Mathematical Connections: A Modeling Approach to Business Calculus, Vol. I- Preliminary Edition, 1/e
Bruce Pollack-Johnson, Villanova University
Audrey Fredrick Borchardt, Villanova University
Published January, 1998 by Prentice Hall Engineering/Science/Mathematics
Copyright 1998, 553 pp.
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Applied Calculus with Graphing Calculators-Mathematics
Mathematics for Business with Graphing Calculators-Mathematics
The text's overall approach is problem-driven with topics motivated
and developed using interesting and useful real-world examples, many
from actual student projects. The focus of the text is on the entire
process of problem-solving, including the formulation and validation
of mathematical models. It emphasizes conceptual understanding so
students can use techniques and technology intelligently as a tool
for solving real problems. (Graphing calculator and/or spreadsheet
Helps students understand mathematical functions and
models, including the ability to identify and validate assumptions
of models, make ballpark estimates, verify calculations, perform sensitivity
analysis, and identify an appropriate level of precision to reflect
a reasonable margin of error.
Helps students to think critically, become independent
problem-solvers, and to gain experience with commonly used technology.
Integrates all aspects of the course through student-
generated projects. Each student chooses a topic and uses that
to experience the problem-solving process from beginning to end.
Introduces each section with interesting and relevant problems
as well as a list of concepts and skills to be studied.
Connects topics together and to students' other courses,
careers, and personal lives.
= VOLUME I (Business Calculus):
1. Problem Solving Functions, and Models.
2. Rates of Change.
3. Single-Variable Optimization and Analysis.
4. Continuous Probability and Integration.
= VOLUME II (Finite Mathematics):
5. Multivariable Functions and Models.
6 Descriptive Statistics and Least Squares Regression.
8. Multivariable Optimization and Analysis.
9. Linear Programming and Constrained Optimization.
Appendix 1. Answers to Selected Problems.
Appendix 2. Student Generated Projects: Topic Ideas and
Appendix 3. Mathematical Background and Proofs.