1 / 7

Learning Objectives: Students will/I can…

In Chapter 6 of AP Calculus BC, we delve into Differential Equations and Mathematical Modeling. Students will learn to construct antiderivatives using the Fundamental Theorem of Calculus, solve initial value problems, and interpret slope fields as visual representations of differential equations. The chapter emphasizes mathematical practices such as recognizing structures and patterns in functions. Students will solve problems involving polynomials, exponentials, and trigonometric functions, enhancing their ability to apply antiderivatives in real-world contexts.

melvina-hartnett
Télécharger la présentation

Learning Objectives: Students will/I can…

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. 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.

  2. Mathematical Practice: • Look for and make use of structure. • Mathematically proficient students look closely to discern a pattern or structure.

  3. AP Calculus BC Standards • Integrals: • Applications of antidifferentiation. • Finding specific antiderivatives using initial conditions, including applications to motion along a line.

  4. Quote of the Day: • “…regarding the fundamental investigations of mathematics, there is no final ending…no first beginning.” • Felix Klein( 1849 - 1925)

  5. 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.

  6. 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.

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

More Related