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AP??/College Calculus BC
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Meet an AP?? teacher who uses AP?? Calculus in his classroom
Bill Scott uses Khan Academy to teach AP?? Calculus at Phillips Academy in Andover, Massachusetts, and he’s part of the teaching team that helped develop Khan Academy’s AP?? lessons. Phillips Academy was one of the first schools to teach AP?? nearly 60 years ago.
Learn moreMeet an AP?? teacher who uses AP?? Calculus in his classroom
Bill Scott uses Khan Academy to teach AP?? Calculus at Phillips Academy in Andover, Massachusetts, and he’s part of the teaching team that helped develop Khan Academy’s AP?? lessons. Phillips Academy was one of the first schools to teach AP?? nearly 60 years ago.
Learn moreAbout the course: Limits and continuityDefining limits and using limit notation: Limits and continuityEstimating limit values from graphs: Limits and continuityEstimating limit values from tables: Limits and continuityDetermining limits using algebraic properties of limits: limit properties: Limits and continuityDetermining limits using algebraic properties of limits: direct substitution: Limits and continuityDetermining limits using algebraic manipulation: Limits and continuitySelecting procedures for determining limits: Limits and continuity
Determining limits using the squeeze theorem: Limits and continuityExploring types of discontinuities: Limits and continuityDefining continuity at a point: Limits and continuityConfirming continuity over an interval: Limits and continuityRemoving discontinuities: Limits and continuityConnecting infinite limits and vertical asymptotes: Limits and continuityConnecting limits at infinity and horizontal asymptotes: Limits and continuityWorking with the intermediate value theorem: Limits and continuityOptional videos: Limits and continuity
Defining average and instantaneous rates of change at a point: Differentiation: definition and basic derivative rulesDefining the derivative of a function and using derivative notation: Differentiation: definition and basic derivative rulesEstimating derivatives of a function at a point: Differentiation: definition and basic derivative rulesConnecting differentiability and continuity: determining when derivatives do and do not exist: Differentiation: definition and basic derivative rulesApplying the power rule: Differentiation: definition and basic derivative rulesDerivative rules: constant, sum, difference, and constant multiple: introduction: Differentiation: definition and basic derivative rules
Derivative rules: constant, sum, difference, and constant multiple: connecting with the power rule: Differentiation: definition and basic derivative rulesDerivatives of cos(x), sin(x), ??, and ln(x): Differentiation: definition and basic derivative rulesThe product rule: Differentiation: definition and basic derivative rulesThe quotient rule: Differentiation: definition and basic derivative rulesFinding the derivatives of tangent, cotangent, secant, and/or cosecant functions: Differentiation: definition and basic derivative rulesOptional videos: Differentiation: definition and basic derivative rules
The chain rule: introduction: Differentiation: composite, implicit, and inverse functionsThe chain rule: further practice: Differentiation: composite, implicit, and inverse functionsImplicit differentiation: Differentiation: composite, implicit, and inverse functionsDifferentiating inverse functions: Differentiation: composite, implicit, and inverse functionsDifferentiating inverse trigonometric functions: Differentiation: composite, implicit, and inverse functions
Selecting procedures for calculating derivatives: strategy: Differentiation: composite, implicit, and inverse functionsSelecting procedures for calculating derivatives: multiple rules: Differentiation: composite, implicit, and inverse functionsCalculating higher-order derivatives: Differentiation: composite, implicit, and inverse functionsFurther practice connecting derivatives and limits: Differentiation: composite, implicit, and inverse functionsOptional videos: Differentiation: composite, implicit, and inverse functions
Interpreting the meaning of the derivative in context: Contextual applications of differentiationStraight-line motion: connecting position, velocity, and acceleration: Contextual applications of differentiationRates of change in other applied contexts (non-motion problems): Contextual applications of differentiationIntroduction to related rates: Contextual applications of differentiation
Solving related rates problems: Contextual applications of differentiationApproximating values of a function using local linearity and linearization: Contextual applications of differentiationUsing L’H?pital’s rule for finding limits of indeterminate forms: Contextual applications of differentiationOptional videos: Contextual applications of differentiation
Using the mean value theorem: Applying derivatives to analyze functions Extreme value theorem, global versus local extrema, and critical points: Applying derivatives to analyze functions Determining intervals on which a function is increasing or decreasing: Applying derivatives to analyze functions Using the first derivative test to find relative (local) extrema: Applying derivatives to analyze functions Using the candidates test to find absolute (global) extrema: Applying derivatives to analyze functions Determining concavity of intervals and finding points of inflection: graphical: Applying derivatives to analyze functions
