Hyperbola - conic section, foci, transverse and conjugate axes, vertices, asymptotes, standard formTMM 002 PRECALCULUS (Revised March 21, 2017)AdditionalOptional Learning Outcomes:2. Geometry: The successful Precalculus student can:2f. Represent conic sections algebraically via equations of two variables and graphically by drawing curves.Sample Tasks:The student can perform the process “completing the square” transforming the equation into a standard form.The student can draw curves representing conic sections.The student can solve systems of equations involving linear and quadratic functions.The student can parametrize conic curves.
"2010 marks the 400th anniversary of Galileo's astonishing sightings of features on the moon, stars, and moons around Jupiter that no one had seen before. Recreate these new ways of seeing and exploring from the materials and techniques Galileo had on hand, while you reflect on the times and works of Galileo. What was it like to improvise new ways of seeing and exploring from the materials and techniques on hand? What do we notice? What surprises us? How can we relate to past experience and ideas? What are we curious to research? How does our experimenting grow into our learning? Let your own curiosity drive your explorations."
Global Satellite Navigation Systems (GNSS), such as GPS, have revolutionized positioning and navigation. Currently, four such systems are operational or under development. They are the American GPS, the Russian Glonass, the European Galileo, and the Chinese Beidou-Compass. This course will address: (1) the technical principles of Global Navigation Satellite Systems (GNSS), (2) the methods to improve the accuracy of standard positioning services down to the millimeter accuracy level and the integrity of the systems, and (3) the various applications for positioning, navigation, geomatics, earth sciences, atmospheric research and space missions. The course will first address the space segment, user and control segment, signal structure, satellite and receiver clocks, timing, computation of satellite positions, broadcast and precise ephemeris. It will also cover propagation error sources such as atmospheric effects and multipath. The second part of the course covers autonomous positioning for car navigation, aviation, and location based services (LBS). This part includes the integrity of GNSS systems provided for instance by Space Based Augmentation Systems (e.g. WAAS, EGNOS) and Receiver Autonomous Integrity Monitoring (RAIM). It will also cover parameter estimation in dynamic systems: recursive least-squares estimation, Kalman filter (time update, measurement update), innovation, linearization and Extended Kalman filter. The third part of the course covers precise relative GPS positioning with two or more receivers, static and kinematic, for high-precision applications. Permanent GPS networks and the International GNSS Service (IGS) will be discussed as well. In the last part of the course there will be two tracks (students only need to do one): (1) geomatics track: RTK services, LBS, surveying and mapping, civil engineering applications (2) space track: space based GNSS for navigation, control and guidance of space missions, formation flying, attitude determination The final lecture will be on (scientific) applications of GNSS.
This is an introduction to the study of the solar system with emphasis on the latest spacecraft results. The subject covers basic principles rather than detailed mathematical and physical models. Topics include: an overview of the solar system, planetary orbits, rings, planetary formation, meteorites, asteroids, comets, planetary surfaces and cratering, planetary interiors, planetary atmospheres, and life in the solar system.
The emergence of Western science: the systematization of natural knowledge in the ancient world, the transmission of the classical legacy to the Latin West, and the revolt from classical thought during the scientific revolution. Examines scientific concepts in light of their cultural and historical contexts.
Three assignments for use in an Astronomy 101 course. These assignments will be showcased by the Open Education Group for open faculty usage.