Relevant material from MIT's introductory courses to support students as they study and educators as they teach the AP Physics curriculum.

Partial differential equations (PDEs) describe the relationships among the derivatives of an unknown function with respect to different independent variables, such as time and position. Experiment and observation provide information about the connections between rates of change of an important quantity, such as heat, with respect to different variables. Upon successful completion of this course, the student will be able to: State the heat, wave, Laplace, and Poisson equations and explain their physical origins; Define harmonic functions; State and justify the maximum principle for harmonic functions; State the mean value property for harmonic functions; Define linear operators and identify linear operations; Identify and classify linear PDEs; Identify homogeneous PDEs and evolution equations; Relate solving homogeneous linear PDEs to finding kernels of linear operators; Define boundary value problem and identify boundary conditions as periodic, Dirichlet, Neumann, or Robin (mixed); Explain physical significance of boundary conditions; Show uniqueness of solutions to the heat, wave, Laplace and Poisson equations with various boundary conditions; Define well-posedness; Define, characterize, and use inner products; Define the space of L2 functions, state its key properties, and identify L2 functions; Define orthogonality and orthonormal basis and show the orthogonality of certain trigonometric functions; Distinguish between pointwise, uniform, and L2 convergence and show convergence of Fourier series; Define Fourier series on [0,pi] and [0,L] and identify sufficient conditions for their convergence and uniqueness; Compute Fourier coefficients and construct Fourier series; Use the method of characteristics to solve linear and nonlinear first-order wave equations; Solve the one-dimensional wave equation using d'Alembert's formula; Use similarity methods to solve PDEs; Solve the heat, wave, Laplace, and Poisson equations using separation of variables and apply boundary conditions; Define the delta function and apply ideas from calculus and Fourier series to generalized functions; Derive Green's representation formula; Use Green's functions to solve the Poisson equation on the unit disk; Define the Fourier transform; Derive basic properties of the Fourier transform of a function, such as its relationship to the Fourier transform of the derivative; Show that the inverse Fourier transform of a product is a convolution; Compute Fourier transforms of functions; Use the Fourier transform to solve the heat and wave equations on unbounded domains. (Mathematics 222)

In this course, the student will learn about the three laws of thermodynamics, thermodynamic principles, ideal and real gases, phases of matter, equations of state, and state changes. The student will also take a look at chemical kinetics--a branch of study concerned with the rates of reactions and other processes--as well as kinetic molecular theory and statistical mechanics, which relate the atomic-level motion of a large number of particles to the average thermodynamic behavior of the system as a whole. Upon successful completion of this course, the student will be able to: State and use laws of thermodynamics; Perform calculations with ideal and real gases; Design practical engines by using thermodynamic cycles; Predict chemical equilibrium and spontaneity of reactions by using thermodynamic principles; Describe the thermodynamic properties of ideal and real solutions; Define the phases of matter, describe phase changes, and interpret/construct phase diagrams; Relate macroscopic thermodynamic properties to microscopic states by using the principles of statistical thermodynamics; Describe reaction rates and then do calculations to determine them; Relate reaction kinetics to potential reaction mechanism; Calculate the temperature dependence of rate constants and relate that to activation energy; Describe a variety of complex reactions; Describe catalysis; Describe enzymatic catalysis. (Chemistry 105)

"This course introduces the structure, composition, and physical processes governing the terrestrial planets, including their formation and basic orbital properties. Topics include plate tectonics, earthquakes, seismic waves, rheology, impact cratering, gravity and magnetic fields, heat flux, thermal structure, mantle convection, deep interiors, planetary magnetism, and core dynamics. Suitable for majors and non-majors seeking general background in geophysics and planetary structure."

The course Solar Energy will teach you to design a complete photovoltaic system. The course will introduce you to the technology that converts solar energy into electricity, heat and solar fuels with a main focus on electricity generation. Photovoltaic (PV) devices are presented as advanced semiconductor devices that deliver electricity directly from sunlight. The emphasis is on understanding the working principle of a solar cell, fabrication of solar cells, PV module construction and the design of a PV system. You will understand the principles of the photovoltaic conversion (the conversion of light into electricity). You will learn about the advantages, limitations and challenges of different solar cell technologies, such as crystalline silicon solar cell technology, thin film solar cell technologies and the latest novel solar cell concepts as studied on lab-scale. The course will treat the specifications of solar modules and show you how to design a complete solar system for any particular application. The suitable semiconductor materials, device physics, and fabrication technologies for solar cells are presented. The guidelines for design of a complete solar cell system for household application are explained. Alternative storage approaches through solar fuels or conversion of solar energy in to heat will be discussed. The cost aspects, market development, and the application areas of solar cells are presented.

Thermodynamics is the study of energy and its transfers though work. This course will focus on the fundamentals of thermodynamics, including the First and Second Laws, thermodynamic properties, ideal gases, and equations of state. Upon successful completion of this course, the student will be able to: Identify and use units and notations in thermodynamics; State and illustrate the first and second laws of thermodynamics; Identify and explain the concepts of entropy, enthalpy, specific energy, reversibility, and irreversibility; Apply the first and second laws of thermodynamics to formulate and solve engineering problems for (i) closed systems, (ii) open systems under steady-state and transient conditions, and (iii) power cycles; Use thermodynamic tables, charts, and equation of state (e.g. the ideal gas law) to obtain appropriate property data to solve thermodynamics problems. (Mechanical Engineering 103)