Calculus Unit 9

Big Idea:

Integration and The Fundamental Theorem of Calculus

Student Expectations:

Focus Standards

EU 2.3: The derivative has multiple interpretations and applications including those that involve instantaneous rates of change.

• EK 2.3E1: Solutions to differential equations are functions or families of functions.
• EK 2.3E2: Derivatives can be used to verify that a function is a solution to a given differential equation.
• EK 2.3F1: Slope fields provide visual clues to the behavior of solutions of first order differential equations.
• EK 2.3F2: (BC) For differential equations, Euler’s method provides a procedure for approximating a solution or a point on a solution curve.

EU 3.5: Antidifferentiation is an underlying concept involved in solving separable differential equations. Solving separable differential equations involves determining a function or relation given its rate of change.

• EK 3.5A1: Antidifferentiation can be used to find specific solutions to differential equations with given initial conditions, including applications to motion along a line, exponential growth and decay.
• EK 3.5A2: Some differential equations can be solved by separation of variables.
• EK 3.5A3: Solutions to differential equations may be subject to domain restrictions.
• EK 3.5A4: The function defined by isa general solution to the differential equation , and is a particular solution to the differential equation satisfying ..
• EK 3.5B1: The model for exponential growth and decay that arises from the statement, “The rate of change of a quantity is proportional to the size of the quantity,” is .

Student Learning Targets:

• I will analyze differential equations to obtain general and specific solutions
• I will interpret, create, and solve differential equations from problems in context

Essential Questions:

Extra Information:

Adopted Textbook:

District Grading Policy

Texas Gateway Online Resource Center