Determining concavity of intervals and finding points of inflection: algebraic: Applying derivatives to analyze functions Using the second derivative test to find extrema: Applying derivatives to analyze functions Sketching curves of functions and their derivatives: Applying derivatives to analyze functions Connecting a function, its first derivative, and its second derivative: Applying derivatives to analyze functions Solving optimization problems: Applying derivatives to analyze functions Exploring behaviors of implicit relations: Applying derivatives to analyze functions Calculator-active practice: Applying derivatives to analyze functions
Exploring accumulations of change: Integration and accumulation of changeApproximating areas with Riemann sums: Integration and accumulation of changeRiemann sums, summation notation, and definite integral notation: Integration and accumulation of changeThe fundamental theorem of calculus and accumulation functions: Integration and accumulation of changeInterpreting the behavior of accumulation functions involving area: Integration and accumulation of changeApplying properties of definite integrals: Integration and accumulation of changeThe fundamental theorem of calculus and definite integrals: Integration and accumulation of changeFinding antiderivatives and indefinite integrals: basic rules and notation: reverse power rule: Integration and accumulation of change
Finding antiderivatives and indefinite integrals: basic rules and notation: common indefinite integrals: Integration and accumulation of changeFinding antiderivatives and indefinite integrals: basic rules and notation: definite integrals: Integration and accumulation of changeIntegrating using substitution: Integration and accumulation of changeIntegrating functions using long division and completing the square: Integration and accumulation of changeUsing integration by parts: Integration and accumulation of changeIntegrating using linear partial fractions: Integration and accumulation of changeEvaluating improper integrals: Integration and accumulation of changeOptional videos: Integration and accumulation of change
Modeling situations with differential equations: Differential equationsVerifying solutions for differential equations: Differential equationsSketching slope fields: Differential equationsReasoning using slope fields: Differential equations
Approximating solutions using Euler’s method: Differential equationsFinding general solutions using separation of variables: Differential equationsFinding particular solutions using initial conditions and separation of variables: Differential equationsExponential models with differential equations: Differential equationsLogistic models with differential equations: Differential equations
Finding the average value of a function on an interval: Applications of integrationConnecting position, velocity, and acceleration functions using integrals: Applications of integrationUsing accumulation functions and definite integrals in applied contexts: Applications of integrationFinding the area between curves expressed as functions of x: Applications of integrationFinding the area between curves expressed as functions of y: Applications of integrationFinding the area between curves that intersect at more than two points: Applications of integrationVolumes with cross sections: squares and rectangles: Applications of integration
Volumes with cross sections: triangles and semicircles: Applications of integrationVolume with disc method: revolving around x- or y-axis: Applications of integrationVolume with disc method: revolving around other axes: Applications of integrationVolume with washer method: revolving around x- or y-axis: Applications of integrationVolume with washer method: revolving around other axes: Applications of integrationThe arc length of a smooth, planar curve and distance traveled: Applications of integrationCalculator-active practice: Applications of integration
Defining and differentiating parametric equations: Parametric equations, polar coordinates, and vector-valued functionsSecond derivatives of parametric equations: Parametric equations, polar coordinates, and vector-valued functionsFinding arc lengths of curves given by parametric equations: Parametric equations, polar coordinates, and vector-valued functionsDefining and differentiating vector-valued functions: Parametric equations, polar coordinates, and vector-valued functions
Solving motion problems using parametric and vector-valued functions: Parametric equations, polar coordinates, and vector-valued functionsDefining polar coordinates and differentiating in polar form: Parametric equations, polar coordinates, and vector-valued functionsFinding the area of a polar region or the area bounded by a single polar curve: Parametric equations, polar coordinates, and vector-valued functionsFinding the area of the region bounded by two polar curves: Parametric equations, polar coordinates, and vector-valued functionsCalculator-active practice: Parametric equations, polar coordinates, and vector-valued functions
Defining convergent and divergent infinite series: Infinite sequences and seriesWorking with geometric series: Infinite sequences and seriesThe nth-term test for divergence: Infinite sequences and seriesIntegral test for convergence: Infinite sequences and seriesHarmonic series and p-series: Infinite sequences and seriesComparison tests for convergence: Infinite sequences and seriesAlternating series test for convergence: Infinite sequences and seriesRatio test for convergence: Infinite sequences and series
Determining absolute or conditional convergence: Infinite sequences and seriesAlternating series error bound: Infinite sequences and seriesFinding Taylor polynomial approximations of functions: Infinite sequences and seriesLagrange error bound: Infinite sequences and seriesRadius and interval of convergence of power series: Infinite sequences and seriesFinding Taylor or Maclaurin series for a function: Infinite sequences and seriesRepresenting functions as power series: Infinite sequences and seriesOptional videos: Infinite sequences and series
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