Calculus: Vector Functions

Over in the Orbital Mechanics section we recommended studying chapters 10, 12 and 13 of James Stewart's Calculus textbook as preparation to studying orbital mechanics. In the links below I've attached solutions from old exercise sets I've done for two of these chapters. I used computer aids like Python scripts and online graphing tools for some of the problems. Computers are useful for these problems because: 

• they can instantly crunch through tedious computations like cross products so that you can focus on conceptual learning

• they can quickly render points, lines, surfaces and volumes in three dimensions, again allowing you to focus on conceptual learning

For vector functions and plotting, I used a Python library from the first edition of Math for Programmers by Paul Orland. In the future I may rework these exercises with NumPy and Plotly to make them simpler and clearer.

Chapter 10: Parametric Equations and Polar Coordinates

• Lost most of it, sorry!

Chapter 12: Vectors and the Geometry of Space

• 12.1 - 12.3: Can't find 'em

• 12.4: The Cross Product

• 12.5: Equations of Lines and Planes

• 12.6: Cylinders and Quadric Surfaces

Chapter 13: Vector Functions

• 13.1: Vector Functions and Space Curves

• 13.2: Derivatives and Integrals of Vector Functions

• 13.3: Arc Length and Curvature

• 13.4: Motion in Space: Velocity and Acceleration