This course is an introduction to mathematical ideas and techniques that are useful in understanding and solving problems arising in economics and business. Mathematical concepts are introduced through interesting business problems. Using available computer technology, real life problems, which may lead to non-trivial computations and graphs, are considered. Topics include integration, differential equations, Taylor polynomial approximations, unconstrained and constrained optimization for functions of several variables, probability and statistics, with interesting real-life applications throughout.
Upon completion of this course you should have learned the basic calculus ideas and techniques that are useful in understanding and solving problems arising in economics and business. It will enhance problem solving skills, critical thinking, rational decision making and appreciation for mathematics. Our major goals include:
- Students will be able to identify and explain fundamental principles and theories in calculus and its applications to business.
- Students will be able to identify connections between mathematical ideas and life experiences.
- Students will be able to express ideas and arguments clearly and persuasively.
- Students will be able to analyze, question and evaluate ideas, assumptions, arguments and points of view.
- Students will be able to apply ideas, theories, principles, and concepts in new contexts and situations, and solve real world problems that are quantitative in nature.
- Understanding mathematical symbols and formulas.
Learn how to read and understand mathematical symbols and formulas and to be able to express thoughts in symbols and equations. Realize that each formula expresses a precise and clear relation between the variables involved. It is often said, that the best way for clarifying one's thoughts is to put them into an equation. Equations are not there to be memorized but to be understood. In many situations they form the bridge between mathematics and our world.
- Emphasizing conceptual learning.
For example, understanding the definite integral as expressing total change by summing up instantaneous change is fundamental for being able to use it. More importantly, by learning the fundamental concepts you are able to understand that there is a commonality in the world of mathematics and there are connections. There are fundamental concepts (like the integral) from which many others are derived (like future and present value of income streams and the producer and consumer surplus). This learning helps you see the big picture of mathematics and its connections to our world.
- Learning modeling skills.
They include describing the situation under consideration clearly, translating appropriate aspects into equations using suitable variables, symbols, and mathematical concepts, and interpreting possible mathematical solutions in terms of the original process. Models should be thought as approximations of real situations and as such require continuous adjustments.
- Making connections.
We stress the connections between mathematics and modern society by considering a wide variety of problems ranging from environmental and economic issues to social and political situations that can be modeled and solved by mathematical means. Take advantage of this opportunity to make your own connections between the mathematics considered in the class and your other courses and consider working on a special project that exploits your own interests and expertise.
MATH 10250 Elements of Calculus I or equivalent
- Calculus: Ideas and Applications (ISBN 0471654957), by Alex Himonas and Alan Howard.
- Calculus: Ideas and Applications, Student Solutions Manual
Activities and Technology manual
Examinations, homework and quizzes are conducted under the honor code. While collaboration in small groups in doing homework is permitted (and strongly encouraged) in this course, copying is not. In particular, copying from the Student Solutions Manual is a violation of the Honor Code. Exams are closed book and are to be done completely by yourself with no help from others.
Homework problems are assigned daily. You are encouraged to work on homework problems in groups, but the assignments must be turned in individually. Remember that you will not learn anything by simply copying another student's work or the Student Solutions Manual. The main purpose of the homework is to help you learn the material and assess yourself. Experience shows that students who take their homework seriously do very well in the course because they have a better understanding of the material.
The goal of these projects is to give students the opportunity to make their own connection between mathematics and modern society by considering a wide variety of problems ranging from economic and environmental issues to social and political situations that can be modeled and solved by mathematical means. They will help students establish connections between Math 10260 and other courses. In addition, they will provide students with an opportunity to interact and collaborate with classmates. Please read project rules and the project options open to you.
You may use a graphing calculator on homework assignments and exams.