This text fosters the teaching of critical thinking and problem solving to facilitate learning and understanding. OUR TOP PRIORITY IS TO HELP STUDENTS BE SUCCESSFUL IN DIFFERENTIAL CALCULUS AND OTHER MATHEMATICS. Critical thinking and problem solving are the main outcomes of understanding and understanding is the key to learning and retention. Mathematics is the gateway to many occupations and the many advances in technology has caused this gateway to be ever widening in the number of occupations requiring some competency in mathematics.

Among the meanings of the word critical are the concepts of "involving skillful judgment as to truth or merit," and "of decisive importance in respect to the outcome." Critical Thinking in mathematics involves an understanding of the vocabulary, algorithms, and problems encountered in using mathematics. These materials were specifically developed to help students understand mathematics, to help students be able to read mathematical material, and to help students be better able to solve problems using mathematics. These materials were also developed to help students learn mathematics without total dependence upon rote memory. The role of memory in the process of learning is significant; but no subject, including mathematics, can be learned solely by rote memory. An understanding of the concepts and the language is equally important. To accomplish these goals the materials of this text have been organized by objectives; and attention has been given to the three areas of vocabulary, computation, and understanding of mathematical concepts by incorporating the suggestions of Piaget, Polya, and others who have conducted sufficient research in the learning of mathematics.

Students cannot be good at problem solving unless they possess more than a short-term "rote memory knowledge" of mathematics; they must have an understanding of the concepts involved. The best positions in business and industry have been offered to the graduates with the highest potential as problem solvers. Studying mathematics in general, and these materials in particular, will help develop better problem solving skills. The CRITICAL THINKING APPROACH TO DIFFERENTIAL CALCULUS contains Exercises for Understanding which consist of Discussion, Explanation, and Discovery Exercises which are designed to foster class discussions about key topics and concepts. Many of these exercises do not have unique answers causing discussions of trade-offs and possible decisions. The Exercises for Understanding are located at the end of each Section with the other sets of exercises.

Students cannot be good at problem solving unless they possess more than a short term "rote memory knowledge" of mathematics or are good at buttonology; they must have an understanding of the concepts involved. In recent times the best positions in business and industry have been offered to the graduates with the highest potential as problem solvers. Studying mathematics in general, and these materials in particular, will help develop better problem solving skills. Again, the Exercises for Understanding at the end of each Unit can be used for class discussions to promote the understanding of key concepts.

OBJECTIVES

Following the introduction of each Section is a list of the objectives for that Section. Students are expected to master the objectives as they study the materials. Since mathematics is cyclic, future mathematics learning will be dependent upon the success students have with each Section. Each Objective, in turn, becomes the heading and code for the Subsection containing the text material for that objective. Students will find a complete discussion of the concepts of the objective in that Subsection. Students will also find that the Exercise Sets and the Self Tests contain the Objective code that relates the material to each Subsection.

INTEGRAL CALCULUS TEXT

There is a text for Integral Calculus now under development and hopefully it will be available by 12/15/10