Date Range: October 20 – October 26
Hours Spent: 17 hours
- 5 hours on lectures Professor Leonard – Calculus 2 Lecture: 8.1
- 12 hours on exercises (Thomas 13th ed, questions 1 – 34)
Summary:
This was an introduction to differential equations – I’ve never dealt with them before. These are essentially equations involving two different functions, each in terms of separate variables. I first familiarized myself with them via pure calculation, e.g. dy/dx = y/x. This transitioned into word problems centered around growth and decay, and the variables that influenced said growth or decay. In a nutshell, I applied familiar algebraic concepts of separating variables and corresponding integration tools that I’ve been developing throughout Calculus 2, where necessary, to find general relationships and particular solutions where initial values were given.
Personal Observations:
- I really enjoyed the added layer of complexity that came from comparing two rates of change to each other
- The word problems were a blast, as each peeled back a layer on the world around me to give me a glimpse of the underlying math from phenomena such as decreasing average teeth size of Homo sapiens over millenia, to visibility under water relative to increasing depth, to the administration of antibiotics – so cool!
- The word problems were challenging in understanding how to frame them, i.e. how to convert the verbal problem into its corresponding differential equation
Reflections:
The world around me is an interplay of changes, one affecting the next, affecting the next, affecting the next. Differential equations is a fascinating way to quantify the relationships of change. I look forward to studying Differential Equations in the future.