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 mathematical tools for differentials of functions of multiple variables and their practical applications in thermodynamics and real-life scenarios.
Discusses differentiation of multivariable functions and coordinate transformations, including polar and cylindrical coordinates, along with the Laplacian operator and its applications.
Explores polar coordinates, position, velocity, and acceleration vectors in Cartesian and polar systems, including cylindrical and spherical coordinates.
Covers differentiability in multivariable functions and the existence of tangent planes, emphasizing geometric interpretations and practical applications.
