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This is an introductory college mathematics course in finite difference equations and linear algebra. The topics we cover include sequences, differences, linear and nonlinear difference equations, systems of difference equations, numerical solutions of linear and nonlinear equations, and analytical techniques for solving linear systems using linear algebra.
Applications from many fields are studied and the role of mathematical modeling is a central focus. Formal computer labs are a part of the course each week, with spreadsheets being the primary software employed.
This course satisfies a general liberal arts requirement for all students and the mathematics requirement for business majors.
Prerequisite: three years of high school mathematics through Algebra II.
| Week | Date | Topic | Homework | Handouts |
|---|---|---|---|---|
| Week 1 | Jan 10 | Course Introduction | ||
| Jan 12 | Mathematical Modeling | HW 1: Discrete Dynamical Systems | Modeling with Difference Equations | |
| Jan 14 | Lab 1: Calculating Interest | Lab 1: Interest and Credit Cards | ||
| Week 2 | Jan 19 | Modeling Change | HW 2: Modeling Change | |
| Jan 21 | Lab 2: Retirement and Warehouses | Lab 2: Retirement and Warehouses | ||
| Week 3 | Jan 24 | Determining Stability and Equilibria | HW 3: Equilibria and Stability | Equilibria.xls (spreadsheet) |
| Jan 26 | Finding Equilibria | HW 4: Predicting the Future | ||
| Jan 28 | Lab 3: Mortgages | HW 5: Making Models | Lab 3: Mortgages | |
| Week 4 | Jan 31 | Equilibria |
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| Feb 2 | Review | |||
| Feb 4 | Big Quiz 1 | |||
| Week 5 | Feb 7 | No Class - Flu Day | ||
| Feb 9 | No Class - Flu Day II | |||
| Feb 11 | Analytical Solutions | HW 6: Testing Solutions | ||
| Week 6 | Feb 14 | Classification of Systems | HW 7: Revenge of the Analytical Solutions | |
| Feb 16 | Verification of Analytical Solutions, II | HW 8: Night of the Analytical Solutions | ||
| Feb 18 | s(k)=rk a(0) and Logarithms | HW 9: Do the Log Thing | ||
| Week 7 | Feb 23 | No Class - Flu Day III | ||
| Feb 25 | Nonhomogenous Linear Systems | HW 10: Nonhomogenous | ||
| Week 8 | Feb 28 | Nonhomogeneous Linear Systems II | ||
| Mar 2 | Nonhomogeneous Linear Systems III | HW 11: Revenge of the Nonhomogeneous Linear Systems | ||
| Mar 4 | Nonhomogeneous Linear Systems III: The Mother of all Retirement Problems |
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| Week 9 | Mar 14 | Nonhomogeneous Linear Systems IV: Population Models |
HW 12: Wrath of the Nonhomogeneous Linear Systems | HW 12 Solutions |
| Mar 16 | Review | Review Problems | ||
| Mar 18 | Big Quiz 2 | |||
| Week 10 | Mar 21 | Introduction to Systems of Difference Equations | HW 13: Systems of Difference Equations | |
| Mar 23 | Systems, Part II | |||
| Week 11 | Mar 30 | Lab 4: Systems | Lab 4: Systems | |
| Apr 1 | No Class - Flu Day IV | |||
| Week 12 | Apr 4 | Lab 5: Predator - Prey | Lab 5: Rabbits and Owls | |
| Apr 6 | Exploring Systems of Difference Equations | HW 14: More Systems of Difference Equations | ||
| Apr 8 | Lab 6: Modeling and the Logistic Equation | Lab 6: Yellowstone Bison Yellowstone Bison.xls |
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| Week 13 | Apr 11 | Systems of Equations - graphing | ||
| Apr 13 | Systems of Equations - algebraic solutions | HW 15: Systems of Equations |
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| Apr 15 | Review | Review 3 Solutions |
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| Week 14 | Apr 18 | Big Quiz 3 | ||
| Apr 20 | Using RREF to solve systems with technology | HW 16: Linear Equations | ||
| Apr 22 | Parameterizing Solutions | HW 17: The Matrix | ||
| Week 15 | Apr 25 | Matrix Multiplication | HW 18: Matrices | |
| Apr 27 | Matrix Inverse | |||
| Apr 29 | Review | |||
| May 4 | Final Exam - Wednesday: 3:00 - 4:45 | Sample Final Sample Final Solutions |
| Assignment | Percentage |
|---|---|
| Homework, Labs, and In-Class Work | 35% |
| 3 Big Quizzes | 45% |
| Final Exam | 20% |
Your grade will translate to a letter grade as follows :