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AP Calculus BC – Chapter 6 Differential Equations and Mathematical Modeling 6.1: Antiderivatives and Slope Fields. Learning Objectives: Students will/I can… Construct antiderivatives using the Fundamental Theorem of Calculus.

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AP Calculus BC – Chapter 6Differential Equations and Mathematical Modeling 6.1: Antiderivatives and Slope Fields

Learning Objectives: Students will/I can…

Construct antiderivatives using the Fundamental Theorem of Calculus.

Find antiderivatives of polynomials, ekx, and selected trigonometric functions of kx, as well as linear combinations of these functions.

Solve initial value problems of the form dy/dx = f(X),

y0 = f(x0).

Construct slope fields using technology and interpret slope fields as visualizations of differential equations.

mathematical practice
Mathematical Practice:
  • Look for and make use of structure.
    • Mathematically proficient students look closely to discern a pattern or structure.
ap calculus bc standards
AP Calculus BC Standards
  • Integrals:
    • Applications of antidifferentiation.
      • Finding specific antiderivatives using initial conditions, including applications to motion along a line.
quote of the day
Quote of the Day:
  • “…regarding the fundamental investigations of mathematics, there is no final ending…no first beginning.”
    • Felix Klein( 1849 - 1925)
warm up
Warm Up:
  • Find all functions y that satisfy

dy/dx = sec2 x + 2x + 5.

  • Find the particular solution to the equation dy/dx = ex – 6x2, with

y(1) = 0.

some examples
Some examples:

1. Find the particular solution to the equation dy/dx = 2x – sec2x whose graph passes through the point (0, 3).

2. Find the solution to the differential equation f’(x)= e-x2 for which f(7) = 3.

3. Graph the family of functions that solves the differential equation

dy/dx = cos x.

assignment
Assignment:
  • HW 6.1A:
    • Quick Review
    • Group Activity Exploration Worksheet
    • Read Lesson 6.1.
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