AP Calculus BC Help - Learn by Concept

Learn by Concept

Concepts

• AP Calculus BC

  • Derivatives

    • Applications of Derivatives

      • Euler's Method and L'Hopital's Rule

      • Velocity, Speed, Acceleration

    • Computation of Derivatives

      • Chain Rule and Implicit Differentiation

      • Derivative Rules for Sums, Products, and Quotients

      • Derivatives of Parametric, Polar, and Vector Functions

      • Rules of Basic Functions: Power, Exponential Rule, Logarithmic, Trigonometric, and Inverse Trigonometric

    • Derivative as a Function

      • Equations Involving Derivatives

      • Finding Maximums

      • Graphs of f and f'

      • The Mean Value Theorem

    • Derivative at a Point

      • Derivative Defined as Limit of Difference Quotient

      • Instantaneous Rate of Change, Average Rate of Change, and Linear Approximation

    • Second Derivatives

      • Concavity

      • Inflection Points

  • Functions, Graphs, and Limits

    • Asymptotic and Unbounded Behavior

      • Comparing Relative Magnitudes (exponential growth,logarithmic growth, polynomial growth)

      • Identifying Asymptotes Graphically

    • Continuity

      • Continuity in Terms of Limits

    • Limits

      • Calculating Limits with Algebra (including one-sided limits)

      • Estimating Limits from Graphs and Tables

    • Parametric, Polar, and Vector Functions

      • Parametric Form

      • Polar Form

      • Vector Form

  • Integrals

    • Application of Integrals

      • Initial Conditions

      • Length of Curve, Distance traveled, Accumulated Change, Motion of Curve

      • Modeling by Solving Separable Differential Equations

      • Volume of Cross Sections and Area of Region

    • Fundamental Theorem of Calculus and Techniques of Antidifferentiation

      • Fundamental Theorem of Calculus with Definite Integrals

      • Improper Integrals

      • Substitution of Variables (by parts and simple partial fractions)

    • Numerical Approximations to Definite Integrals

      • Riemann Sum: Left Evaluation

      • Riemann Sum: Midpoint Evaluation

      • Riemann Sum: Right Evaluation

      • Trapezoidal Sums

  • Polynomial Approximations and Series

    • Series of Constants

      • Alternating Series with Error Bound

      • Geometric Series

      • P-Series

      • Ratio Test and Comparing Series

    • Taylor Series

      • Lagrange Error Bound for Taylor Polynomials

      • Maclaurin Series

      • Maclaurin Series for exponential and trigonometric functions

      • Radius and Interval of Convergence of Power Series

      • Taylor Polynomial Approximation