Civil Engineering
Coordinate systems, distance formula, midpoint formula, slope, angle between lines, symmetry, and area of polygons.
Coordinate systems, distance formula, midpoint formula, slope, and area of polygons.
Equations of lines, slopes, intercepts, distances, and angles between lines.
Practice problems covering standard forms, parallel/perpendicular lines, distances, and angles between straight lines.
Equations of circles, finding center and radius, tangent lines, and degenerate cases.
Practice problems covering circle equations, tangents, and intersections.
Equations of parabolas, vertex, focus, directrix, and applications.
Practice problems covering standard equations, focus/directrix properties, and real-world applications.
Equations of ellipses, finding foci, vertices, eccentricity, and area.
Equations of hyperbolas, finding foci, vertices, transverse axis, asymptotes, and eccentricity.
Polar coordinate system, conversion between rectangular and polar, and graphing polar curves.
Transformation of coordinates through translation and rotation of the axes, and eliminating the xy-term in conic sections.
Defining curves using an independent parameter, converting to rectangular form, and applications to conic sections.
Three-dimensional coordinate systems, distance, direction cosines, equations of lines and planes in space.
Understanding 3D surfaces including spheres, ellipsoids, paraboloids, and hyperboloids.
Equations of tangent and normal lines to circles, parabolas, ellipses, and hyperbolas.
Introduction to vectors, dot product, cross product, and their applications in analytic geometry.
Advanced 3D coordinate systems and their relationship with rectangular coordinates.
Analysis of advanced planar curves including cycloids, epicycloids, hypocycloids, and lemniscates.
Practice problems applying vector operations, dot product, and cross product in 3D geometry.
Practice problems for converting coordinates and analyzing 3D surfaces.
Practice problems for identifying and analyzing special higher plane curves.