AP Calculus BC Semester II: Course Outline

1. Unit 5: Antiderivatives and Definite Integrals
   1. Lesson 40: Differential Equations and Slope Fields
      1. Topic 1: Differential Equations
      2. Topic 2: Slope Fields
   2. Lesson 41: Antiderivatives
      1. Topic 1: Introduction to antiderivatives
      2. Topic 2: Basic antidifferentiation rules
      3. Topic 3: Trigonometric antidifferentiation rules
   3. Lesson 42: The Chain Rule for Antiderivatives
      1. Topic 1: Simple substitutions
      2. Topic 2: Trigonometric Integrals
   4. Lesson 43: Antiderivatives of Exponentials
      1. Topic 1: Natural exponential functions
      2. Topic 2: General exponential functions
   5. Lesson 44: Antiderivatives of Logarithms
      1. Topic 1: Natural logarithmic functions
      2. Topic 2: General logarithmic functions
   6. Lesson 45: Antiderivatives of Inverse Trigonometric Functions
      1. Topic 1: Rules yielding inverse trig functions
      2. Topic 2: Rules yielding inverse trig cofunctions
   7. Lesson 46: Integration by Parts
      1. Topic 1: Integration by parts formula
   8. Lesson 47: Integration by Partial Fractions
      1. Topic 1: Integration of rational functions
      2. Topic 2: Rational functions with quadratic factors
   9. Lesson 48: Trigonometric Substitutions
      1. Topic 1: Substitution technique
      2. Topic 2: Types of expressions
   10. Lesson 49: The Definite Integral
       1. Topic 1: Riemann sums
       2. Topic 2: Definition of the definite integral
       3. Topic 3: Area between curves
       4. Topic 4: Approximate integration
   11. Lesson 50: Fundamental Theorem of Calculus
       1. Topic 1: Properties of the definite integral
       2. Topic 2: The Fundamental Theorem of Calculus
       3. Topic 3: Integral defined functions
       4. Topic 4: The Mean Value Theorem
   12. Lesson 51: Improper Integrals
       1. Topic 1: Infinite limits of integration
       2. Topic 2: Discontinuous integrands
2. Unit 6: Applications of Integrals
   1. Lesson 52: Net Change and Displacement
      1. Topic 1: Net Change Theorem
      2. Topic 2: Displacement vs total distance
   2. Lesson 53: Volume
      1. Topic 1: Volume of a solid of revolution: circular disks & rings
      2. Topic 2: Volume of a solid of revolution: cylindrical shells
      3. Topic 3: Volume of a solid of known cross-section
   3. Lesson 54: Separable Differential Equations
      1. Topic 1: Separable equations
      2. Topic 2: Exponential, bounded growth & decay
   4. Lesson 55: Numerical Solutions to Differential Equations
      1. Topic 1: Approximations using slope fields
      2. Topic 2: Euler's method
   5. Lesson 56: Logistic Growth
      1. Topic 1: Logistic equation & population growth
      2. Topic 2: Other examples: Spread of disease, rumor
   6. Lesson 57: Work
      1. Topic 1: Work done moving an object
      2. Topic 2: Work done on a fluid
   7. Lesson 58: Arc Length and Surface of Revolution
      1. Topic 1: Arc length
      2. Topic 2: Surface of revolution
   8. Lesson 59: Integration of Vector-Valued Functions
      1. Topic 1: Position & Velocity
      2. Topic 2: Projectile motion
   9. Lesson 60: Parametric Integrals
      1. Topic 1: Area bounded by a parametric curve
      2. Topic 2: Arc length of a parametric curve
   10. Lesson 61: Polar Integrals
       1. Topic 1: Area bounded by a polar curve
       2. Topic 2: Arc length of a polar curve
   11. Lesson 62: Other Applications of Definite Integrals
       1. Topic 1: Center of mass & density
       2. Topic 2: Costs & probability
3. Unit 7: Infinite Sequences and Series
   1. Lesson 63: Sequences
      1. Topic 1: Definition and notation
      2. Topic 2: Limit of a Sequence
      3. Topic 3: Finding the Terms of a sequence
      4. Topic 4: Monotonic and Bounded Sequences
   2. Lesson 64: Series
      1. Topic 1: Definition and notation
      2. Topic 2: Geometric series
      3. Topic 3: Testing for divergence
   3. Lesson 65: Estimating Sums
      1. Topic 1: Integral test
      2. Topic 2: Comparison test
      3. Topic 3: Limit comparison test
      4. Topic 4: Estimating the sum of a series
   4. Lesson 66: Other Tests for Convergence
      1. Topic 1: Ratio test
      2. Topic 2: Absolute convergence
      3. Topic 3: Alternating series
      4. Topic 4: Estimating the sum of an alternating series
   5. Lesson 67: Power Series
      1. Topic 1: What is a power series?
      2. Topic 2: Radius and interval of convergence
      3. Topic 3: Representing functions as power series
      4. Topic 4: Differentiation and integration of power series
   6. Lesson 68: Taylor and Maclaurin series
      1. Topic 1: Approximating functions using polynomials
      2. Topic 2: Taylor series
      3. Topic 3: Maclaurin series
      4. Topic 4: Applications of Taylor series