~CALCULUS I~


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~NOTE: The following review & enrichment sections are written primarily for beginning Calculus students. Many are not math or math related majors. Consequently, much rigor has been eliminated. I will be concentrating on basic understanding & feel for the concepts discussed. For a good number of students, calculus I is the last calculus course they will take. No special knowledge, outside of what I cover in class, is required to understand these concepts.
 


 ~REVIEW 

EXPONENTS & LOGS
THE DERIVATIVE
Calculator Procedures
CONTINUITY  & DIFFERENTIABILITY
CAUCHY'S DEFINTION
CHAIN RULE  
INVERSE TRIG IDENTITIES
DERIVATIVE FORMULAS
RATE OF CHANGE
RELATED RATES    
TANGENTS & NORMALS
MEAN VALUE THEOREM
MAX - MIN
INTEGRATION FORMULAS
AREA UNDER A CURVE
THE DEFINITE INTEGRAL
The 2nd Derivative in Business
THE DIFFERENTIAL
Implicit & Logarithmic Differentiation
The Biggest Box
Sketching Using Derivatives
The Bug-Frog Problem
Continuous Compound Interest
Euler's Formula
Implicit Differentiation
Maximizing Profit
Common Integration Mistakes


 ~ENRICHMENT~

    CAUCHY'S CRITERION                                        MATHEMATICAL INDUCTION
                 GLB & LUB                                                         THE "HOLEY FUNCTION"
DIFFERENTIAL EQUATIONS                         SYNTHETIC DIVISION & FACTORING
      L'HOSPITAL'S RULE                                      UNIFORM CONTINUITY
   Carbon 14 Dating                                                   CURVATURE
TYPES OF OPTIMIZATION PROBLEMS                    Curve Fitting

The 2nd Fundamental Theorem                   Wind Chill Factor

Simple Growth/Decay
Growth and Decay

~SOME BASIC CONCEPTS~

~Popular Algebraic Techniques~
~Functional Notation~

~Average Rate of Change of a Function~
Limits & Continuity---General Overview

The Derivative--General Overview

The Derivative Power Rule

The Derivative Quotient Rule

Finding Max/Min Points

Integrals

The Integration Power Rule
The Binomial Expansion & Pascal's Triangle






 

                                       

~WILL BE UPDATING MY SITE PERIODICALLY~

~THESE ARE MY OWN PERSONAL VIEWS ON THE SUBJECTS DISCUSSED & SOME MATH TEACHERS MAY HAVE DIFFERENT APPROACHES, WHICH ARE WELL RESPECTED, IN ANY CASE.