Text: Stewart, Calculus (Concepts and Contexts),
3rd ed, Brooks/Cole
It is departmental policy
that graphing calculators are required of all students in Math 1220. However, the department has agreed that the
symbolic calculation of basic derivatives, limits, and integrals is part of the
language of mathematics, and students should be proficient in this
language. Thus, your exam over Chapter 3
(which is heavily symbolic) should not permit calculators of any kind. Also, the Final Exam could be given in two
parts, the first part not allowing calculators.
Generally, however, calculators should be permitted in most testing
situations.
Warning: the students have
access to Student Solutions Manual containing worked-out solutions to
all odd-numbered problems. Thus, you
should avoid assigning these for credit.
Course Prerequisites: A passing grade (C or better) in Math 1180 or a satisfactory score on an appropriate placement exam (ACT, SAT, WMU math placement exam). There will be an advisory algebra exam on prerequisite skills for this course.
Objectives:
1. Understanding the concept of limit and how it relates average and
instantaneous quantities.
2. Understanding the concept of derivative, interpreting it
geometrically, physically and using it in optimization and linear
approximation.
3. Understanding integration and its relationship with differentiation
and applying integration in goemetrical and physical problems.
4. Learning the proper use of mathematical notation.
5. Developing sufficient computational skills in differential
and integral operations for subsequent calculus courses and for
applications in other areas.
6. Developing abilities to tackle multi-step problems and to explain
the process.
7. Understanding the possibilities of modern computer algebra
systems in assisting the analysis of problems in
calculus and the visualization of their solutions.
8. Developing skills in mathematical reasoning.
9. Developing a broad perspective of how various different topics in
this course fit together.
Schedule: The schedule below allows for
covering 30 sections ( plus appendices D and F) in 12 weeks, leaving about 1.5
weeks for expanding and testing. Chapter 1
is omitted (except for section 1.7) since this material is covered in
Precalculus (Math 1180). Ask students to
review this material on their own.
Chapter Title
Sections
Weeks
2 Limits and Derivatives
1 - 9
3
Cover
Appendix D (precise definitions) just after section 2.2.
3 Differentiation Rules
1 - 8
3
Sec 3.3: Cover only the Physics portion of this section.
Sec 3.5: Review section 1.7 on parametric equations before
covering
tangents to parametric curves.
4 Applications of Differentiation 1 - 4, 6, 8 - 9 3.5
Sec
4.5 (l’Hospital’s Rule) will be covered in Math 1230.
Sec 4.8: Use the TI calculators to generate Newton iterates.
5 Integrals
1 - 5
2.5
Add
Appendix F (sigma notation) to section 5.1.
The TI calculators can be used to quickly obtain left sums, right sums, and the midpoint rule, using sum seq (expression, variable, start, stop, increment). For example, the right sum for the integral of sin x between 0 and 2, using n = 10 subintervals, is
sum seq (sin x, x, 0.2, 2, 0.2)(0.2).