OpenCognita

AP Calculus AB

Limits and Continuity through Applications of Integration.

8 units · 46 chapters · 8–11 hours · 2 published

Unit 1

Limits and Continuity

  1. 01Can Change Happen in an Instant?Not yet published · 11–15 min
  2. 02Reading Limits from Graphs and TablesNot yet published · 10–14 min
  3. 03Computing Limits ExactlyWatch · 12–16 min
  4. 04The Squeeze TheoremNot yet published · 10–14 min
  5. 05What It Means to Be ContinuousNot yet published · 10–14 min
  6. 06Continuity on Intervals — and Repairing BreaksNot yet published · 10–14 min
  7. 07Limits at the Edges: AsymptotesNot yet published · 11–15 min
  8. 08The Intermediate Value TheoremNot yet published · 10–13 min
Unit 2

Differentiation: Definition and Fundamental Properties

  1. 09Defining the DerivativeNot yet published · 12–16 min
  2. 10When Derivatives Exist — and When They Don'tNot yet published · 10–14 min
  3. 11The First Derivative RulesNot yet published · 10–14 min
  4. 12The Derivatives Nature Chose: sin, cos, eˣ, lnNot yet published · 11–15 min
  5. 13Products, Quotients, and the Rest of TrigNot yet published · 12–16 min
Unit 3

Differentiation: Composite, Implicit, and Inverse Functions

  1. 14The Chain RuleWatch · 11–15 min
  2. 15Implicit DifferentiationNot yet published · 10–14 min
  3. 16Derivatives of Inverse FunctionsNot yet published · 11–15 min
  4. 17The Complete Toolkit — and Higher DerivativesNot yet published · 10–14 min
Unit 4

Contextual Applications of Differentiation

  1. 18The Derivative in MotionNot yet published · 12–16 min
  2. 19Rates of Change Beyond MotionNot yet published · 10–13 min
  3. 20Related RatesNot yet published · 12–16 min
  4. 21Linear ApproximationNot yet published · 10–14 min
  5. 22L'Hospital's RuleNot yet published · 10–14 min
Unit 5

Analytical Applications of Differentiation

  1. 23The Mean Value TheoremNot yet published · 10–14 min
  2. 24Where Extremes Live: Critical PointsNot yet published · 10–13 min
  3. 25Finding Extrema with the First DerivativeNot yet published · 12–16 min
  4. 26Concavity and the Second Derivative TestNot yet published · 11–15 min
  5. 27The Complete Portrait: f, f′, f″ TogetherNot yet published · 12–16 min
  6. 28OptimizationNot yet published · 12–16 min
  7. 29How Implicit Curves BehaveNot yet published · 10–13 min
Unit 6

Integration and Accumulation of Change

  1. 30Accumulation: The Other Half of CalculusNot yet published · 10–14 min
  2. 31Riemann Sums and the Definite IntegralNot yet published · 12–16 min
  3. 32The Fundamental Theorem, Part 1: Accumulation FunctionsNot yet published · 12–16 min
  4. 33The Fundamental Theorem, Part 2: Evaluating IntegralsNot yet published · 11–15 min
  5. 34AntiderivativesNot yet published · 10–14 min
  6. 35SubstitutionNot yet published · 11–15 min
  7. 36Harder Antiderivatives and Choosing a TechniqueNot yet published · 11–15 min
Unit 7

Differential Equations

  1. 37Differential Equations: Laws of ChangeNot yet published · 10–14 min
  2. 38Slope FieldsNot yet published · 10–14 min
  3. 39Separation of VariablesNot yet published · 11–15 min
  4. 40Exponential Growth and DecayNot yet published · 10–14 min
Unit 8

Applications of Integration

  1. 41The Average Value of a FunctionNot yet published · 10–13 min
  2. 42Integrals in Context: Motion and AccumulationNot yet published · 12–16 min
  3. 43Area Between CurvesNot yet published · 12–16 min
  4. 44Volumes from Cross SectionsNot yet published · 11–15 min
  5. 45Volumes of Revolution: DiscsNot yet published · 11–15 min
  6. 46Volumes of Revolution: WashersNot yet published · 11–15 min