Foundations of Engineering: The Mathematics and Shape of Motion

Description of Course Goals and Curriculum

This course is equivalent to MAT 104 (Calculus II) and complements EGR 151. Like EGR 151, this course approaches calculus from an engineering-based, applications perspective. In both lectures and problem sets, there is significant focus on the applications of calculus to solving problems in physics, engineering/modern technology, epidemiology, and other scientific fields. This course has two 80 minute lectures a week, which differs from the shorter, smaller, and more frequent class sessions of MAT courses. The course covers sequences and series, advanced integration techniques, and introduces differential equations. Most of the time in the course is spent on sequences and series, which also includes Fourier series and Taylor series.

Learning From Classroom Instruction

Professor Houck’s lectures are engaging, but very fast-paced! He is highly interested in teaching the course content, but it is important to pay close attention and ask questions as needed for clarification. Most of the lecture is spent introducing new concepts and demonstrating example problems. There is some time focused on proving the concepts introduced in lecture, but this content is not explicitly tested on problem sets/exams. In addition to class notes, Professor Houck uploads his handwritten lecture notes each week. These notes are equally as useful for reviewing for exams and working on problem sets. Additionally, Professor Houck is very accommodating when students need to miss class for excused reasons and is flexible in making sure students get caught up on course content.

Learning For and From Assignments

The majority of the problem sets are dedicated to practicing the calculus concepts discussed in lecture. These problems are more straightforward and are similar to standard textbook problems. The end of the problem set is dedicated to the applications question(s), which often require assistance from the TAs during office hours. Students can also post on Piazza with questions, which are answered clearly and quickly. These problem sets also benefit from collaboration with classmates. There were two midterm exams, one at midterms and one after Thanksgiving break, as well as a final exam. For exams, the problem sets are the best guide, as many exam problems are connected to the problem sets. The applications questions on these exams are also related to the problem sets, so understanding the broader way a concept is applied to engineering problems is especially useful when studying. Overall, learning how to recognize what approach should be taken to solve a given problem is a key skill, especially since the three parts of the course are made up of different approaches to integration, finding series convergence, and solving differential equations. These are three broad topics, so it is important to understand each given concept within these fields in order to know when it should be applied.

External Resources

Attending course office hours with the TAs was highly useful for completing the problem sets, especially the applications portion of the assignment. Attending group study hall at McGraw was also useful. There was no textbook assigned for this course. However, I did reference the textbook used in MAT 104 for additional practice problems when preparing for exams.

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

Students should feel comfortable with calculus concepts from Calculus I. Past exposure to Calculus II is certainly helpful, but not needed. Professor Houck clearly demonstrates the importance of calculus in real world situations and brings in relevant examples during class and through problem sets. This course is designed quite well and is a great fit for students who enjoy finding connections between math and the world around them. Though this course is taken to fulfill a requirement, it did not feel as such and was highly enjoyable.