R
2
S Nexus Video Archives
V-REC FILES
Advanced Level Mathematics
A Phase I Preparatory Course for College/University
G. David Boswell • BÖ§ZïK Inc.™
BASIC ALGEBRA & FUNCTIONS
TRIGONOMETRY, COORDINATE GEOMETRY & VECTORS
CALCULUS I (Limits, Differentiation and Integration)
Real Number System
•
Introduction
Reasoning and Logic
•
Algebra of Propositions
Binary Operations
•
Theory & Examples
Algebra of Surds
•
Surds & Irrationals
Sigma Notation
•
Intro and Examples
Mathematical Induction
•
Proof by Induction
Algebraic Operations
•
Polynomials, Factorizations and the Binomial Theorem & Pascal’s Triangle
Exponents & Logarithms
•
Exponents & Logarithms
•
A Modeling Problem
Functions & Graphs
•
Function Classifications
The Modulus Function
•
Modulus Function Primer
•
Modulus Function
(
Skeleton files
)
•
Interpretations and Examples
Quadratic Equations
•
Quadratics
(Viète’s work)
Cubic Equations
•
Cubics
(Viète’s work)
RETIRED!!!
(
R2S EXODUS 2020-2021
)
•
Functions - Domain & Range
•
Algebra of Functions
•
Quadratic Equations
•
The Modulus Function - Examples
•
Quadratics - Proof of Formula
•
Quadratics and Cubic Equations
•
Cubic Equations
Coordinate Geometry
•
Introduction to Straight Lines
Trigonometry
•
“Pretty Angles,” CAST and intro to Trig Identities
•
Trig Identities & CAST (revisited)
•
Definitions & Identities - Review Solutions
(
+ pdf
)
•
Solutions (Roots) of Trig Equations
(
+ pdf
)
Vectors in 3-D
•
Replaced by In-Class Notes and Examples
Infinitesimals, Limits and Continuity of Functions (
2021
)
•
Limits 01
•
Limits 02
Differentiation (
2021
)
•
Introduction
•
The Chain Rule
•
The Product and Quotient Rules
•
L’Hopital’s Rule
•
Rates of Change
•
Critical Points (Turning, Stationary and Inflection)
•
The Second Derivative & Tangents and Normals
•
Differentiation of Special LIATE Functions and Differentiation Tutorial
Integration (
2021
)
•
Introduction
•
Exploits in Easter
•
Areas under Curves
•
Volumes of Revolution
•
Review Session
Applied Calculus (Basics)
•
Differentiation and Integration
•
Mathematical Modelling
R2S Nexus
Auspices of BÖ§ZïK Inc.™
“Changing the World … One Scholar at a Time”
G. David | BÖ§ZïK Inc.™
Mathematics, Science and Engineering (MSE)
Energy and Power Systems Engineering (EPSE)
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