bank.xml

<?xml version='1.0' encoding='UTF-8'?>
<bank xmlns="https://checkit.clontz.org" version="0.2">
    <title>VecIt! Vector and Multivariable Calculus</title>
    <slug>vecit-calculus</slug>
    <url>http://matthematician.github.io/vecit</url>
    <outcomes>
        <outcome>
            <title>Surfaces and Graphs</title>
            <slug>N1</slug>
            <path>outcomes/N1</path>
            <description>
                Use traces and contours to describe surfaces in three-space that are graphs of two-variable functions and level sets of three-variable functions, including quadric surfaces.
            </description>
        </outcome>
        <outcome>
            <title>Vector Arithmetic</title>
            <slug>N2</slug>
            <path>outcomes/N2</path>
            <description>
                Perform and geometrically interpret sums, differences, scalar multiples, and magnitudes of vectors in n-dimensional space.
            </description>
        </outcome>
        <outcome>
            <title>Vector Geometry</title>
            <slug>N3</slug>
            <path>outcomes/N3</path>
            <description>
                Choose among, and use, dot products and cross products of vectors to compute quantities of geometric interest, including angles and areas.
            </description>
        </outcome>
        <outcome>
            <title>Parametrized Lines</title>
            <slug>N4</slug>
            <path>outcomes/N4</path>
            <description>
                Determine parametric equations for a line in three-space, given sufficient information to determine a point and a direction vector.
            </description>
        </outcome>
        <outcome>
            <title>Planes</title>
            <slug>N5</slug>
            <path>outcomes/N5</path>
            <description>
                Determine a level set equation for a plane in three-space defined either by a point and a normal vector, or by three given non-collinear points.
            </description>
        </outcome>
    
      
        <outcome>
            <title>Parameterized Curve</title>
            <slug>NA</slug>
            <path>outcomes/NA</path>
            <description>
                Sketch and parameterize portions of oriented curves, including those defined by intersections of surfaces and those which involve circular motions.
            </description>
        </outcome>
        
        <outcome>
            <title>Derivatives and Curvature</title>
            <slug>NB</slug>
            <path>outcomes/NB</path>
            <description>
                Use derivatives to determine, and distinguish among, a parameterized curve’s tangent, speed, velocity, and acceleration.
            </description>
        </outcome>
        
        <outcome>
            <title>Derivatives and Curvature</title>
            <slug>NB2</slug>
            <path>outcomes/NB2</path>
            <description>
                Use derivatives to determine, and distinguish among, a parameterized curve’s tangent, speed, velocity, and acceleration.
            </description>
        </outcome>
        
        <outcome>
            <title>Equilibrium</title>
            <slug>NC</slug>
            <path>outcomes/NC</path>
            <description>
                Solve vector equations to find the equilibrium state of a system.
            </description>
        </outcome>
        
        <outcome>
            <title>Intersections</title>
            <slug>ND</slug>
            <path>outcomes/ND</path>
            <description>
                Find the intersection of lines and planes.
            </description>
        </outcome>

        
            
        -->
        <outcome>
            <title>Partial Derivative Computations</title>
            <slug>D1</slug>
            <path>outcomes/D1</path>
            <description>
                Compute the partial derivatives of a given multivariable function, up to second order.


            </description>
        </outcome>
        <outcome>
            <title>Tangent Planes</title>
            <slug>D2</slug>
            <path>outcomes/D2</path>
            <description>
                Find equations for tangent planes to surfaces expressed as graphs of two-variable functions and as level sets of three-variable functions.
            </description>
        </outcome>        
        
        <outcome>
            <title>The Gradient of f(x,y)</title>
            <slug>D3</slug>
            <path>outcomes/D3</path>
            <description>Compute the gradient vector of a two-variable function, give its geometric interpretation with respect both to the contours of the function and to its graph, and use it to calculate directional derivatives in a given direction.</description>
        </outcome>
        
