Section 17.4 The Flow of a Vector Field. Often we are concerned with the path an object will travel We can use the information from the velocity vector.

Slides:

Advertisements

Similar presentations

Precalculus 2 Section 10.6 Parametric Equations

Advertisements

Section 18.2 Computing Line Integrals over Parameterized Curves

Shortcuts: Solution by Inspection for Two Special Cases A Lecture in ENGIANA AY 2014 – 2015.

Vector Operations in R 3 Section 6.7. Standard Unit Vectors in R 3 The standard unit vectors, i(1,0,0), j(0,1,0) and k(0,0,1) can be used to form any.

Section 7.2: Direction Fields and Euler’s Methods Practice HW from Stewart Textbook (not to hand in) p. 511 # 1-13, odd.

Ch 3.5: Nonhomogeneous Equations; Method of Undetermined Coefficients

Ch 2.2: Separable Equations In this section we examine a subclass of linear and nonlinear first order equations. Consider the first order equation We can.

Differential Equations (4/17/06) A differential equation is an equation which contains derivatives within it. More specifically, it is an equation which.

Ch 3.3: Linear Independence and the Wronskian

Ch 7.1: Introduction to Systems of First Order Linear Equations

Math 3120 Differential Equations with Boundary Value Problems

4.3.1 – Systems of Inequalities. Recall, we solved systems of equations What defined a system? How did you find the solutions to the system?

Ch 2.2: Separable Equations In this section we examine a subclass of linear and nonlinear first order equations. Consider the first order equation We can.

Gravitation Two-Body System. Gravitation m1m1 m2m2 F 12 F 21.

Vector-Valued Functions Section 10.3a. Standard Unit Vectors Any vector in the plane can be written as a linear combination of the two standard unit vectors:

Initial Value Problems, Slope Fields Section 6.1a.

Ch 2.2: Separable Equations In this section we examine a subclass of linear and nonlinear first order equations. Consider the first order equation We can.

AAT(H) 9.5 SYSTEMS OF INEQUALITIES. EX 1) GRAPH THE INEQUALITY Remember! use a dashed line for and a solid line for ≤ or ≥ Test one point in each region.

We will use Gauss-Jordan elimination to determine the solution set of this linear system.

Section 17.2 Position, Velocity, and Acceleration.

Ch 2.2: Separable Equations In this section we examine a subclass of linear and nonlinear first order equations. Consider the first order equation We can.

Volume 4: Mechanics 1 Equations of Motion for Constant Acceleration.

10.2 Vectors in the Plane Quick Review What you’ll learn about Two-Dimensional Vectors Vector Operations Modeling Planar Motion Velocity, Acceleration,

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)

Section 6-1 continued Slope Fields. Definition A slope field or directional field for a differentiable equation is a collection of short line segments.

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

4.1 Antiderivatives and Indefinite Integration. Suppose you were asked to find a function F whose derivative is From your knowledge of derivatives, you.

Math – Antiderivatives 1. Sometimes we know the derivative of a function, and want to find the original function. (ex: finding displacement from.

Rolle’s Theorem: Let f be a function that satisfies the following 3 hypotheses: 1.f is continuous on the closed interval [a,b]. 2.f is differentiable on.

Section Direct and Inverse Variation. Lesson Objective: Students will: Formally define and apply inverse and direct variation.

1 Example 1 Syrup from a 500 liter container of 10% sugar syrup flows into a candy making machine at 2 liters per minute. The vat is kept full by adding.

Differential Equations Linear Equations with Variable Coefficients.

Antiderivatives and Indefinite Integration Lesson 5.1.

Warm Up. Solving Differential Equations General and Particular solutions.

Boyce/DiPrima 9 th ed, Ch 2.2: Separable Equations Elementary Differential Equations and Boundary Value Problems, 9 th edition, by William E. Boyce and.

Chapter 6 Integration Section 3 Differential Equations; Growth and Decay.

6.1 Slope Fields and Euler’s Method. Verifying Solutions Determine whether the function is a solution of the Differential equation y” - y = 0 a. y = sin.

Chapter 1.3 Acceleration. Types of Acceleration  Acceleration is a vector quantity  Positive Acceleration  1. when change in magnitude and direction.

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.

6.1 – 6.3 Differential Equations

LESSON 90 – DISTANCES IN 3 SPACE

We will be looking for a solution to the system of linear differential equations with constant coefficients.

Vectors in the Plane Section 10.2.

Calculus II (MAT 146) Dr. Day Monday, March 19, 2018

Section Euler’s Method

Differential Equations Growth and Decay

Differential Equations Separation of Variables

Differential Equations (10/14/13)

Class Notes 11.2 The Quadratic Formula.

Section 6.1 Slope Fields.

Antiderivatives and Indefinite Integration

Solve the differential equation. {image}

Calculus II (MAT 146) Dr. Day Monday, March 19, 2018

Section 14.4 Gradients and the Directional Derivatives in the Plane

Rotational and Irrotational Flow

Section 11.3 Euler’s Method

Section 2.2: Solving Absolute Value Equations

Unit 1: Learning Target 1.3 Differentiate between speed (a scalar quantity) and velocity (a vector quantity)

Section 7.1: Modeling with Differential Equations

Unit 3 Functions.

73 – Differential Equations and Natural Logarithms No Calculator

Total Distance Traveled

The Kinematics Equations

12.6: Vector Magnitude & Distance

Which equation does the function {image} satisfy ?

Find the set of points (x, y) such that F(x, y) = 0 if F(x, y) = (r - 4)x, {image} , and r = |x|

Integration by Substitution part 3 (Section 4.5)

The Chain Rule Section 3.4.

Introduction to Kinematics

Presentation transcript:

Section 17.4 The Flow of a Vector Field

Often we are concerned with the path an object will travel We can use the information from the velocity vector field in order to determine a path This will depend on the direction and magnitude of the vector as well as the starting point Let’s revisit our flow of the gulf stream example beginning with the vector field and then on to the flow lines Does this sound familiar?

Suppose we have a velocity vector field –We will let t be in seconds and use a 2D field Then we have If Then Thus the flow of the field is the general solution to the above system of differential equations

Given the system of differential equations and some initial condition we can find the particular flow line through the given field

Example Pg. 857, #4 Sketch the vector field and the flow. Find the system of differential equations associated with the vector field and check that the flow satisfies the system. Let’s take a look with Maple