Learning expectations for first midterm
- Understand from both an algebraic and geometric perspective the notions of adding two vectors, subtracting two vectors, and multiplying a vector by a scalar.
- Understand from both an algebraic and geometric persepcitve the notion of dot product and cross product and use them to solve geometric problems like finding the angle between two planes, finding the distance from a point to a line, etc....
- Be able to find the equations of a line in both parametric and symmetric form.
- Be able to find the equation of a plane
- Be able to recognize and graph surfaces defined by degree two equations, for example, paraboloids, ellipsoids, and hyperboloids. Especially be able to recognize and derive equations of spheres.
- Be able to recognize and/or understand functions of two variables using their graphs and/or their contour plots. For example, you should be able to match equations of functions with their graphs and/or their contour plots.
- Be able to compute the domain of a function
- Compute the limit of a function at a point or demonstrate that such a limit does not exist by taking the limit approaching the point in different directions.
- Be able to compute partial derivatives and higher partial derivatives. For example, show that a function satisfies a given PDE (partial differential equation).
- Use implicit differentiation to compute partial derivatives for a function defined implicitly.
- Understand and use the multivariable chain rule.
- Find the equation of the plane tangent to a graph of a function at a point.
- Use linear approximation and total differentials to estimate small changes in a function or the values of a function near a point with a known value.