MTH 201 Fall 2020 Course and Module Objectives.md

MTH 201 Fall 2020 Course and Module Objectives

• Group F: Use functions and other pre-Calculus mathematics proficiently.
  • F.1: I can find the average rate of change of a function on an interval.
• Group L: Calculate, use, and explain the concept of limits.
  • L.1: (CORE) I can find the limit of a function at a point using numerical, graphical, and algebraic methods.
  • L.2: I can identify limits in indeterminate form and apply L'Hopital's Rule to evaluate them.
• Group D: Explain and interpret the meaning of the derivative of a function.
  • D.1 (CORE): I can find the derivative of a function, both at a point and as a function, using the definition of the derivative.
  • D.2 (CORE): I can use derivative notation correctly, state the units of a derivative, estimate the value of a derivative using difference quotients, and correctly interpret the meaning of a derivative in context.
  • D.3 (CORE): Given information about $f$, $f'$, or $f''$, I can correctly give information about $f$, $f'$, or $f''$ and the increasing/decreasing behavior and concavity of $f$ (and vice versa).
  • D.4: I can determine where a function is continuous or differentiable given a graph or formula of the function and explain my reasoning.
  • D.5: I can find the equation of the tangent line to a function at a point and use the tangent line to estimate values of the function.
• Group DC: Use shortcuts to calculate derivatives efficiently.
  • DC.1 (CORE): I can compute derivatives correctly for power, polynomial, and exponential functions and the sine and cosine functions, and basic combinations of these (constant multiples, sums, differences).
  • DC.2 (CORE): I can compute derivatives correctly for products, quotients, and composites of functions.
  • DC.3: I can compute derivatives correctly using multiple rules in combination.
  • DC.4: I can compute the derivatives correctly for logarithmic, trigonometric, and inverse trigonometric functions.
• Group DA: Use derivatives to solve authentic real-life application problems.
  • DA.1 (CORE): I can find the critical values of a function, determine where the function is increasing and decreasing, and apply the First and Second Derivative Tests to classify the critical points as local extrema.
  • DA.2: I can determine the intervals of concavity of a function and find all of its points of inflection.
  • DA.3: I can use the Extreme Value Theorem to find the absolute maximum and minimum values of a continuous function on a closed interval.
  • DA.4 (CORE): I can set up and use derivatives to solve applied optimization problems.
  • DA.5: I can compute the derivative of an implicitly-defined function and find the slope of the tangent line to an implicit curve.
  • DA.6: I can set up and use derivatives to solve related rates problems.
• Group INT: Use definite integrals and the Fundamental Theorem of Calculus to find areas and total change.
  • INT.1: I can calculate the area between curves, net change, and displacement using geometric formulas and Riemann sums.
  • INT.2: I can explain the meaning of each part of the definition of the definite integral in terms of a graph, and interpret the definite integral in terms of areas, net change, and displacement.
  • INT.3: I can evaluate a definite integral using geometric formulas and the Properties of the Definite Integral.
  • INT.4 (CORE): I can evaluate a definite integral using the Fundamental Theorem of Calculus.
  • INT.5 (CORE): I can correctly antidifferentiate basic functions and identify antiderivatives.
  • INT.6: I can find the average value of a function and the net change in a function over an interval using a definite integral.