Math. (II)
- Introduction to R2 and R3- vectors- Dot product in R2, R3, and Rn- Equation(s) of a line.
- The cross product in R3- Equations of lines and planes in R3- Functions, graphs, and surfaces- Cylindrical and spherical coordinates
- Vector-valued functions -parameterized curves in R2 and R3- Velocity and acceleration vectors- Arclength- Equations tangential and normal components of acceleration.
- Parametric surfaces- Functions of several variables- limits and continuity- graphs and level curves of a function of two variables- Partial derivatives.
- Partial derivatives- differentiability- linear approximation and tangent planes- rate of change of a function along a parameterized curve- the Chain Rule.
- Directional derivatives and the gradient vector- Level surfaces of a function of three variables
- Optimization; maximum and minimum values of a function- The Method of Lagrange Multipliers.
- Integration over regions in R2 and R3- Average value of a function- Iterated double integrals and the Fubini Theorem- Double integrals in polar coordinates.
- Applications of double integrals- Surface area- Triple integrals in Cartesian coordinates.
- Triple integrals in cylindrical coordinates and spherical coordinates- applications of triple integrals- Change of variables in multiple integrals- Jacobian matrices.
- Vector fields in R2 and R3- Line integrals and work done by a variable force along a parameterized curve- Fundamental Theorem of Line Integrals- independence of path- conservative vector fields.
- Green's Theorem- Curl and divergence of a vector field- surface integrals- flux of a vector field through a surface.
- Stokes' Theorem- the Divergence Theorem