Mathematical techniques in GIS

Characteristics of Geographic Information
Geographic Information and Data
Categories of Data
Summary

Numbers and Numerical Analysis
The Rules of Arithmetic
The Binary System
Square Roots
Indices and Logarithms
Summary

Algebra: Treating Numbers as Symbols
The Theorem of Pythagoras
The Equations for Intersecting Lines
Points in Polygons
The Equation for a Plane
Further Algebraic Equations
Functions and Graphs
Interpolating Intermediate Values
Summary

The Geometry of Common Shapes
Triangles and Circles
Areas of Triangles
Centers of a Triangle
Polygons
The Sphere and the Ellipse
Sections of a Cone
Summary

Plane and Spherical Trigonometry
Basic Trigonometric Functions
Obtuse Angles
Combined Angles
Bearings and Distances
Angles on a Sphere
Summary

Differential and Integral Calculus
Differentiation
Differentiating Trigonometric Functions
Polynomial Functions
Linearization
Basic Integration
Areas and Volumes
Summary

Matrices and Determinants
Basic Matrix Operations
Determinants
Related Matrices
Applying Matrices
Rotations and Translations
Simplifying Matrices
Summary

Vectors
The Nature of Vectors
Dot and Cross Products
Vectors and Planes
Angles of Incidence
Vectors and Rotations
Summary
Curves and Surfaces
Parametric Forms
The Ellipse
The Radius of Curvature
Fitting Curves to Points
The Bezier Curve
B-Splines
Summary

2D/3D Transformations
Homogeneous Coordinates
Rotating an Object
Hidden Lines and Surfaces
Photogrammetric Measurements
Summary

Map Projections
Map Projections
Cylindrical Projections
Azimuthal Projections
Conical Projections
Summary
Basic Statistics

Probabilities
Measures of Central Tendency
The Normal Distribution
Levels of Significance
The T-Test
Analysis of Variance
The Chi-Squared Test
The Poisson Distribution
Summary

Correlation and Regression
Correlation
Regression
Weights
Spatial Autocorrelation
Summary

Best-Fit Solutions
Least Square Solutions
Survey Adjustments
Satellite Position Fixing
Summary

Further Reading
Index