So quick change, I originally planned on studying rocket engineering, but realized, that's such a hard path to start with. Slight pivot, and now I'm starting with rocket science instead, which is the easier of the two.
It's funny because the saying, "it's not rocket science" has for some reason put the concept of learning rocket science at the apex of insanely hard things you could learn, but in reality rocket engineering/aerospace engineering is much, much harder in practice.
I am continuing to use SuperGrok Heavy to setup and guide my learning plan, so today I gave it an update on the change in plans.
And now I'm starting at Phase 0, which starts with Calculus study. I took a lot of Calculus in college, like a crazy amount, so I'm actually kinda excited to get back in and I thought it was pretty neat that it recommended the Stewart textbook since that's the exact one I learned from, and yes, still have!
Of course, there's no way I can go through the entire textbook, and I also know I only need specific concepts to understand the formulas and equations used in rocket science. So I asked SuperGrok Heavy, and here's what it came back with:
Quick Review Strategy (2–4 weeks total)
- Goal: Rebuild intuition and muscle memory for the math you’ll actually use — rates of change, integration for energy/impulse, parametric curves for orbits, basic differential equations, and vectors in 3D space.
- Approach: Skim the chapter summaries and examples first, then do 8–12 key problems per chapter (focus on the odd-numbered ones with answers in the back). Skip proofs unless you enjoy them.
- Time: 1–2 chapters per day if you’re rusty; slower if you want deeper practice.
Recommended Chapters (in priority order)
| Priority | Chapters | Why It Matters for Rocket Science | What to Focus On |
|---|---|---|---|
| 1 (Must-do) | 2–4 (Limits & Derivatives, Differentiation Rules, Applications of Differentiation) | Velocity, acceleration, thrust as rates of change; optimizing mass ratios and burn times | Related rates, optimization (max/min problems), implicit differentiation |
| 2 (Must-do) | 5–7 (Integrals, Applications of Integration, Techniques of Integration) | Impulse, work done by thrust, deriving the rocket equation via integration of variable mass | Definite integrals, integration by parts, substitution; area/volume applications as warm-up |
| 3 (High priority) | 9 (Differential Equations) | Solving the actual equations of rocket motion (acceleration = thrust/mass – gravity – drag); basic orbital DEs | Separable equations, first-order linear DEs, exponential growth/decay models (very similar to mass expulsion) |
| 4 (Important) | 10 (Parametric Equations & Polar Coordinates) | Describing trajectories, orbits as parametric curves (position vs. time) | Parametric curves, arc length, polar graphs (useful for conic sections in orbits) |
| 5 (Important) | 12–13 (Vectors & the Geometry of Space, Vector Functions) | 3D space, velocity/acceleration vectors, position as a vector function | Dot/cross products, vector-valued functions, curvature, motion in space |
| 6 (Helpful later) | 14–16 (Partial Derivatives, Multiple Integrals, Vector Calculus) | Gravitational potential fields, line integrals for work/energy in orbits, divergence/gradient for fluid flow in propulsion | Partial derivatives, gradients, line/surface integrals (skip the heaviest theorems if time is short) |
Skip or skim lightly:
- Chapter 1 (Functions & Models) — just review if your precalc is weak.
- Chapter 8 (Further Applications of Integration) — mostly physics applications you’ll see again later.
- Chapter 11 (Infinite Sequences & Series) — useful for approximations but not critical right away.
- Chapter 17 (Second-Order DEs, if your edition has it) — nice-to-have for vibrations/damped systems, but you can pick it up later.
To start with, I'm going to do the must-do and high priority chapters and then dive in, so that means Chapters 2–4 (Limits & Derivatives, Differentiation Rules, Applications of Differentiation) and Chapters 5–7 (Integrals, Applications of Integration, Techniques of Integration), and of course, can't escape anything without a little DiffEq.
Excited to crack open Stewart again, it's been a while, but I loved Calculus, miss it, never ended up getting to use it for work, so it's going to be fun to brush up on it a bit!