Systems of Two Linear Equations in Two Variables Video 1
Explaining the format and possible solutions for a system of two linear equations
Problem: Solve the following system of linear equations: \begin{align*} x+y&=2\\
-2x+y&=-1\end{align*}
Explaining the format and possible solutions for a system of two linear equations
Solving a system of two linear equations with two variables using the elimination method
Solving a system of two linear equations using a TI-84 calculator
Solving a system of two linear equations using a TI-84 calculator
Solving a system of two linear equations using a TI-84 calculator
Explaining the format and possible solutions for a system of two linear equations
Finding the point where two lines in three-dimensional space intersect
Explaining the main three forms for linear equations
Discussing properties of linear functions
Discussing the types of linear graphs including horizontal and vertical lines and their properties
Discussing how to write the equation of a line through two given points
Writing a linear equation of profit from a business word problem
Solving a linear equation algebraically and showing how this relates to the graph
Solving a linear equation algebraically
Solving a linear equation algebraically and showing how this relates to the graph
Writing the equation of a line that passes through two points
Finding the slope of a line through a pair of points
Writing the equation of a line with an undefined slope and a given point
Writing the equation of a line with a zero slope given a point
Finding the x and y-intercepts for a line
Solving for a constant so a line has a particular x-intercept
Graphing a line without using technology
Graphing a line without using technology
Graphing a line without using technology
Determining the change in y as x increases for a line
Determining the change in x as y decreases for a line
Determining the slope of a line given points containing a variable
Writing a function for the value of an item depreciating linearly over time
Finding linear functions for the cost, revenue, and profit of a business
Finding the linear cost function for a company
Finding the linear revenue function for a company
Finding the linear profit function for a company
Finding a linear demand equation
Finding a linear supply function
Finding the change in y as x increases for a given line
Writing a linear function representing the depreciation of a car
Writing the augmented matrix for a system of linear equations
Determining if given values are solutions to a system of linear equations
Solving a system of linear equations without using technology
Finding the solution to a system of linear equations by graphing
Using a TI-84 to solve a system of linear equations in three variables
Using a TI-84 to solve a system of linear equations in three variables
Writing a system of equations for a given word problem
Answering questions about a demand and supply word problem
Graphing the solution set of an inequality with two variables
Graphing the solution set of an inequality with two variables
Graphing the solution set of system of linear inequalities
Finding the piecewise-defined function for a given graph along with its domain and range
Graphing a piecewise function
Explaining the definition of logarithmic scale and double-log plots
Using logarithms to transform a power function into a linear function
Writing a non-linear function to represent the line graphed on a semilog plot
Finding the equation of a line through two points
Finding the equation of a line through two points
Finding the equations of parallel and perpendicular lines
Finding the equation of a parallel line
Solving a linear system of equations using substitution
Solving a linear system of equations using elimination
Solving a linear system of equations
Cartesian equations and parametric equations of curves
Review of vector functions and parametric equations
Review of the limit definition of a derivative and calculating the derivative
Review of the limit definition of a derivative and calculating the derivative
Review of derivatives and tangent lines to functions and vector equations
Review of the limit definition of a derivative and calculating the derivative
Review of derivatives and tangent lines to functions and vector equations
Review of the limit definition of a derivative and calculating the derivative
Derivatives and tangents to curves
Finding the distance between a point and a line using scalar projection
Finding a vector equation for the line through two points
Finding a parallel vector through a point
Finding a line perpendicular to a vector and passing through a point
Find the Cartesian form and sketch the graph for the parametric equation of a line
Finding a vector equation for the line passing through two points
Examples finding a volume using disks, washers, and by slicing
Cartesian equations and parametric equations of curves
Using the limit definition to find derivatives of functions and vector functions
Review of vector functions and parametric equations
Review of the limit definition of a derivative and calculating the derivative
Review of the limit definition of a derivative and calculating the derivative
Review of derivatives and tangent lines to functions and vector equations
Proving limits using the epsilon-delta definition
Using the limit definition to find derivatives of functions and vector functions
Using the limit definition to find derivatives of functions and vector functions
Review of the limit definition of a derivative and calculating the derivative
Review of derivatives and tangent lines to functions and vector equations
Proving facts about differentials including a product rule
Review of the limit definition of a derivative and calculating the derivative
Review of derivatives and tangent lines to functions and vector equations
