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Math Analysis IIP                 

 

1st Term Topical Overview:

 

linear functions

solving linear systems

Gauss elimination

matrix operations

inverses

quadratic functions

solving quadratic equations using

derivation of quadratic formula

completing the square

matrices

cubic functions

position, velocity, and acceleration relationships

average velocity from data

symmetric difference quotient

zeros of model velocity function

solution of radical functions

Binomial Theorem/Pascal’s triangle

combinations, permutations

variation and standard deviation of normal models

normal model for binomial densities

Central Limit Theorem

distribution of means

 

2nd Term Topical Overview:

 

instantaneous vs. average velocity

tangent line to point on a graph

relative extrema

optimization

derivative as a rate of change

cost, demand, revenue, profit functions

marginal cost, profit

inflection points

sinusoidal functions

derivative of sine and cosine

second derivatives

acceleration

angle sum identity

trig identities involving sine and cosine

probability applied to genetics

Hardy-Weinberg Equilibrium Principle

 

3rd Term Topical Overview:

 

radical, reciprocal functions

odd/even functions

composites

inverse variation

asymptotes

derivative rules

power functions

sum/difference rule

chain rule

scalar multiplication

product rule

mathematical induction

polynomial approximators for sinusoidal functions

geometric sequences

recursive/explicit functions

exponential functions

linear approximation

 

4th Term Topical Overview:

 

finite difference equations

increasing/decreasing functions

concavity

derivative rules for

reciprocals

exponential functions

log functions

exponential growth/decay

bounded exponential growth

logistic functions

sequence of partial sums

infinite geometric series

Newton’s Law of Cooling

Euler’s Method

Logarithmic functions

discrete and continuous models

parametric model for projectile motion

analysis of relationships