.1. Least Square Solutions
- 14.2. Survey Adjustments
- 14.3. Satellite Position Fixing
- Summary
- Further Reading
- Index
