The Goals of the Course

The primary purpose of the calculus sequence is to provide the student with the mathematical tools necessary to successfully complete a science or engineering program at the undergraduate level.  Associated with this general objective are many secondary goals, some of which are nearly as important as learning calculus.  They are: 

          -  develop the capacity to generalize from a specific example to broad concept 
          -  develop the capacity to handle increasing abstract ideas 
          -  improve your ability to communicate mathematically by learning standard notation 
             and acceptable style 
          -  make a significant shift from learning by memorization to learning through 
          -  develop the capacity to separate the key ideas from the less significant 
          -  for every mathematical concept be able to link a geometrical representation 
             with an analytic representation 
          -  improve your ability to translate verbal problems into mathematical problems 
          -  be able to recognize a valid proof and detect ‘sloppy’ thinking 
          -  increase your ability to recognize mathematical patterns 
          -  improve your ability to move back and forth between  the geometrical 
             (graph) to the analytical (equation) 
          -  improve your mathematical intuition by abandoning  naive assumptions and 
             developing a more critical attitude 

The end result of development along the lines of the above list is termed ‘mathematical maturity’.  Thus we could succinctly state that the goal of our calculus sequence is the development of mathematical mature students by means of teaching them calculus.  Many majors across the University require calculus primarily for this reason.  Calculus is viewed as an excellent means by which to develop what is popularly termed 
‘critical thinking’.