Takeaways

At the beginning of every section of these notes, I will write the major takeaways for that section, since sometimes the important points often get lost in the fray. Also, I made the CME 102 notes before I made these, so there is definitely some duplication between the two (especially in the tips I give or annecdotes I include).

What CME 100 is All About

CME 100 is a hard class, because it’s about a lot of things. The description description is “vector and multivariable calculus.” If I could sum it up though, I would say it is about:

1. Vectors
2. Derivatives of functions of multiple variables
3. Integrals across multiple variables, especially over volumes and surfaces

This class also covers the crossover of these things extensively and tends to build on itself, so it’s really necessary to understand everything as you go. Also, this class is very computational in that you will be working out a lot of derivatives/integrals. This class is not theoretical: you will not be expected to do mathematical proofs. The focus of this class is solidly on engineering and related applications of the material, and the proof-based aspects of this material is relegated to equivalent classes in the math department.

As a heads-up, you’re probably going to feel like you’re drowning a little bit in this class, and that’s okay. This class covers an absurd amount of material in a short amount of time, and it’s probably not going to be easy but that’s how you’re going to grow as a student through this course. Having said that, it’s also important to go into the class with enough background knowledge, which brings me to…

What are the actual prerequisites?

The official prerequisite for this class is MATH 21 or equivalent (a.k.a. AP Calculus BC), and having taken/taught this class, I think the listed prereq is spot-on. I strongly advise against taking this class if you don’t have an understanding of calculus at the level of getting a 4 on the AP Calc BC exam: this class is very fast-paced, and there’s just no realistic way you’ll “learn it as you go” or “catch up during the quarter.” The first step in succeeding as an undergraduate (at any university) is being realistic with yourself with how much time you’ll spend on something or how quickly you’ll learn material. Taking this class without AP Calc BC-level material is setting yourself up to receive a poor grade and not properly learn the material.

How to study for CME 100

My dad was a college statistics teacher at Fresno State for many years, and something he always told students about was “Randy’s Recipe for Success” (his name is Randy). This was basically an outline of what students needed to do to succeed in his class. So, in that same vein, I’ll present to you Tim’s Recipe for Success in CME 100:

1. Read through the material (course reader or textbook) the night before lecture. This is a habit I picked up when I was in CME 104, and I can tell you it made a huge difference in both my performance and lowering my stress level.

2. Go to lecture and annotate your course reader or textbook. Too often I see students in lecture or section scrambling to write down every detail that’s written on the board and every word out of the professor’s or TA’s mouth. The course reader typically follows closely with lecture, so save yourself the hassle and write directly on the course reader/textbook. And yes, even if you were just planning to use a PDF file, you should print out the PDF and annotate that. (If you don’t want to pay for printing credits, then ask yourself how much a good grade in this class is worth to you and compare.)

3. Study over the material the same day right after lecture. Learning math—especially methods for computing answers like in CME 100—is all about repetition and consistency. If you make three passes over the material (the night before, during lecture, and immediately afterwards), you will be learning the material thoroughly and efficiently.

Closing Remarks

An amazing analogy I first heard from my undergraduate advisor and mentor Prof. Margot Gerritsen was that mathematics is like weightlifting. Some people get stronger faster than others, some people find it easier, and some find it more enjoyable. Some of us start off stronger than others, had better coaches or trainers, etc. In the end though, everyone can reach their goals through enough hard work and determination: the limiting factor is never natural ability. In weightlifting, this means training in a way that’s effective for you and hitting the gym regularly. In mathematics and engineering, it’s about developing study habits that fit your learning style and consistently challenging yourself.

I know many of you may feel intimidated by this class, and that’s perfectly understandable. This class is definitely non-trivial, and especially if you have a weaker high school background this class can be rough. It doesn’t matter if you have a poor background or think you’re just “not a math person” or say you’re a “fuzzy” instead of a “techie”. (Saying you’re a “math person” or a “non-math person” is completely ridiculous anyways, since besides those few who placed high at the International Math Olympiad or won a Fields Medal, I’d contend almost none of us are really “math people”.) What really matters in the end is putting in the work necessary to do well. Just like with Prof. Gerritsen’s analogy, we may not all start in the same place and we may not all learn at the same speed, but with discipline and consistency, all of us can get there. All of you reading this are capable of earning an A in CME 100—it is just up to you to work for it.