Calculus - An Introduction Using Concrete Examples

About the Book

This book is intended to introduce calculus through examples to prepare the reader for the diverse problems he/she will have to solve using derivatives and integrals. The derivative is introduced right at the beginning of the book as the slope of a tangent. The reader is then exposed to a cross-section of problems that may be solved by knowing how to calculate slopes of tangents. College students have to master techniques of diffrentiation within a semester. The early introduction of derivatives gives them ample time to practice these techniques. The integral is introduced as a limit of sums with its applications to physical problems in mind. A number of problems that may be reduced to limits of sums are then addressed. Techniques of integration are also addressed as are methods of approximating definite integrals. Limits, which are the foundations of calculus are treated rigorously and most of the statements used in the course are proved. Finally, detailed solutions, (not just numerical answers), to about half the problems in the book are given. In particular, the solutions to all "Test - your - self" exercises are given. These are problems the student should attempt to do in the indicated time to test his/her mastery of some fundamental topics.

About the Author

Dr. Semwogerere has taught undergraduate and graduate mathematics for over 30 years. He received his MS and PhD from Northwestern University and UC Berkeley respectively. Dr. Shabazz received his MS and PhD from MIT and Cornell University respectively. He has taught graduate and undergraduate mathematics for over 40 years. He has received many teaching awards including the Presidential Award of Excellence in Mentoring Underrepresented Students (2000).