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AP Calculus BC

10 units · 84 topics · 3,338 lessons · Exam: May

All ten units of the College Board course: limits through infinite series, including everything in AB plus parametric, polar, and vector functions and series.

Start: Introducing Calculus: Change at an Instant Find a tutor Exam Sprint
  1. 1Limits and Continuity
  2. 2Differentiation: Definition and Fundamental Properties
  3. 3Differentiation: Composite, Implicit, and Inverse Functions
  4. 4Contextual Applications of Differentiation
  5. 5Analytical Applications of Differentiation
  6. 6Integration and Accumulation of Change
  7. 7Differential Equations
  8. 8Applications of Integration
  9. 9Parametric Equations, Polar Coordinates, and Vector-Valued Functions
  10. 10Infinite Sequences and Series
Course pathAll videos
1

Limits and Continuity

What a function approaches, and when it actually gets there.

  1. 1Introducing Calculus: Change at an InstantUp next31 lessons
  2. 2What a Limit Means28 lessons
  3. 3Estimating Limits from Graphs and Tables15 lessons
  4. 4Finding Limits AlgebraicallyCoverage growing
  5. 5The Squeeze Theorem30 lessons
  6. 6Types of Discontinuity19 lessons
  7. 7Continuity at a Point and on an IntervalCoverage growing
  8. 8Infinite Limits and Vertical Asymptotes40 lessons
  9. 9Limits at Infinity35 lessons
  10. 10Intermediate Value Theorem39 lessons
2

Differentiation: Definition and Fundamental Properties

What a derivative is, and the basic rules for finding one.

  1. 1Average and Instantaneous Rates of Change15 lessons
  2. 2The Definition of the DerivativeCoverage growing
  3. 3Estimating Derivatives from Graphs and Tables33 lessons
  4. 4Differentiability and Continuity7 lessons
  5. 5The Power Rule28 lessons
  6. 6Derivatives of sin x, cos x, eˣ, and ln x23 lessons
  7. 7Product and Quotient Rules65 lessons
  8. 8Derivatives of tan, cot, sec, and csc38 lessons
3

Differentiation: Composite, Implicit, and Inverse Functions

The chain rule and everything it unlocks.

  1. 1Chain Rule67 lessons
  2. 2Implicit Differentiation58 lessons
  3. 3Derivatives of Inverse Functions29 lessons
  4. 4Derivatives of Inverse Trig Functions28 lessons
  5. 5Choosing the Right Derivative RuleLessons from this unit
  6. 6Higher-Order Derivatives33 lessons
4

Contextual Applications of Differentiation

Derivatives as rates in the real world: motion, related rates, and approximation.

  1. 1Interpreting the Derivative in Context41 lessons
  2. 2Position, Velocity, and Acceleration39 lessons
  3. 3Rates of Change in Applied Contexts21 lessons
  4. 4Related Rates54 lessons
  5. 5Local Linearity and Linearization43 lessons
  6. 6L'Hôpital's Rule47 lessons
5

Analytical Applications of Differentiation

What derivatives tell you about a graph: extrema, concavity, and optimization.

  1. 1Mean Value Theorem41 lessons
  2. 2Extreme Value Theorem and Critical Points45 lessons
  3. 3Increasing and Decreasing Intervals40 lessons
  4. 4The First Derivative Test42 lessons
  5. 5Absolute Extrema: The Candidates Test39 lessons
  6. 6Concavity and Inflection Points41 lessons
  7. 7The Second Derivative Test36 lessons
  8. 8Connecting f, f′, and f″34 lessons
  9. 9Optimization54 lessons
  10. 10Behavior of Implicit Relations28 lessons
6

Integration and Accumulation of Change

Adding up rates to find totals, and the Fundamental Theorem that links it all.

  1. 1Accumulation of Change36 lessons
  2. 2Riemann Sums43 lessons
  3. 3Fundamental Theorem of Calculus43 lessons
  4. 4Accumulation Functions22 lessons
  5. 5Properties of Definite Integrals37 lessons
  6. 6Antiderivatives and Indefinite IntegralsCoverage growing
  7. 7u-Substitution51 lessons
  8. 8Integrating with Long Division and Completing the Square38 lessons
  9. 9Integration by Parts59 lessons
  10. 10Partial Fractions41 lessons
  11. 11Improper Integrals39 lessons
  12. 12Choosing an Integration TechniqueCoverage growing
7

Differential Equations

Equations about rates of change, and how to solve them.

  1. 1Modeling with Differential Equations13 lessons
  2. 2Slope Fields39 lessons
  3. 3Euler's Method98 lessons
  4. 4Separation of Variables49 lessons
  5. 5Exponential Growth and Decay45 lessons
  6. 6Logistic Growth32 lessons
8

Applications of Integration

Using integrals for average value, motion, area, volume, and length.

  1. 1Average Value of a Function22 lessons
  2. 2Motion with Integrals7 lessons
  3. 3Definite Integrals in Applied Contexts18 lessons
  4. 4Area Between Curves38 lessons
  5. 5Volumes with Known Cross Sections36 lessons
  6. 6Volumes of Revolution36 lessons
  7. 7Arc Length43 lessons
9

Parametric Equations, Polar Coordinates, and Vector-Valued Functions

Curves that move: parametric, polar, and vector motion. BC only.

  1. 1Parametric Derivatives69 lessons
  2. 2Arc Length of Parametric Curves33 lessons
  3. 3Motion with Vectors30 lessons
  4. 4Polar Coordinates and Derivatives29 lessons
  5. 5Area in Polar Coordinates35 lessons
10

Infinite Sequences and Series

When adding infinitely many terms gives a finite answer, and Taylor series. BC only.

  1. 1Convergent and Divergent Series21 lessons
  2. 2Geometric Series34 lessons
  3. 3The nth Term Test for Divergence41 lessons
  4. 4Integral and Comparison Tests177 lessons
  5. 5Harmonic Series and p-Series40 lessons
  6. 6Alternating Series43 lessons
  7. 7The Ratio Test21 lessons
  8. 8Absolute and Conditional Convergence42 lessons
  9. 9Alternating Series Error Bound28 lessons
  10. 10Taylor Polynomials55 lessons
  11. 11Lagrange Error Bound33 lessons
  12. 12Radius and Interval of Convergence38 lessons
  13. 13Taylor and Maclaurin Series30 lessons
  14. 14Representing Functions as Power Series44 lessons