Mathematics I :: Geometry, Algebra, Trigonometry, and Calculus

This text covers what I consider as “fundamental mathematics.” This includes what many would consider advanced geometry, algebra, and calculus. However, to the scientist, this is basic information that must be utterly mastered, and it can be fairly quickly.

Geometry

• Surface Area of a Sphere
• <<<Eccentricity>>>
• <<<Ellipse>>>
  • <Semi-Major and Semi-Minor Axes>
  • <Calculating the Perimeter of an Ellipse>

Algebra

• Polynomials
  • The Polynomial :: An Introduction
  • Finding the Average Rate of Change of Polynomials
• Logarithms
  • Introduction to the Logarithm
  • Evaluating Advanced Logarithmic Functions
    • Logarithmic Function Problems #1
  • Order of Magnitude :: The Scale of a Number

Calculus I

1. Introductory Concepts
   1. < Calculus I Intro>
2. Limits & Differentiation
   1. The Limit of a Function*
   2. One-Sided Limits*
   3. Infinite Limits*
   4. The Meaning of d/dt in Physics & Mathematics*
   5. Using Limit Laws to Calculate Limits
3. Integrals & Integration
   1. <Integrals>
   2. <Integrals:: The Area Problem>