Logic mastery strengthens comprehension and so improves home, work & study abilities .
Logic 5 Chapters Arithmetic 10 Steps Algebra 12 Starter Steps & 5 Advanced Steps
Work & Study 23 Tips Geometry 15 Steps Calculus 70 Lessons

Ages 15+: Why study slopes Polynomials Quadratics Why factor polynomials Logarithms Functions
What is similarity Euclidean geometry leanly Coordinates + complex no.s Vectors DC Electric Circuits

Ages 14+: Prime factorization Written work formats Decimal place value Extend arithmetic skills orally
What is a variable 5 fraction operations by raising terms Solving Linear Equations: Take I Take II

Online Volumes: 1 - Elements of Reason, 2 - 3 Skills For Algebra, 3 - Why Slopes and
More Math, 1A - Pattern Based Reason, 1B - Skill Development Principles + Troubles
Forewords + leading chapters give original reasons, still valid, for site content & growth.

70 Calculus Starter Lessons

Calculus prequel, starter and companion lessons.

The folder 13 Lessons on Limits and Continuity and Volume 3, chapter 15, Algebraic Evaluation of Limits, may ease or avoid the algebraic difficulties.

The folder 43 Lessons on Calculating Derivatives explains many rules of differentiation and includes a geometric derivation of rules for differentiation of sines, cosines and their ratios. It coverage of the chain rule begins with a derivation of it in the simpler case where one function is substituted in a power or in polynomial. This long route depends on the product rule and repeated mathematical induction. This long is not technically required, but following it almost by stealth leads to students to a mastery of the composition of functions and the mind-set needed to understand the chain rule in general. The proof of the chain rule in the general case follows from a discussion of linear approximation to function and the role of the derivative in that. Here further motivation for the chain rule follows from a discussion of the composition or substitution of one linear function into another. The Chapter 19 in Volume 3 includes an area under the curve definition of the natural logarithm which sets the stage for derivation of a formula for its derivative. This folder explains and derives the link between the derivatives of a function and its inverse, and so derives the derivative of the exponential function from its introduction as the inverse to the natural logarithm. That together with the careful derivation of formulas for roots and powers in terms of the exponential function and the natural logarithm provides a direct route for obtaining derivatives of roots and powers from the chain rule.

The folder 4 Lessons on Using Derivatives briefly employs the first derivative test in cubic function sketching exercises and then informally explains the second derivative test.

The 5 Lessons on Integration includes a precise and careful account of how using the chain rule in reverse leads to the change of variable methods for integration.

12 Webvideo Lessons on Area and Volume Calculation explains formulas and present examples with the aid of a dozen flash videos. These examples might come at the end of a first course in calculus or the start of a second.

Arithmetic - Ages 10+
1. Deciml Place Value - fun
2. Decimals for Tutors
3. Prime Factors - quickly
4. Fractions + Ratios
5. Arith with units - science