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

• Calculus 3

  • 3-Dimensional Space

    • Arc Length and Curvature

    • Cylindrical Coordinates

    • Equations of Lines and Planes

    • Spherical Coordinates

  • Applications of Partial Derivatives

    • Absolute Minimums and Maximums

    • Gradient Vector, Tangent Planes, and Normal Lines

    • Lagrange Multipliers

    • Relative Minimums and Maximums

    • Tangent Planes and Linear Approximations

  • Calculus Review

    • Derivatives

    • Integration

  • Line Integrals

    • Curl

    • Divergence

    • Fundamental Theorem of Line Integrals

    • Green's Theorem

    • Line Integrals of Vector Fields

    • Parametric Curves

  • Multiple Integration

    • Double Integrals

      • Double Integration in Polar Coordinates

      • Double Integration over General Regions

      • Double Integration with Change of Variables

      • Surface Area

    • Triple Integrals

      • Triple Integration in Cartesian Coordinates

      • Triple Integration in Cylindrical Coordinates

      • Triple Integration in Spherical Coordinates

  • Partial Derivatives

    • Limits

    • Multi-Variable Chain Rule

    • Differentials

    • Directional Derivatives

    • Partial Derivatives

  • Surface Integrals

    • Divergence Theorem

    • Stokes' Theorem

  • Vectors and Vector Operations

    • Angle between Vectors

    • Binormal Vectors

    • Cross Product

    • Distance between Vectors

    • Dot Product

    • Matrices

    • Normal Vectors

    • Parametric Curves

    • Vector Addition

    • Vector Subtraction