## Workshops for Calculus 151-2 (in GIF)

This material is also available in Postscript format.

What's presented here are suggestions for workshops. Each lecturer selected their own workshop problems and sometimes added on to those written here. In most cases, no more than three or possibly four problems were presented to students. The ideal problem is somewhat open-ended and may be difficult to understand. "Real" problems are seldom well-written or precisely formulated, and some of these problems have similar features. This supplied a good excuse for poorly written problems!

As you read the problems remember that students were to do them in groups, with textbook and graphing calculator available. The instructors (graduate students and peer mentor undergraduates) circulated to stimulate work with suggestions for exploration and discussion.

No "official" solutions were ever written or presented, and alternative approaches to solutions were valued. Writeups were graded for both presentation and content.

### Math 151 (First Semester) Workshops

• Workshop 1: Polynomials, rational functions, graphs, simple inequalities: "pre"-calculus.
• Workshop 2: Limits, tangents
• Workshop 3: Continuity, Intermediate Value Theorem, definition of limits, rates of growth
• Workshop 4: Derivatives, continuity, differentiability
• Workshop 5: Tangents, derivatives
• Workshop 6: Derivatives: the chain rule, simple uses of derivatives
• Workshop 7: Newton's method, the exponential function in various guises
• Workshop 8: Inverse functions, linear approximation, more exponential function problems
• Workshop 9: Inverse functions, l'Hopital's rule
• Workshop 10: Monotonicity, concavity, the Mean Value Theorem
• Workshop 11: Curve sketching, max and min
• Workshop 12: More max and min
• Workshop 13: Riemann sums for the definite integral; antiderivatives

### Math 152 (Second Semester) Workshops

• Workshop 1: Recall some facts about transcendental functions; some problems about the Fundamental Theorem of Calculus
• Workshop 2: Work, volumes, averages
• Workshop 3: Integration by partial fractions, integration by parts, estimation of integrals
• Workshop 4: Numerical methods for the definite integral
• Workshop 5: Improper integrals
• Workshop 6: The beginnings of sequences and some of their applications in calculus
• Workshop 7: The beginnings of series and estimations of their sums
• Workshop 8: Conditional convergence and absolute convergence
• Workshop 9: Power series and estimation of sums with errors
• Workshop 10: Parametric curves and polar coordinates

 Exams Syllabi Discussion of the changes