        <outcome>
            <title>Critical Points of Multivariable Functions</title>
            <slug>D4</slug>
            <path>outcomes/D4</path>
            <description>Use its gradient vector to locate critical points of a multivariable function, and its second-order partial derivatives to classify critical points as local maximum, local minimum, saddle points, or degenerate.</description>
        </outcome>
        
        <outcome>
            <title>Critical Points of Multivariable Functions pt 2</title>
            <slug>D4a</slug>
            <path>outcomes/D4a</path>
            <description>Use its gradient vector to locate critical points of a multivariable function, and its second-order partial derivatives to classify critical points as local maximum, local minimum, saddle points, or degenerate.</description>
        </outcome>

        
        <outcome>
            <title>Multivariable Limits</title>
            <slug>DA</slug>
            <path>outcomes/DA</path>
            <description>
                Use continuity and polar-coordinate methods to calculate limits of multivariable functions, and use multiple-approach methods to demonstrate when such a limit does not exist.

            </description>
        </outcome>
        
        <outcome>
            <title>Partial Derivative Interpretations</title>
            <slug>DB</slug>
            <path>outcomes/DB</path>
            <description>
                Carefully interpret the first- and second-order partial derivatives of a multivariable function as slopes and concavities of its graph’s traces.



            </description>
        </outcome>
        
        <outcome>
            <title>Multivariable Chain Rule</title>
            <slug>DC</slug>
            <path>outcomes/DC</path>
            <description>
                Identify all routes of composition when two or more multivariable functions are composed, and use the multivariable chain rule to compute such a function’s partial derivatives.
            </description>
        </outcome>
        
        <outcome>
            <title>The Gradient of f(x,y,z)</title>
            <slug>DD</slug>
            <path>outcomes/DD</path>
            <description>
                Compute the gradient vector of a three-variable function, give its geometric interpretation with respect to its level
surfaces, and use it to calculate directional derivatives in a given direction.
            </description>
        </outcome>
        
        <outcome>
            <title>Optimization and Extreme Values of Multivariable Functions</title>
            <slug>DE</slug>
            <path>outcomes/DE</path>
            <description>
                Use both critical points and a parametrization of its boundary to find absolute maximum and minimum values of a multivariable function on a closed and bounded domain.
            </description>
        </outcome>
        
        
        <outcome>
            <title>Constrained Optimization</title>
            <slug>DF</slug>
            <path>outcomes/DF</path>
            <description>
                Use Lagrange multipliers to determine absolute maximum and minimum values of a multivariable function subject to one or more constant constraints.

            </description>
        </outcome>
        
        
        <outcome>
            <title>Differentiability</title>
            <slug>DG</slug>
            <path>outcomes/DG</path>
            <description>
                Prove or disprove that a continuous function is differentiable.

            </description>
        </outcome>
        
        <outcome>
            <title>Mixed Partials</title>
            <slug>DH</slug>
            <path>outcomes/DH</path>
            <description>
                Identify when a function's mixed partial derivatives are not equal.

            </description>
        </outcome>

        
        <outcome>
            <title>The "Tape-Measure" Method</title>
            <slug>S1</slug>
            <path>outcomes/S1</path>
            <description>Describe a given region in the xy-plane using coordinate inequalities, in at least two distinct ways.</description>
        </outcome>
        <outcome>
            <title>Double Integrals</title>
            <slug>S2</slug>
            <path>outcomes/S2</path>
            <description>Set up and evaluate double integrals over general regions, using iterated integrals with "tape-measured" bounds.</description>
        </outcome>


        
        
        <outcome>
            <title>Double Integrals in Polar Coordinates</title>
            <slug>SA</slug>
            <path>outcomes/SA</path>
            <description>
                Use polar coordinates to transform the integrand, the bounds, and the area element of a given double integral.

            </description>
        </outcome>
        
        
         <outcome>
            <title>Surface Area</title>
            <slug>SB</slug>
            <path>outcomes/SB</path>
            <description>
                Set up double integrals to compute surface areas of portions of parametrized surfaces.

            </description>
        </outcome>
        
        
        <outcome>
            <title>Triple Integrals</title>
            <slug>SC</slug>
            <path>outcomes/SC</path>
            <description>
                Set up and evaluate triple integrals over general regions, using iterated integrals and “tape-measured” bounds.

