MATH 11012: INTUITIVE CALCULUS

   It is important that you cover the entire departmental syllabus. You’ll need to make a
    day-by-day schedule for yourself in order to keep up with this departmental syllabus.
    If you’re teaching a 2-day/week class you may want to remind students (and
    yourself?) that each class meeting is 11/2 regular classes (meaning 3 hours homework
    for the next class is not unreasonable).

   COMMENTS: Your students will have poor algebra skills. Do not take class time to
    review algebra skills, but you might:
        give review sheets, or
        assign problems from Chapter 1.
    Do explain algebra as you work calculus. Stress ‘why’ not ‘proof’. This is “Intuitive” or
    experience-based. Remember to teach by example.

Notation: It is important throughout the course to stress notation (standard notation not
student inventions!). Help them to understand the meaning and value of notation and
how to use it correctly. I try to stress writing the solution not just finding the answer.

Chapter 2. You might want to briefly review (x + 1)3 = . . . , fractions, point-slope line
form, supply, demand, and split functions as they come up.
        Try to help students separate notions of limit, continuity, and differentiability. Try
to help students make the connection between geometric, algebraic and numeric
explanations. Draw lots of pictures and graphs. Work lots of problems. The students
have a hard time with the notion of function. I use: “X is ‘where’ and Y is ‘how tall.’” This
text does not do limits as x approaches  until chapter 6. You might consider introducing
this idea here, enabling you to relate horizontal asymptotes and limits in chapters 3 and

Chapter 2. Section 1. There is a nice (for both traditional and calculator sections)
calculator example showing a hole in a function on page 85, Graphing Calculator
Exploration. Because the hole in the example occurs at an integer one can use
ZINTEGER or ZDECIMAL on the TI-82 or 83 (TI-81: Zoom: INTEGER).

Chapter 3. Sections 1-2 (graphing). Teach by example. I attempt to quickly cover the
complete graph. Make sure students can graph polynomials, then take on corners or
rational functions. To help students get organized, make a list of steps and always follow
this list.

Note: Using the graphing calculator does not seem to make this topic significantly easier
for students. The object is not to create the perfect graph, but to relate the derivative
and the graph. I tend to take off extra points if a student has the correct graph, but
incorrect intervals of increasing/decreasing for example. Probably the most useful
feature of the graphing calculator is the table (TI-82&83) for functional values.

Chapter 3, Sections 3-5 (optimization). Our students have a very hard time with story
problems. Many tell me they can’t do them or they never have done them. I tell them
now they will learn! Try to help them to break down the story phrase by phrase.
Sometimes I have them price each piece: cost of front fence, cost of side fence, etc. To
help them get organized give the steps and do every problem following those steps. I
have students write their plan: To Max Area: A' = 0
Be sure to do economic problems, remembering that most of our students are business
majors. If you’ve extra time Chapter 3 can use it.
Chapter 4 (logs & exponents). These students have studied logarithms and exponents,
they just forgot! Don’t get bogged down here. Review quickly. They need to know the
derivative of the natural logarithm and exponential functions. I encourage my students
to use their calculator and to give decimal solutions so they have some feel for size of
their answer. (I require a calculator in my traditional classes.) I go over the use of the log
and exponential features of the various calculators. The notion of present value is

Notation: The book uses some nonstandard notation here. In Section 1, the usual A=Pert
is given as (Value after n years)=Pern. Compound interest is given as (Value after n
periods)=P(1+r)n. Also in Section 4.3 E(p) denotes consumer expenditure while in Section
4.4 E(p) denotes elasticity of demand. I suggest CE(p) for the former.

Chapter 4, Section 4 (elasticity): (See preceding comment on notation.) Be sure to
cover relative rates first. The book does a nice job of explaining elasticity using relative
rates. If your class has students who have had economics, you might ask for their input.
Students have offered insulin as very elastic and heroin as ‘perfectly’ elastic starting a
nice conversation. The Application Preview, blue section, looks interesting.

Chapter 5 (integration).. Consider introducing section 6 (substitution) earlier in the

Chapter 5, Section 4 (areas): Asking for “set-up” only is a good ploy for tests. (Some
instructors of calculator sections allow students to use the numeric integration feature for
                                2 3
some of the area problems.
                                0 
                                  x dx is approximated by math 9: fnInt (x3,x,0,2) on the TI-
82 and 83. Be aware some functions take a very long time or give inaccurate results.)
You may wish to supplement this exercise set. Goldstein has good exercises.

Chapter 5. Section 6 (substitution): For students of weak algebra skills this section is very
hard and may take several days or returning to the subject several times. You might wish
to supplement the exercise set with more difficult substitution problems. (Goldstein has
some.) Students must be given problems of sufficient difficulty to force them to write out
all the steps, otherwise they think they understand when they do not. Be aware that the
exercise set in our text includes a number of examples which cannot be done with

Chapter 5. Section 5. Be sure to do Consumers' and Producers' Surplus. (I have other
texts with explanations, if you’d like to read up on the subject.) It is important to our
students that they understand that this is a sum and an area. You might ask members of
your class who have had economics to explain equilibrium point. Students tell me that
they calculate Consumers' and Producers' Surplus in their economics class. They use
linear supply and demand functions and find areas of triangles.
        The Gini Index of Income Distribution is both accessible and interesting to our
students. It does not take long to explain.

Note: Recall that the Business School has specifically asked us to cover many
applications in this course.

By Nancy Smith, December, 2002
Revised August 2005 by Darci Kracht


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