Math 1                        Calculus (3 credits), Difference and Differential Equations (1 credit)

Prerequisite:            High school math at least through precalculus.

Course Description:

Math 1 is the first in a series of four, one-semester, integrated mathematics courses. Topics include sequences, finite differences and finite-difference equations in dynamical systems, solutions of difference equations, limits and continuity, and derivatives.

Math 2            Calculus (3 credits), Linear Algebra (1 credit), and Difference and Differential Equations

Prerequisite: Math 1 or equivalent

Course Description:

This course is the second in a seriesoffour, one-semester, integrated mathematics courses. The focus is ondefiniteintegrals and the fundamental theorem of calculus, differentialequations,systems of difference equations, and an introduction to linearalgebraup through eigenvalue problems.

Notes on the First Year:

There is heavy emphasis on applications, mathematical modeling, and problem solving techniques. Computers andTI-92Plus/TI-89 calculators are used extensively. Each student is requiredto have aTI-92 Plus or a TI-89 calculator. The class meets once weekin the computerlaboratory. Software used includes MS Excel, Mathematica , MS Wordwith equation editor, MS Power Point. Students are requiredto write formalreports with graphs and typed mathematical symbols, andto prepare andgive presentations. Much of the in-class work and the workdone on projectsare done in groups. Daily assignments include reading of the course materialin advance andwritten exercises. There is an additional, optional, 75-minuteclass meetingeach week that is treated as a recitation.

Course Goals (for the first year):

·          Extend knowledge and understanding of mathematical concepts, specifically in the study of finite differences and difference equations, differential and integral calculus for functions of a single variable, and differential equations.

·          Develop skills in formulating and solving problems involving sequences and finite differences, difference equations, differential calculus,integral calculus, and optimization.

·          Recognize and identify patterns of change in real-world contexts, specifically, those situations where difference equations or differential equations can be used to describe behavior or a phenomenon.

·          Design mathematical models using difference equations and differential equations to capture the essence of real-world patterns and phenomena.

·          Classify, analyze, transform, and solve mathematical constructs involving finite differences, difference equations, derivatives, and differential equations.

·          Interpret mathematical models and their solutions in the context of their real-world applications.

·          Critique mathematical models to identify their strengths and weakness and modify them to make them better models.

·          Expand knowledge and understanding of the real world through mathematical analysis.

·          Develop skills to effectively use modern computing, information, and communication technologies.

Student-Identified Goals (for the first year):

·          Learn the mathematics and develop the mathematical skills needed for further studies in mathematics, science (quantum mechanics, chemistry), engineering, computer science, and social science (model sales tax).

·          Learn how to use mathematics to solve real world problems that areof interest to me.

·          Learn to effectively use modern computer and calculator technology.

·          Develop social and interpersonal skills.

·          Continue liking mathematics and maybe even develop a “love” for the subject.

·          Gain a more complete understanding of mathematics that I have studied before.

·          Utilize resources (instructors, academic resources, computers, communications) to help me succeed (to get my money’s worth).

·          Succeed and earn a good grade.

·          Have an interesting and fun experience studying mathematics and its applications.

Required Textbooks and Calculator:

Discrete Dynamical Systems: Mathematics, Models, and Methods (4 ^th revised preliminary edition), by Arney, Giordano, and Robertson, © 2000, McGraw-Hill

Thomas’ Calculus: Early Transcendentals (10^th edition), by Finney, Weir, and Giordano, © 2001, Addison Wesley Longman

TI-89 or TI-92 Plus Calculator

Supplementary Materials:

Student Solutions Manual for Thomas’ Calculus: Early Transcendentals (10^th edition), by Weir and Scharf, © 2001, Addison Wesley Longman

Course Requirements and Grading:

·          RATs (Readiness Assessment Tests) - 10% of final grade

Each day (except Thursday) there willbea short (5 minute) quiz on the reading preparation for that day's material. Each of these will be graded 2, 1, or 0.

·          Homework Exercise Sets - 10% of final grade

Homework exercises from the text willgenerallybe assigned and collected daily

·          TGIFS (Teacher Gets Input From Students) - 0% of final grade

For each Wednesday class, you should prepare a list of the three topics from the preceding week that you feel most satisfied with and three topics from the preceding week that you feel could use some more work. These should be written on a single 8.5 X 11 sheet of paper and should be anonymous.

·          Project Reports and Presentations - 10% of final grade

Two projects will be assigned during the semester. The report will be done using MS Word with the equation editor and imported graphics. The presentation should use Power Point.

·          Periodic Exams - 55% of final grade

There will be a 50-minute exam approximately every two weeks. While these exams focus on the material since the preceding one, there may be questions from prior material.

·          Final Exam - 15% of final grade

The final exam is comprehensive covering material from the entire semester, including class projects.

Math 1 Course Outline (Overview)

Math 2 Course Outline (Overview)