Mathematics 150B Lab

Spring 2008

Introduction:

This course is a laboratory for Calculus. The main objectives of the course are

1. to learn more Calculus and some of its applications

2. to communicate mathematical ideas in writing

3. to use a computer algebra system and technical typesetting program

When you are writing solutions you may be asked to generalize observations in form of a theorem, and prove this theorem, i.e. show how it follows logically from known principles of Calculus.

Assignments:

There will be four assignments in this course as well as several in class projects. There are only two possible grades for each assignment, satisfactory and unsatisfactory.

A satisfactory assignment answers all questions correctly and is well written, i.e. each solution is clearly explained. There can be no incomplete sentences or numbers sitting meaninglessly on the paper. (Please refer to the example below.) Unsatisfactory assignments will be returned to the student. He/she may redo the assignment(s) a second time.

Example of satisfactory and unsatisfactory solutions:

Let us consider the following problem: An open cardboard box is made from a rectangle measuring 40cm by 30cm by cutting away corners and

folding up the flaps. Find the dimension of the box with the largest volume.

Satisfactory Solution:

Let be the length of the removed corners in centimeters (cm). Then the area of the base of the resulting box is square centimeters. It follows that the volume (in cubic centimeters) is given by the formula

We need to find the global maximum of this function for , since negative values of make no sense and do values greater than 15 make no sense either. To find the maximum, we compute