Examples involving the tangent line to an exponential function and finding the derivative of hyperbolic cosine
What the derivatives of a function tell us about the shape of its graph
Optimizing values in word problems
Examples finding a volume using disks, washers, and by slicing
Finding an equation of the plane containing two given lines in three-dimensional space
Using the method of Lagrange multipliers to find the extreme values of a function subject to a constraint
Evaluating a line integral along a curve in space
Explaining the concepts of existence and uniqueness for solutions of systems of equations
Solving a system of equations with three equations and three variables
Solving a two systems of equations
Using the Gauss-Jordan algorithm to solve a system of equations
Solving a system of equations by row reducing the augmented matrix
Solving a matrix equation using the inverse of the matrix
Finding the domain of a function with a denominator, square root, and logarithm
Finding the domain of a function with a natural logarithm and denominator
Finding the domain of a function with a square root in the denominator
Finding the domain of a function with a root and a logarithm in the denominator
Finding the domain of a logarithmic function
Finding the domain of even and odd roots
Finding the domain of functions with even and odd roots
Finding the domain of several rational functions
Finding the domain of a rational function
Explaining how to find any holes and vertical asymptotes of a rational function
Finding the domain of a rational function using factoring
Explaining domain restrictions for denominators, even roots, and logarithms
Explaining the standard form for a quadratic equation and the possible number of solutions
Solving quadratic equations with the difference of two squares formula
Solving quadratic equations by factoring
Solving a quadratic equation by factoring
Solving a quadratic equation by factoring
Solving quadratic equations with the quadratic formula and discussing the number of possible solutions
Explaining when a quadratic equation does not have a real solution
Explaining the graph and properties for the parent function of quadratics
Discussing properties of quadratic functions including the vertex, domain, range, and end behavior
Explaining the general properties of even and odd root functions
How to rewrite radical terms as power terms
Explaining how to solve radical equations and then solving example problems
Solving equations with even roots and checking the solutions
Solving equations with odd radicals
Solving equations with multiple radicals
Properties of exponents applied to power and exponential expressions
Properties of multiplying and simplifying power and exponential expressions
Properties of exponents applied to power and exponential expressions
Properties of exponential growth and decay functions
Properties of the exponential function with base e
Simplifying power and exponential expressions using properties of exponents
Simplifying power and exponential expressions using properties of exponents
Simplifying power and exponential expressions using properties of exponents
Simplifying an expression with both power and exponential functions using properties of exponents
Explaining how to solve equations with power and exponential terms
Solving equations with exponential terms
Solving equations with base e exponential terms
Explaining the terminology and rules of logarithms
Explaining the basic properties of logarithmic functions
Expanding logarithmic expressions using logarithm rules
Condensing a logarithmic expression into a single logarithm
Explaining how to solve logarithmic equations
Solving logarithmic equations with a single logarithm term
Solving logarithmic equations with multiple logarithm terms
Solving logarithmic equations with multiple logarithm terms on both sides
Discussing parent functions of rational functions and their properties
Finding horizontal asymptotes for rational functions
Explaining how to do polynomial long division
Finding horizontal asymptotes for rational functions
Determining the end behavior and horizontal asymptotes for rational functions
Explaining basic algebraic operations for fractions
How to simplify rational expressions
Adding and subtracting rational expressions by finding a common denominator
Explaining how to multiply and divide rational expressions
Performing algebraic operations with rational expressions and simplifying the answer
Solving equations that contain rational expressions
Solving an equation that contains rational expressions
Solving an equation that contains rational expressions
Solving a system of equations by using the Gauss-Jordan algorithm to row reduce the augmented matrix
Solving a system of equations by using the Gauss-Jordan algorithm to row reduce the augmented matrix
Solving a system of equations by using the Gauss-Jordan algorithm to row reduce the augmented matrix
Solving a system of equations by using the Gauss-Jordan algorithm to row reduce the augmented matrix
Solving a system of equations by using the Gauss-Jordan algorithm to row reduce the augmented matrix
Solving a system of equations by using the Gauss-Jordan algorithm to row reduce the augmented matrix
Solving a system of equations by using the Gauss-Jordan algorithm to row reduce the augmented matrix
Solving a system of equation by writing it as a matrix equation and using the matrix inverse
Finding all local extrema and saddle points for a function of two variables
Explaining matrix operations including addition and multiplication
Solving a system of linear equations with three equations and three variables
Determining the solutions of a system of equations depending on the value of the constants
Defining linear independence for a set of vectors
Determining if three vectors are linearly independent