Differential Equations

Office Hours: Tuesday and Thursday 1-4 pm; other times by discovery.

Core Criteria and Outcomes: As a Core Exploration Course in Mathematics, Math 311 Differential Equations meets the following criteria relative to Concordia’s Goals for Liberal Learning (GLL) in our core curriculum, Becoming Responsibly Engaged in the World:

• Emphasize arithmetical, algebraic, geometric, algorithmic, or statistical methods (GLL 1,2,3);
• Develop an understanding of mathematical models such as formulas, graphs, tables, schematics, or algorithms (GLL 2,3,5);
• Incorporate mathematical models and methods to solve problems (GLL 1,2,35).

• Students will demonstrate an understanding of mathematical methods and models: By completing Differential Equations, students will demonstrate an understanding of the following mathematical methods: quantitative and qualitative analysis of first-order ordinary differential equations (Chapters 1 & 2); analytic derivation of solutions (Chapters 4 & 5); Laplace transforms (Chapter 7); separation of variables for partial differential equations (Chapters 11 & 12). In conjunction with these methods, students will demonstrate an understanding of the following mathematical models: exponential and logistic growth (Chapters 2 & 3); Newton’s law of heating and cooling (Chapter 3); harmonic oscillator and spring-mass system (Chapter 5); heat, wave, and potential equations (Chapter 12).
• Students will represent mathematical information symbolically, visually, and numerically: In exams and project write-ups, students will represent mathematical information symbolically by deriving general solution forms through the methods listed above; visually through Mathematica (a computer algebra system) notebooks and graphing calculators, the use of slope fields and graphs, and the employment of phase line and bifurcation diagrams; and numerically with Mathematica notebooks and via Euler’s method.
• Students will apply mathematical methods and models to solve multi-step problems: Students will apply these methods and models in write-ups to exams, and through their solutions to the two major group projects. In-class exams tend to emphasize problems involving a few to several steps, while group projects and take-home exams require extended multi-step problem-solving skills. For example, in Project 1, Harvesting Natural Resources, the students begin with the logistic-growth model for a salmon fishery, with no harvesting. After an initial analysis of this model, they move to a logistic-growth model with constant harvesting. For various constant-harvest values, the students determine the fate of the salmon population. The constant-harvesting model is then compared with a proportional harvesting model. Students are then asked to make a policy decision as to which model to follow and why as they manage the fishery.

Text/Mathematica: Differential Equations with Boundary Value Problems, 7th edition, by Zill and Cullen, ISBN-10: 0495108367; ISBN-13: 9780495108368. We will also be using Mathematica, a computer algebra system. Mathematica 6.0 is available on the campus network, and can be downloaded onto the personal computer of any Concordia College student free of charge.

Prerequisite: Math 122 (Calculus II) or equivalent

Homework/Projects: Homework will be assigned each day for your practice in mastering the material. Homework that is turned in should be neat and organized. You will not only be graded on correct answers but also on the neatness, organization, steps used to derive your answers, and the use of correct grammar and complete sentences. All students must abide by the college's expectations regarding academic integrity and quality. Even-numbered problems with be due the second class period after they are assigned, while odd-numbered problems are suggested for practice, as you may check your answers in the back of the text. Each homework assignment is worth 30 points; your 4 lowest homework grades will be dropped, and your overall homework grade will be scaled to 150 points out of the remaining ones. Project write-ups should be neat and organized. You will not only be graded on correct answers but also on the neatness and organization of your results, the explanation of your reasoning and the steps used to derive your answers, and the use of correct grammar and complete sentences. All students must abide by the college's expectations regarding academic integrity and quality. You may work in groups on the projects, but no more than four students will be allowed in any one group. The composition of the groups may change from project to project. Keep in mind that under normal circumstances everyone in the group will receive the same score on the project, although exceptions may be made for obvious freeloaders. No late projects will be accepted.

Exams: There will be four in-class exams. Attendance is required for all of them on the dates listed. If you should miss an exam for an emergency you will be allowed to make it up only if you have notified me before the exam, which must be made up in a timely manner (to be discussed with me individually).

Daily Schedule and Assignments: