Learning expectations for the 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/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
• 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.
• 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.
• Understand and use the multivariable chain rule.
• Be able to compute the directional derivative of a function in the direction of a given unit vector.
• Be able to compute the gradient of a function.
• Understand the meaning of the gradient and its relationship to contour plots and countour surfaces.
• Use the gradient to find the equation of the plane tangent to a level surface F(x,y,z)=C at a point.