Workshop Content

• Different forms for the equation of a line
• Graphs and properties of lines
• Slope of lines
• Solving linear equations
• Solving systems of two linear equations

• Properties of exponents applied to power and exponential expressions
• Multiplying and simplifying power expressions and exponential expressions
• Nested exponents and distributing exponents across multiplication and division
• Simplifying expressions with power and exponential functions

• Explaining the basic terminology and rules of logarithms
• Explaining the basic properties of logarithmic functions such as the graph, domain, range, end behavior, asymptotes, and 𝑥-intercepts
• Expanding or condensing logarithmic expressions using the logarithm rules

• Rules for derivatives
• Power rule 
• Product and Quotient Rule
• Chain Rule

• Finding the derivatives of functions with the natural exponential function and general exponential functions

• Derivatives of logarithmic functions including the natural logarithm
• Combining the derivative rules for logarithmic functions with the other derivative rules such as the product, quotient, and chain rule

• The definition of a function of two variables
• The graph of a function of two variables with domain D and range R
• The level curves of a function of two variables

• The definition the partial derivative of \(f(x,y)\) with respect to \(x\) and \(y\)
• The geometric interpretation of the partial derivative
• Higher order partial derivatives and Clairaut’s Theorem

• Using the first derivative to determine where a function is increasing and decreasing
• Using the First Derivative Test to find the local maximums and local minimums of a function
• Using the second derivative to determine where a function is concave upward and concave downward and to find all inflection points
• Using the Second Derivative Test to find the local maximums and local minimums of a function
• The Second Derivative Test for Local Extrema
• Local and absolute extrema of a function \(z=f(x,y)\)
• Extreme Value Theorem for Functions of Two Variables

• Using the first derivative to determine where a function is increasing and decreasing
• Using the First Derivative Test to find the local maximums and local minimums of a function
• Using the second derivative to determine where a function is concave upward and concave downward and to find all inflection points
• Using the Second Derivative Test to find the local maximums and local minimums of a function

• Finding an antiderivative
• Solving an indefinite integral
• Finding a function from its derivative and a given function value

• Properties of definite integrals
• Integral comparison properties
• The Fundamental Theorem of Calculus
• Evaluating definite integrals
• Finding the area between curves

• The Substitution Rule
• The Substitution Rule for definite integrals
• Integrating symmetric functions

• Using integration by parts to solve integrals
• Using integration by parts multiple times and possibly having the original integral reappear in the solution

• Kolmogorov’s Axioms
• Discrete Uniform Probability Spaces
• Complement Rule
• Monotonic Property and Inclusion & Exclusion

• Conditional Probability
• Law of Total Probability
• Bayes' Formula
• Independence of Two Events
• Complement of Independent Events Conceptual
• Independence of Events
• Bernoulli Trials

• Discrete Random Variable 
• Probability Distribution and Probability Mass Function
• Functions of Random Variables
• Cumulative Distribution Function

• Expectation
• Variance and Standard Deviation
• Properties of Expectation and Variance
• Continuous Random Variable and Probability Density Function
• Probability Density Function
• Expectation of Continuous Random Variable
• Uniform Probability Density Function