MATH 241 - Calculus 3

1. Understand Cartesian, polar and spherical coordinates. Understand vectors and vector operations, dot and cross products, their geometric and physical meaning, use of vector algebra for solving geometric and physical problems.
2. Understand equations of lines and planes in three-dimensional space, use of vector algebra in deriving these equations. Understand vector representation of curves (paths) in two and three dimensional spaces, derivatives and integrals of vector functions of one variable, their geometric and physical meaning.
3. Understand vectors and vector operations in n-dimensional space, understand matrices and matrix operations, determinants, inverse and transpose matrices. Understand linear transformations and formulas for areas and volumes of parallelograms and parallelepipeds under linear transformations.
4. Understand a concept of vector function of several variables, limit and continuity. Student should be able to check continuity of functions at a given point. Understand partial derivatives including higher order ones, a concept of differentiable function and total derivatives, chain rule. Vector analysis operations: gradients, divergence, curl, and their physical meaning. Understand approximation of functions by Taylor polynomials, use them for deriving first and second order conditions for minima and maxima.
5. Understand line integrals, geometric and physical applications. Understand multiple integrals, their geometric and physical applications, and change of variables for multiple integrals.