Explanation:
Vectors in 3D Space: Introduction to vectors and vector operations in three-dimensional space.
Multivariable Functions: Study of functions of several variables, including limits, continuity, and partial derivatives.
Multiple Integrals: Extension of integration to functions of two or more variables, including double integrals and triple integrals.
Vector Calculus: Introduction to vector fields, line integrals, surface integrals, and the fundamental theorems of vector calculus (Green's theorem, Stokes' theorem, and the divergence theorem).
Parametric Surfaces: Representing surfaces using parameterizations and understanding surface integrals.
Polar, Cylindrical, and Spherical Coordinates: Applications of alternative coordinate systems for integrals in two and three dimensions.
Gradient, Divergence, and Curl: Understanding vector operations in the context of multivariable calculus.
Partial Differential Equations (PDEs): Basic concepts of partial differential equations and their applications.