Slope Fields and Differential Equations

Slides:

Advertisements

Similar presentations

Warm up Problems After correcting the homework, we will be taking Derivative Quiz #2.

Advertisements

Differential Equations Separable Examples Prepared by Vince Zaccone For Campus Learning Assistance Services at UCSB.

Warm Up. 7.4 A – Separable Differential Equations Use separation and initial values to solve differential equations.

W-up Get out note paper Find 12.3 notes

6.8 –Systems of Inequalities. Just like systems of equations, but do the inequality part!

Slope Fields and Differential Equations By: Jonathan Herlong & Curt Harper.

3x – 5y = 11 x = 3y + 1 Do Now. Homework Solutions 2)2x – 2y = – 6 y = – 2x 2x – 2(– 2x) = – 6 2x + 4x = – 6 6x = – 6 x = – 1y = – 2x y = – 2(– 1) y =

3.5 – Solving Systems of Equations in Three Variables.

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.

Implicit Differentiation

6.2 Integration by Substitution & Separable Differential Equations.

1 Implicit Differentiation. 2 Introduction Consider an equation involving both x and y: This equation implicitly defines a function in x It could be defined.

Section 2.5 Implicit Differentiation

Ms. Battaglia AB/BC Calculus. Up to this point, most functions have been expressed in explicit form. Ex: y=3x 2 – 5 The variable y is explicitly written.

Objectives: 1.Be able to determine if an equation is in explicit form or implicit form. 2.Be able to find the slope of graph using implicit differentiation.

Implicit Differentiation - Used in cases where it is impossible to solve for “y” as an explicit function of “x”

Lesson 3-5: Solving Equations with the Variable on Each Side.

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)

GOAL: USE DEFINITION OF DERIVATIVE TO FIND SLOPE, RATE OF CHANGE, INSTANTANEOUS VELOCITY AT A POINT. 3.1 Definition of Derivative.

Differential Equations Separable Examples Prepared by Vince Zaccone For Campus Learning Assistance Services at UCSB.

Differential Equations and Slope Fields 6.1. Differential Equations  An equation involving a derivative is called a differential equation.  The order.

Implicit Differentiation Objective: To find derivatives of functions that we cannot solve for y.

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.

1.1 Solving Linear Systems by Graphing 9/14/12. Solution of a system of 2 linear equations: Is an ordered pair (x, y) that satisfies both equations. Graphically,

Differential Equations Separation of variables Exact factors of Differential Equations Integrating factors Before you begin you should be confident with:

Logarithmic Differentiation

Slope Fields (6.1) March 12th, I. General & Particular Solutions A function y=f(x) is a solution to a differential equation if the equation is true.

2.1 The Derivative and The Tangent Line Problem Slope of a Tangent Line.

9.1 Solving Differential Equations Mon Jan 04 Do Now Find the original function if F’(x) = 3x + 1 and f(0) = 2.

Differential Equations

Blue part is out of 50 Green part is out of 50  Total of 100 points possible.

Logarithmic Functions. Examples Properties Examples.

Review after Christmas!. Solve the below equations for the variable..5 (6x +8) = 16 1.

System of Equations Solve by Substitution. A System of Equations:  Consists of two linear equations  We want to find out information about the two lines:

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,

2.4 – Solving Equations with the Variable on Each Side.

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

Section 9.4 – Solving Differential Equations Symbolically Separation of Variables.

DIFFERENTIAL EQUATIONS

6.1 – 6.3 Differential Equations

Differential Equations

Implicit Differentiation

Completing the Square.

3.3 – Solving Systems of Inequalities by Graphing

Implicit Differentiation

4.2 – Implicit Differentiation

Implicit Differentiation

Derivatives of inverse functions

Implicit Differentiation

4.2 – Implicit Differentiation

Chapter 4: Graphing Linear Equations

2.5 Implicit Differentiation

Slope Fields & Differential Equations

Implicit Differentiation

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 Separation of Variables

Implicit Differentiation

AP Calculus BC April 18, 2016 Mr. Agnew

Repeating this process 8 more times gives us our slope field.

Implicit Differentiation

Warm up Tell whether the relation is a function.

Solving Equations with Variables on Both Sides

Solving Equations with Variables on Both Sides

Part (a) dy dx = 1+y x dy dx = m = 2

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.

Implicit Differentiation & Related Rates

Objectives: To graph lines using the slope-intercept equation

9.3 Separable Equations.

Diff-Eqs and Slope Fields

Presentation transcript:

Slope Fields and Differential Equations By Charlie Chun and Tiffany Kwok

Step 1: Move all your “y”s to one side and all your “x”s to the other 47. Steps for Solving a Differential Equation with Separation of Variables Step 1: Move all your “y”s to one side and all your “x”s to the other Ex: dy/dx= 2x dy=2xdx Step 2: Take the integral of both sides (Don’t forget your cookies) Ex: ∫dy=∫2xdx y=x + c Step 3: If given the initial condition then substitute it in to find “c” Ex: Initial condition: (0,2) 2=(0) +c c=2 y=x +2 Step 4: Solve for y Ex: y=x +2 2 2 2 2

48. Slope Fields Take the derivative of f(x) at each point Graph it

Homework #1,3,4,10,12,13,15

Quizizz https://quizizz.com/admin/quiz/5cae429ddeeead001bea97ee