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Hi! START HERE: Course overview
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Introduction to functions
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Vertical line test
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Domain and range
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Domain and range from a graph
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Even, odd, or neither
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Equation modeling
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Modeling a piecewise-defined function
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Sketching graphs from story problems
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Equation of a line in point-slope form
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Equation of a line in slope-intercept form
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Graphing parabolas
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Center and radius of a circle
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Graphing circles
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Combinations of functions
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Composite functions
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Composite functions, domain
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Horizontal line test (1-to-1)
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Inverse functions
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Finding the equation of a function from points on its inverse
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Laws of logarithms
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Completing the square
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Long division of polynomials
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Unit circle
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Introduction to idea of the limit
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Idea of the limit
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One-sided limits
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Proving that the limit does not exist
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Precise definition of the limit
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Introduction to combinations and composites
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Limits of combinations
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Limits of composites
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Introduction to continuity
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Point discontinuities
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Jump discontinuities
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Infinite discontinuities
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Introduction to intermediate value theorem
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Intermediate value theorem with an interval
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Intermediate value theorem without an interval
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Introduction to solving limits
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Solving with substitution
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Solving with factoring
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Solving with conjugate method
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Infinite limits and vertical asymptotes
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Crazy graphs
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Trigonometric limits
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Making the function continuous
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Introduction to squeeze theorem
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Squeeze theorem
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Squeeze theorem, limit of an inequality
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Introduction to definition of the derivative
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Definition of the derivative
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Introduction to derivative rules
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Power rule
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Power rule for negative powers
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Power rule for fractional powers
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Product rule, two functions
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Product rule, three or more functions
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Quotient rule
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Introduction to chain rule
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Chain rule with power rule
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Chain rule with product rule
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Chain rule with quotient rule
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Introduction to derivatives of trig functions
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Trigonometric derivatives
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Inverse trigonometric derivatives
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Hyperbolic derivatives
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Inverse hyperbolic derivatives
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Introduction to derivatives of ln(x) and e^x
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Exponential derivatives
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Logarithmic derivatives
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Logarithmic differentiation
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Introduction to tangent and normal lines
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Tangent lines
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Value that makes two tangent lines parallel
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Values that make the function differentiable
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Normal lines
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Average rate of change
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Introduction to implicit differentiation
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Implicit differentiation
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Equation of the tangent line with implicit differentiation
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Second derivatives with implicit differentiation
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Introduction to optimization and sketching graphs
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Critical points
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Increasing and decreasing
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First derivative test
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Concavity
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Second derivative test
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Vertical asymptotes
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Horizontal asymptotes
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Slant asymptotes
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Sketching graphs
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Extrema on a closed interval
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Sketching f(x) from f'(x)
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Introduction to linear approximation
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Linear approximation
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Estimating a root
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Introduction to related rates
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Price of the product
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Water level in the tank
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Observer and the airplane
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Introduction to applied optimization
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Dimensions of a rectangle that maximize its area
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Dimensions of a rectangle that minimize its perimeter
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Dimensions that minimize page size with a given printed area
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Two real numbers with minimum product
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Two real numbers with minimum sum of squares
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Point on the line closest to another point
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Time when velocity is minimum
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Dimensions that maximize the volume of a box
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Dimensions that minimize the surface area of an open top box
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Width that minimizes the surface area of an open top box
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Dimensions that maximize the volume of a cylinder
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Dimensions that minimize the surface area of a cylinder
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Maximum volume of a cone-shaped cup
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Production level and sale price that maximize profit
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Sales level that maximizes revenue
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Maximum area of a rectangle inscribed in a semicircle
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Dimensions that maximize the area of a rectangle inscribed in a triangle
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Maximum volume of a cylinder inscribed in a sphere
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Introduction to derivative theorems
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Mean Value Theorem
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Rolle's Theorem
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Newton's Method
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L'Hospital's Rule
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Introduction to physics
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Position function
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Position function of a particle
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Ball thrown up from the ground
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Coin dropped from the roof
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Introduction to economics
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Marginal cost, revenue, and profit
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Introduction to exponential growth and decay
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Half life
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Sales decline
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Compounding interest
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Wrap-up
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