Course: MAE 305 / MAT 391 / EGR 305 / CBE 305
Instructor: Howard Stone
F 2019

Description of Course Goals and Curriculum

MAE 305 is all about differential equations. Topics include:
  • Separable Ordinary Differential Equations (ODEs)
  • Linear 1st-order ODEs
  • 2nd-order ODEs
  • Systems of ODEs
  • Laplace Transforms
  • Series solutions
  • Fourier series
  • Introduction to Partial Differential Equations
In many cases, topics in this class build off topics learned in previous weeks. Partial differential equations, for example, is a culmination of several topics. Since this is an engineering math class, practical problem-solving will be the focus, rather than abstract or proof-based math.

Learning From Classroom Instruction

There are three lectures a week plus one weekly precept. Lectures essentially cover all the material there is to learn, and precepts are to recap and focus on example problems. Professor Stone publishes an outline which indicates the topics of each lecture and which readings pertain to the lecture. It is not required to do the readings, but they are there as a resource for those who like to be see the material before lecture. The professor also publishes lecture notes, which he follows very closely during lecture.

Each preceptor has a different style of teaching, so students are permitted to attend any precept regardless of their enrolled section. To make the most of classroom instruction, be sure to ask questions during precept about anything you don’t understand from lecture or lecture notes.

Learning For and From Assignments

MAE 305 gives weekly problem sets. These are meant to test how well you can apply the problem-solving methods that are taught in class. The questions follow the same principles as the problems presented in lecture and precept. However, they tend to be longer or more involved. The best way to prepare for problem sets is to ensure that you understand the course material, especially the material from precept. Reading the professor’s lecture notes while completing the problem sets is a great way to solidify the material.

This class has two midterm exams and a final exam. Exam problems tend to be shorter than problems from problem sets. They also test the students’ abilities to apply the course’s problem-solving methods. Usually, the exam problems guide the students toward the correct solution method, so the main challenge is remembering the method and executing it without error.

External Resources

It is not necessary to attend office hours, but it can save a lot of time if you are stuck on a problem. The TAs are very familiar with the problems and are exceptionally helpful, not only in guiding you towards the right solution, but also in making sure you really understand the math. Office hours are also a great place to collaborate with other students.

Professor Stone suggests several optional textbooks. There are also plenty of free resources online for differential equations. These external resources are helpful whenever you need more detail than what is provided in lecture notes, or if you want to see more example problems. However, the lecture notes and precept materials usually have all the information you need.

Two great resources are Mathematica and Wolfram Alpha. These software programs are helpful for checking your work or simplifying algebra, and the instructors encourage students to use them. Just make sure to show all your work on problem sets for full credit, rather than plugging everything into the solver.

What Students Should Know About This Course For Purposes Of Course Selection

MAE 305 has some differences between the fall and spring. Some say that the spring version is a little easier. However, Professor Stone teaches in the fall, and he is one of the most engaging lecturers I have ever encountered in an engineering department. Read a few course evaluations when deciding which semester is the right time to take it.

Be warned that the first problem set takes a lot of time compared to the rest. If you are worried about dropping the course after the first problem set, you should know that it is not representative of the remaining problem sets.

The difficulty is about the same as that of MAT 201. However, the content is very different. Assignments and exams in MAT 201 require students to figure out the right method and how to apply it, and the mathematical concepts are more abstract. In MAE 305, it is easier to determine how to start a problem and what method to use, and the problems are more tangible. That is not to say that MAE 305 is easier; it is just a different style of math that caters to an engineering focus.

Differential equations arise in many disciplines, not just MAE. This class will give you the confidence you need whenever you encounter a differential equation in another class. Even if differential equations are not part of your future coursework, MAE 305 is a great class to hone your math problem-solving skills. I would lastly like to emphasize that the quality of instruction in MAE 305 is excellent. If you attend class diligently, you will get the most out of MAE 305 and find yourself on the path to success.

Mathematics in Engineering I

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