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1. Solve problems involving triangles, polygons, curves and curve elements, terrestrial baselines (vectors), Global Positioning System, GPS signal vectors, matrices and measurement data.
2. Calculate curve elements, arc lengths and areas of sectors and segments.
3. Analyze and solve problems relating to the dimensions of geometric solids such as earth volumes, cut and fill, tailings, concrete forms.
4. Solve linear equations and inequalities with one, two or three variables such as those found in trilateration methods of GPS ranging.
5. Solve systems of equations through the use of graphing, addition, substitution and comparison as well as through the use of determinants and matrices.
6. Evaluate and solve ratio and proportion problems found in the civil engineering, land surveying, geospatial and construction fields.
7. Evaluate and summarize measurement data using descriptive statistics and exploratory data analysis methods.
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I. Review of fundamental concepts found in geospatial problem solving
A. Real number system
B. Scientific notation and engineering notation
C. Exponents and radicals
E. Algebraic expressions and properties
F. Linear equations
G. Ratio and proportion
II. Review of graphing concepts
A. Functions used in land surveying
B. Graphing linear equations
C. Distance and slope formulas
D. Coordinate systems used in geospatial mapping
III. Review of geometric concepts
A. Lines, angles, distance and direction
B. Triangles, quadrilaterals, polygons, circles, ellipses and other geometric figures
1. Orientation
2. Areas
3. Volumes
C. Arcs, arc length and curves
1. Arc definitions
2. Curve types and curve elements
3. Rays and cardinal points
D. Vectors and scalars
1. Vector components
2. Vector and scalar arithmetic
3. Complex numbers
IV. Review of trigonometric concepts
A. Trigonometric functions of an angle
B. Radians and angular measure
C. Right triangle solutions: Pythagorean Theorem
D. Oblique triangle solutions: Law of Sines/Cosines, identify ambiguities
E. Application of trigonometric functions to:
1. Angular and linear measures
2. Areas and volumes
3. Arc distances, curve lengths, and curve elements
4. Express scalar and vector quantities
5. Graphing simple trigonometric functions
V. Review of systems of linear equations found in surveying and geospatial problems
A. Examples of linear equations and systems of linear equations
B. Methods of solving systems of linear equations
1. Algebraic solutions, graphing
2. Vector solutions, matrices and determinants
C. Obtaining multiple solutions for simple 2 and 3 variable systems of equations
VI. Review of descriptive statistics in civil engineering, surveying and GIS
A. Populations, samples and distributions
B. Summarizing central tendency and spread
C. Other statistical moments
D. Parametric vs. non-parametric statistics
E. Univariate vs bivariate descriptions
F. Characterize and assess data quality with descriptive statistics
G. Present statistical summaries with diagrams, charts and graphs
VII. Measurements and measurement theory in civil engineering, surveying and GIS
A. Measurement theory and methods
B. Error assessment and error management
C. Summarizing measurement variability
D. Assess error associated with measurements and measuring devices
VIII. Calculation methods and tools
A. Hand calculator
B. Spreadsheets
C. Software applications
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