Explores curve integrals of vector fields, emphasizing energy considerations for motion against or with wind, and introduces unit tangent and unit normal vectors.
Covers integrating functions over graph surfaces in vector calculus, emphasizing the interpretation of divergence theorem and special cases of domain between two graphs.
Explores the Eigenstate Thermalization Hypothesis in quantum systems, emphasizing the random matrix theory and the behavior of observables in thermal equilibrium.
Explores the definitions and applications of partial derivatives in functions of several variables, emphasizing the importance of specifying the choice of variables.