Advanced Academic Immersion (A2I) Course Descriptions
Prerequisites are courses that you must complete before enrolling in the course being described.
Synergies are courses that stack well with the course being described. Synergistic courses utilize some of the same skills or build upon shared concepts/applications.
Leads to identifies the next course in a linear sequence. For example, AP Calculus AB leads to AP Calculus BC which leads to Multivariable Calculus.
AP Calculus BC
Explore the concepts, methods, and applications of differential and integral calculus, including topics such as parametric, polar, and vector functions, and series. AP Calculus BC is equivalent to a first-semester college calculus course and the subsequent single-variable calculus course.
Prerequisites: AP Calculus AB
Synergies: Ordinary Differential Equations, Calculus-based Statistics
Leads to: Multivariable Calculus
Multivariable Calculus
This third course of calculus will use all of the skills and concepts learned in the previous two courses to analyze and explore problems requiring multiple variables including vectors and vector-valued functions, partial differentiation, Lagrange multipliers, multiple integrals, and Jacobians; application of the line integral, including Green‘s Theorem, the Divergence Theorem, and Stokes‘ Theorem. Essential for students planning to study advanced physical sciences and/or mathematics in college.
Prerequisites: AP Calculus BC
Synergies: Ordinary Differential equations, Calculus-based Statistics
Ordinary Differential Equations
Provides instruction in the concepts and skills associated with differential equations including solving first-order differential equations, linear differential equations, higher- order linear differential equations, first-order systems, homogeneous and non-homogeneous systems, and real world problems as found in the physical science.
Prerequisites: AP Calculus BC (or concurrent enrollment)
Synergies: Electrical Circuit Theory, Modern Physics
Mathematical Modeling Using Computer Simulation
This one- or two-semester course is designed for students to use an interdisciplinary approach to modeling physical events in the real world. For example, pilots are trained on computer simulators, new medicinal drugs are designed with the aid of computer models, economic projections and weather forecasting are based upon mathematical formats that are solved through intensive computer programming. This course will use skills and concepts learned in various mathematics courses (algebra-calculus, economics, physics, biology, anatomy, and physiology, and computer science). Emphasis is placed upon algorithmic problem solving and the use of numerical analysis.
Prerequisites: AP Calculus AB
Synergies: Calculus-based Statistics
Calculus-based Statistics
Collection, analysis, presentation and interpretation of data, and probability. Analysis includes descriptive statistics, correlation and regression, confidence intervals and hypothesis testing. Topics may include population sampling; collection, tabulation, and graphing of data; frequency distributions; mean and standard deviation; normal distribution; correlation and regression, and tests for significance.
Prerequisites: AP Calculus AB
Synergies: Mathematical Computer Simulation, Modern Physics
Linear Algebra
Introduces and provides models for application of the concepts of vector algebra. Topics include finite dimensional vector spaces and their geometric significance; representing and solving systems of linear equations using multiple methods, including Gaussian elimination and matrix inversion; matrices; determinants; linear transformations; quadratic forms; eigenvalues and eigenvector; and applications in science and engineering.
Prerequisites: AP Calculus AB
Synergies: Electrical Circuit Theory
AP Physics C: Mechanics
Taught over two high school semesters, AP Physics C: Mechanics is equivalent to a one-semester, calculus-based, college-level physics course, especially appropriate for students planning to specialize or major in one of the physical sciences or engineering. Students cultivate their understanding of physics through classroom study and activities as well as hands-on laboratory work as they explore concepts like change, force interactions, fields, and conservation.
Prerequisites: AP Calculus AB, high school physics
Synergies: AP Physics C: Electricity & Magnetism
Leads to: Theoretical Mechanics
AP Physics C: Electricity & Magnetism
Taught over two high school semesters, AP Physics C: Electricity and Magnetism is equivalent to a one-semester, calculus-based, college-level physics course, especially appropriate for students planning to specialize or major in one of the physical sciences or engineering. Students cultivate their understanding of physics through classroom study and activities as well as hands-on laboratory work as they explore concepts like change, force interactions, fields, and conservation.
Prerequisites: AP Calculus AB, AP Physics C: Mechanics (or concurrent enrollment)
Synergies: AP Physics C: Mechanics, Multivariable Calculus
Leads to: Electrical Circuit Theory
Electrical Circuit Theory
The Electrical Circuit Theory course will supplement the basic knowledge of the function of electrical circuits provided by an introductory physics course. This course is modeled after the initial analog circuits course in a university electrical engineering program. Students will engage in theoretical analysis of circuit response via mathematical methods and computer simulation as well as hands-on design, construction, and testing of electrical circuits in a laboratory environment.
Prerequisites: AP Calculus BC (or concurrent enrollment), high school physics
Synergies: AP Physics C: Electricity & Magnetism, Ordinary Differential Equations, Linear Algebra
Optics
In the one semester Optics course, students conduct laboratory and field investigations, use scientific practices during investigations, and make informed decisions using critical thinking and scientific problem solving. Students study a variety of topics that include: the principles of reflection and refraction, reflective optics, lenses and ray tracing, physical optics, and lasers. Students who successfully complete the Optics course will acquire factual knowledge within a conceptual framework, practice experimental design and interpretation, work collaboratively with colleagues, and develop critical-thinking skills.
Prerequisites: AP Calculus BC (or concurrent enrollment), high school physics
Synergies: AP Physics C: Mechanics, AP Physics C: Electricity & Magnetism
Astrophysics
The Astrophysics course will cover the same curricular topics found in the Honors Astronomy course. However, the topics will be explored in greater depth using the advanced mathematics and physics skills including calculus, differential equations, spectrum analysis, and quantum physics. The course will emphasize application and critical thinking for problem solving.
Prerequisites: AP Calculus BC (or concurrent enrollment), high school physics
Synergies: AP Physics C: Mechanics, Optics
Modern Physics
Consisting of one semester of theoretical mechanics and one semester of relativistic and quantum physics, this course is designed for students to use an interdisciplinary approach to explore the physical processes in nature that can only be described by quantum mechanics. This analysis and description is highly mathematical in content. For example, the position of an electron is found in terms of a probability density function. This course will use skills and concepts learned in various mathematics courses (Algebra II – Calculus), physics, and computer science. This stimulating environment will foster creativity and academic growth well beyond an honors curriculum and will open the imagination of students to the science of the 21st century.
Prerequisites: AP Calculus BC, AP Physics C: Mechanics
Synergies: Calculus-based Statistics, Ordinary Differential Equations, Multivariable Calculus
Thermodynamics
Broadly, thermodynamics deals with the transfer of energy from one place to another and from one form to another. The key concept, developed in the early 1800s, is that heat is a form of energy corresponding to a definite amount of mechanical work. This one semester introductory Thermodynamics course provides a relatively comprehensive overview of the field of classical thermodynamics with some statistical mechanics injected toward the end of the semester to tie in with more modern approaches. The class begins with a discussion of the nature of thermodynamics and an introduction to important terms and approaches. The idea of temperature and temperature scales are introduced. The various laws of thermodynamics are then discussed in order (zeroth, first, second, third) along with applications of each law. Simple laboratory experiments will be utilized to solidify conceptual knowledge.
Prerequisites: AP Calculus AB, high school physics
Synergies: Calculus-based Statistics, Ordinary Differential Equations