Objectives


    1. Approximate values of functions and compute average rates of change.
      1. Calculate distances between numbers.
      2. Approximate values of functions to within preselected error tolerances.
      3. Compute average rates of change using difference quotients.

    2. Demonstrate an understanding of limits by relating limit statements to graphical observations and numerical data.
      1. Formulate graphical and numerical consequences of limit statements.
      2. Formulate limit statements to describe graphical features of functions.

    3. Compute limits.
      1. Determine whether a function is continuous at a point.
      2. Compute limits of elementary functions using limit laws and continuity.
      3. Compute limits of selected indeterminate, especially those arising from difference quotients of elementary functions.

    4. Differentiate elementary functions.
      1. Determine whether a given function is differentiable.
      2. Use the linearity of the derivative.
      3. Use the Product and Quotient Rules.
      4. Use the Chain Rule.
      5. Differentiate ranscendental functions.
      6. Use implicit differentiation.

    5. Demonstrate an understanding of the local meaning of the derivative.
      1. Compute and interpret instantaneous rates of change.
      2. Find equations of tangent lines.
      3. Use linear approximation to estimate values of elementary functions.

    6. Demonstrate an understanding of the global meaning of the derivatives of a function.
      1. Find the critical points of a function.
      2. Determine monotonicity and concavity properties of a function.
      3. Find local extreme points and points of inflection of a function.
      4. Solve optimization problems.

    7. Relate functions to their derivatives using ordinary differential equations.
      1. Determine whether a given function is a solution to a given ordinary differential equation.
      2. Find general and specific solutions to a selected set of ordinary differential equations. (y=ky', y=ky'', y(n)=0).
      3. Formulate differential equations describing the behavior of functions that arise in a selected set of applications. (growth and decay, springs, gravity)


    Facility and Mastery: Student performance in CQ Differential Calculus is measured on the basis of demonstrated proficiency in the application of Objective skills. It is recognized that each skill can be measured against progressively more demanding leve ls of proficiency.

    Level 1.
    Students demonstrate competence with a particular skill through successful application of the skill in problems that call for that skill explicitly.

    Level 2.
    Students demonstrate conceptual and contextual understanding of a particular skill through successful application of that skill in problems which require the skill implicitly and yet do not call for that skill explicitly. This l evel of proficiency demands at least these components.

    Level 3.
    Students demonstrate overall mastery through successful application of *multiple* Level 1 and Level 2 skills in problem-solving situations. Level 3 problems require the formulation of nontrivial solution strategies that combine applications of various skills.

       

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