Bruce Alphenaar

Rarely is a quantity of interest—tomorrow’s temperature, unemployment rates across Europe, the cost of a spring-break flight to Fort Lauderdale—a simple function of just one primary variable. Reality, for better or worse, is mathematically multivariable. This course introduces an array of topics and tools used in the mathematical analysis of multivariable functions. The intertwined theories of vectors, matrices, and differential equations and their applications will be the central themes of exploration in this yearlong course. Specific topics to be covered include the algebra and geometry of vectors in two, three, and higher dimensions; dot and cross products and their applications; equations of lines and planes in higher dimensions; solutions to systems of linear equations, using Gaussian elimination; theory and applications of determinants, inverses, and eigenvectors; volumes of three-dimensional solids via integration; spherical and cylindrical coordinate systems; and methods of visualizing and constructing solutions to differential equations of various types. Conference work will involve an investigation of some mathematically-themed subject of the student’s choosing.

Calculus-based general physics is a standard course at most institutions; as such, this course will prepare you for more advanced work in the physical science, engineering, or health fields. The course will cover introductory classical mechanics, including kinematics, dynamics, momentum, energy, and gravity. Emphasis will be placed on scientific skills, including problem solving, development of physical intuition, scientific communication, use of technology, and development and execution of experiments. The best way to develop scientific skills is to practice the scientific process. We will focus on learning physics through discovering, testing, analyzing, and applying fundamental physics concepts in an interactive classroom, as well as in weekly laboratory meetings.

Calculus-based general physics is a standard course at most institutions; as such, this course will prepare you for more advanced work in the physical science, engineering, or health fields. This course will cover waves, geometric and wave optics, electrostatics, magnetostatics, and electrodynamics. We will use the exploration of the particle and wave properties of light to bookend our discussions and ultimately finish our exploration of classical physics with the hints of its incompleteness. Emphasis will be placed on scientific skills, including: problem solving, development of physical intuition, scientific communication, use of technology, and development and execution of experiments. The best way to develop scientific skills is to practice the scientific process. We will focus on learning physics through discovering, testing, analyzing, and applying fundamental physics concepts in an interactive classroom, as well as in weekly laboratory meetings.