• Multivariable Calculus Course Syllabus 

    Unit 5: Functions of several variables and partial derivatives

    Goal: Goal: The student will demonstrate the ability to use a problem-solving approach to interpret and analyze the function of two variables both graphically and algebraically, including using partial derivatives, directional derivatives, and gradients.

    Skills for Unit 5:

    The student will be able to:

    Define a function of two variables.

    Define and determine the domain and range of a function of two variables.

    Sketch the graphs of selected functions of two variables.

    Define and sketch level curves and contour maps.

    Test for continuity and the existence of limits of functions of two variables.

    Define, compute, and interpret geometrically first and second partial derivatives for functions of more than one variable.

    Define and compute the total differential for functions of more than one variable.

     Apply the total differential in finding relative measurement error.

    State and apply the chain rule with one or two independent variables.

    Define, compute, and interpret geometrically the directional derivative of a function of two variables.

    Define, compute, and interpret geometrically the gradient of a function of two variables.

    State and apply the relationship between the gradient and the directional derivative for a function of two variables.

    Determine the equation of a plane tangent to a surface.

     Identify critical points of a surface and apply to extrema of functions of two variables.

    Apply Lagrange multipliers to optimization problems.