            </description>
        </outcome>
        
        
        
         <outcome>
            <title>Change of Variables</title>
            <slug>SD1</slug>
            <path>outcomes/SD1</path>
            <description>
                Use change of variables and come up with a better description.

            </description>
        </outcome>
        
        
        <outcome>
            <title>Triple Integrals in Cylindrical and Spherical Coordinates</title>
            <slug>SD2</slug>
            <path>outcomes/SD2</path>
            <description>
                Use cylindrical and spherical coordinates to transform the integrand, the bounds, and the volume element of a given triple integral.

            </description>
        </outcome>
        
        
        <outcome>
            <title>Applications of Multiple Integrals</title>
            <slug>SE</slug>
            <path>outcomes/SE</path>
            <description>
                Use double and triple integrals to solve applied problems involving mass, density, and probability.


            </description>
        </outcome>
        
-->
        
        
        <outcome>
            <title>Vector Fields</title>
            <slug>V1</slug>
            <path>outcomes/V1</path>
            <description>Sketch and identify vector fields in two and three dimensions, including gradient vector fields of two- and three-variable functions.</description>
        </outcome>
        <outcome>
            <title>Line Integral Computation</title>
            <slug>V2</slug>
            <path>outcomes/V2</path>
            <description>Directly compute the line integral of a vector field over a given oriented path.</description>
        </outcome>

        <outcome>
            <title>Gradient Vector Fields</title>
            <slug>V3</slug>
            <path>outcomes/V3</path>
            <description>Classify a given vector field as gradient (or not), find scalar potential functions for gradient fields, and apply the fundamental theorem of calculus for path-independent line integrals.</description>
        </outcome>
        <outcome>
            <title>Green's Theorem</title>
            <slug>V4</slug>
            <path>outcomes/V4</path>
            <description>Identify when Green’s Theorem may be applied to find the total circulation of a vector field along a closed path, and use the Theorem to carry out this computation using a double integral.</description>
        </outcome> 
        
        
        <outcome>
            <title>Line Integral Heuristics</title>
            <slug>VA</slug>
            <path>outcomes/VA</path>
            <description>Predict from a sketch whether a given line integral of a vector field along an oriented path is positive, negative, or zero.</description>
        </outcome>

        
        <outcome>
            <title>Path-Independent Integrals</title>
            <slug>VB</slug>
            <path>outcomes/VB</path>
            <description>Identify when the Fundamental Theorem of Line Integrals may be applied, and use the Theorem to compute line integrals using a scalar potential function.
            </description>
        </outcome>
        
        <outcome>
            <title>Curl of a Vector Field</title>
            <slug>VC</slug>
            <path>outcomes/VC</path>
            <description>Compute the scalar curl of a two-dimensional vector field and the vector curl of a three-dimensional vector field. Use notions of circulation to predict whether the scalar curl of a given two-dimensional vector field is positive, negative, or zero.
.
            </description>
        </outcome>
        
        
        <outcome>
            <title>Divergence of a Vector Field</title>
            <slug>VD</slug>
            <path>outcomes/VD</path>
            <description>Compute the divergence of a vector field, and use notions of flux to predict whether the divergence of a given vector field is
positive, negative, or zero.
.
            </description>
        </outcome>
        
        
        <outcome>
            <title>Flux Integrals</title>
            <slug>VE</slug>
            <path>outcomes/VE</path>
            <description>Directly compute the flux integral of a vector field through a given oriented surface.
.
            </description>
        </outcome>
        
        
        <outcome>
            <title>Stokes and Divergence Theorems</title>
            <slug>VF</slug>
            <path>outcomes/VF</path>
            <description>Identify when a flux integral calculation
may be made simpler through the application of Stokes’ Theorem (resp. Divergence Theorem), and use the appropriate Theorem to carry out this
computation using a line integral (resp. triple integral).
.
            </description>
        </outcome>
        
        
        
        
        
    </outcomes>
</bank>