AP Calculus AB 6.3 Separation of Variables Objective: Recognize and solve differential equations by separation of variables. Use differential equations.

Slides:



Advertisements
Similar presentations
Differential Equations
Advertisements

Indefinite Integrals 6.1. Integration - Antidifferentiation - method of solution to a differential equation INdefinite Integral Integration Symbol Variable.
Differential Equations Separable Examples Prepared by Vince Zaccone For Campus Learning Assistance Services at UCSB.
Ch 2.1: Linear Equations; Method of Integrating Factors
Technical Question Technical Question
Warm Up. 7.4 A – Separable Differential Equations Use separation and initial values to solve differential equations.
1Chapter 2. 2 Example 3Chapter 2 4 EXAMPLE 5Chapter 2.
A) Find the velocity of the particle at t=8 seconds. a) Find the position of the particle at t=4 seconds. WARMUP.
1Chapter 2. 2 Example 3Chapter 2 4 EXAMPLE 5Chapter 2.
4. Slope Fields. Slope Fields We know that antidifferentiation, indefinite integration, and solving differential equations all imply the same process.
Differential Equations 6 Copyright © Cengage Learning. All rights reserved. 6.1 Day
AP Calculus Ms. Battaglia. Differential equation (in x and y): an equation that involves x, y, and the derivatives of y. A function y=f(x) is called a.
6.1 Antiderivatives and Slope Fields Objectives SWBAT: 1)construct antiderivatives using the fundamental theorem of calculus 2)solve initial value problems.
6.3 Separation of Variables and the Logistic Equation Ex. 1 Separation of Variables Find the general solution of First, separate the variables. y’s on.
Differential Equations and Slope Fields By: Leslie Cade 1 st period.
BC Calculus – Quiz Review
Differential Equations: Slope Fields
Mathematics. Session Differential Equations - 2 Session Objectives  Method of Solution: Separation of Variables  Differential Equation of first Order.
Slope Fields. Quiz 1) Find the average value of the velocity function on the given interval: [ 3, 6 ] 2) Find the derivative of 3) 4) 5)
First, a little review: Consider: then: or It doesn’t matter whether the constant was 3 or -5, since when we take the derivative the constant disappears.
Differential Equations Separable Examples Prepared by Vince Zaccone For Campus Learning Assistance Services at UCSB.
Differential Equations BC CALCULUS. Differential Equations Defn: An equation that contains a derivative ( or a function and a derivative ) is called.
Differential Equations and Slope Fields 6.1. Differential Equations  An equation involving a derivative is called a differential equation.  The order.
Differential Equations: Growth and Decay Calculus 5.6.
AP Calculus AB Chapter 4, Section 1 Integration
Exponential Growth and Decay 6.4. Separation of Variables When we have a first order differential equation which is implicitly defined, we can try to.
Chapter 5 Integration. Indefinite Integral or Antiderivative.
AP Calculus Ms. Battaglia. Equations are separable if all x terms can be collected with dx and all y terms with dy. The solution procedure is called separation.
Suppose we are given a differential equation and initial condition: Then we can approximate the solution to the differential equation by its linearization.
Ch 2.1: Linear Equations; Method of Integrating Factors A linear first order ODE has the general form where f is linear in y. Examples include equations.
Chapter 2 Solutions of 1 st Order Differential Equations.
Differential Equations Linear Equations with Variable Coefficients.
Aim: Growth & Decay Course: Calculus Do Now: Aim: How do we solve differential equations dealing with Growth and Decay Find.
Warm Up. Solving Differential Equations General and Particular solutions.
Ms. Battaglia AP Calculus. Estimate y(4) with a step size h=1, where y(x) is the solution to the initial value problem: y’ – y = 0 ; y(0) = 1.
STROUD Worked examples and exercises are in the text Programme 25: First-order differential equations FIRST-ORDER DIFFERENTIAL EQUATIONS PROGRAMME 25.
Chapter 6 Integration Section 3 Differential Equations; Growth and Decay.
Problem of the Day - Calculator Let f be the function given by f(x) = 2e4x. For what value of x is the slope of the line tangent to the graph of f at (x,
Solving equations with variable on both sides Part 1.
Warm Up Multiply the matrices. 1. Find the determinant. 2. –1 Welcome! I’m so glad you’re here! Please get your Calculator. Please get started on this.
Solving Differential Equations Slope Fields. Solving DE: Slope Fields Slope Fields allow you to approximate the solutions to differential equations graphically.
Section 9.4 – Solving Differential Equations Symbolically Separation of Variables.
Daily Vocabulary Coefficient matrix Matrix of constants.
3-5 More on Solving Equations
DIFFERENTIAL EQUATIONS
6.1 – 6.3 Differential Equations
Differential Equations
Specialist Mathematics
Integration by Substitution
AP Calculus Honors Ms. Olifer
6-2 Solving Differential Equations
Part (a) Keep in mind that dy/dx is the SLOPE! We simply need to substitute x and y into the differential equation and represent each answer as a slope.
Differential Equations
Differential Equations Separation of Variables
Solving Equations with variables on each side
Do Now 1) t + 3 = – 2 2) 18 – 4v = 42.
Section Indefinite Integrals
Chapter 4 Integration.
73 – Differential Equations and Natural Logarithms No Calculator
Solving Equations with Variables on Both Sides
Solving Equations with Variables on Both Sides
Section 9.4 – Solving Differential Equations Symbolically
Part (a) dy dx = 1+y x dy dx = m = 2
Section Indefinite Integrals
Integration by Substitution part 3 (Section 4.5)
Section 6.3 Day 1 Separation of Variable
Reading Between the Lines!
Use Graphs of Functions
One-step addition & subtraction equations: fractions & decimals
Separation of Variables: Day 2
Presentation transcript:

AP Calculus AB 6.3 Separation of Variables Objective: Recognize and solve differential equations by separation of variables. Use differential equations to model and solve applied problems.

Find the General Solution of the Differential Equation

AP Calculus AB 6.1 Slope Fields Solving Differential Equations Objective: Use initial conditions to find particular solutions and use slope fields to approximate solutions of differential equations

6.1 Formative Assessment Pg. 410 (37-48) We are going to do #45 and #46 together

Pg. 410 #45 Separate the Variables Integrate Both Sides

Pg. 410 #46 Separate the Variables Integrate Both Sides

Solve: 3 Minutes

Formative Assessment 6.3 Pg. 429 (1-12) 6.1 Pg. 410 (37-48) 1.Separate the Variables 2.Integrate Both Sides 3.Constant of Integration If you would like the Slope Fields Program for your calculator, please bring me your calculator to download

Formative Assessment Pg. 429 (1-12) 1.Separate the Variables 2.Integrate Both Sides 3.Constant of Integration 4.Still More to Come!