9.1 Vector Functions 1)Def of vector function 2)Curve in xy-plane and xyz-plane 3)Graph r(t) 4)Curve of Intersection 5)Limit 6)Continuity 7)Derivatives.

Slides:

Advertisements

Similar presentations

Vector Functions and Space Curves

Advertisements

Arc Length and Curvature

Limits Pre-Calculus Calculus.

MA Day 24- February 8, 2013 Section 11.3: Clairaut’s Theorem Section 11.4: Differentiability of f(x,y,z) Section 11.5: The Chain Rule.

CHAPTER 11 Vector-Valued Functions Slide 2 © The McGraw-Hill Companies, Inc. Permission required for reproduction or display. 11.1VECTOR-VALUED FUNCTIONS.

DIFFERENTIATION & INTEGRATION CHAPTER 4.  Differentiation is the process of finding the derivative of a function.  Derivative of INTRODUCTION TO DIFFERENTIATION.

Vector-Valued Functions and Motion in Space Dr. Ching I Chen.

Chapter 13 – Vector Functions

17 VECTOR CALCULUS.

Chapter 16 – Vector Calculus

Multiple Integrals 12. Surface Area Surface Area In this section we apply double integrals to the problem of computing the area of a surface.

Chapter 14 Section 14.3 Curves. x y z To get the equation of the line we need to know two things, a direction vector d and a point on the line P. To find.

DEPARTMENT OF MATHEMATI CS [ YEAR OF ESTABLISHMENT – 1997 ] DEPARTMENT OF MATHEMATICS, CVRCE.

THEOREM 2 Vector-Valued Derivatives Are Computed Componentwise A vector-valued function r(t) = x (t), y (t) is differentiable iff each component is differentiable.

Integration in polar coordinates involves finding not the area underneath a curve but, rather, the area of a sector bounded by a curve. Consider the region.

(MTH 250) Lecture 24 Calculus. Previous Lecture’s Summary Multivariable functions Limits along smooth curves Limits of multivariable functions Continuity.

Every slope is a derivative. Velocity = slope of the tangent line to a position vs. time graph Acceleration = slope of the velocity vs. time graph How.

Chapter 8 Plane Curves and Parametric Equations. Copyright © Houghton Mifflin Company. All rights reserved.8 | 2 Definition of a Plane Curve.

10.2 – 10.3 Parametric Equations. There are times when we need to describe motion (or a curve) that is not a function. We can do this by writing equations.

Objective Rectangular Components Normal and Tangential Components

Jeopardy 203. Formulas 100 Lines 100 Planes 100 Surfaces 100 Curves 100 Formulas 101 Lines 200 Planes 200 Surfaces 200 Curves 200 Formulas 102 Lines 300.

Copyright © 2011 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Chapter 12 Functions of Several Variables.

Section 17.2 Position, Velocity, and Acceleration.

Vector Calculus CHAPTER 9.1 ~ 9.4. Ch9.1~9.4_2 Contents  9.1 Vector Functions 9.1 Vector Functions  9.2 Motion in a Curve 9.2 Motion in a Curve  9.3.

MA Day 25- February 11, 2013 Review of last week’s material Section 11.5: The Chain Rule Section 11.6: The Directional Derivative.

Derivatives of Parametric Equations

Chapter 13 – Vector Functions 13.2 Derivatives and Integrals of Vector Functions 1 Objectives:  Develop Calculus of vector functions.  Find vector, parametric,

Copyright © Cengage Learning. All rights reserved. 16 Vector Calculus.

Directional Derivatives and Gradients

Tangent Planes and Normal Lines

Vector Valued Functions

position time position time tangent!  Derivatives are the slope of a function at a point  Slope of x vs. t  velocity - describes how position changes.

Vector-Valued Functions Copyright © Cengage Learning. All rights reserved.

MA Day 14- January 25, 2013 Chapter 10, sections 10.3 and 10.4.

10. 4 Polar Coordinates and Polar Graphs 10

V ECTORS AND C ALCULUS Section 11-B. Vectors and Derivatives If a smooth curve C is given by the equation Then the slope of C at the point (x, y) is given.

Arc Length and Curvature

Parametric Surfaces and their Area Part I

MA Day 34- February 22, 2013 Review for test #2 Chapter 11: Differential Multivariable Calculus.

Vector Functions A vector function is a vector whose components are real-valued functions of a common variable (parameter), usually t.  We’ve seen a vector.

Derivative Shortcuts -Power Rule -Product Rule -Quotient Rule -Chain Rule.

Section 17.8 Stokes’ Theorem. DEFINITION The orientation of a surface S induces the positive orientation of the boundary curve C as shown in the diagram.

11 Vector-Valued Functions VECTOR-VALUED FUNCTIONS 11.2

15 Copyright © Cengage Learning. All rights reserved. Vector Analysis.

MA Day 13- January 24, 2013 Chapter 10, sections 10.1 and 10.2.

Definition: A plane curve is a set C of ordered pairs (f(t), g(t)), where f and g are continuous functions on an interval I. The graph of C consists of.

Functions of Several Variables

Rules for Dealing with Chords, Secants, Tangents in Circles

Chapter 14 Partial Derivatives.

Copyright © Cengage Learning. All rights reserved.

2.1A Tangent Lines & Derivatives

Contents 9.1 Vector Functions 9.2 Motion in a Curve

COORDINATE PLANE FORMULAS:

Calculus III 13.1 Vector-Valued Functions

Find the derivative of the vector function r(t) = {image}

By the end of Week : You would learn how to solve many problems involving limits, derivatives and integrals of vector-valued functions and questions.

Vector Functions and Space Curves

Arc Length and Curvature

Derivatives of Trig Functions

13.7 day 2 Tangent Planes and Normal Lines

If r(t) = {image} , find r''(t).

Derivatives: definition and derivatives of various functions

Lesson 10-3: Circles.

7. Section 8.1 Length of a Curve

Arc Length and Curvature

The Chain Rule Section 3.4.

Find the directional derivative of the function at the given point in the direction of the vector v. {image}

The Chain Rule Section 3.6b.

The Chain Rule Section 2.4.

Find the following limit. {image}

Presentation transcript:

9.1 Vector Functions 1)Def of vector function 2)Curve in xy-plane and xyz-plane 3)Graph r(t) 4)Curve of Intersection 5)Limit 6)Continuity 7)Derivatives 8)Smooth curve 9)Geometic representation of r’(t) 10)Tangent 11)Chain Rule 12)Integral of r(t) 13)Length of curve

Example1 Circular Helix Graph the curve traced by the vector function

ezplot3('2*cos(t)','2*sin(t)','t',[0,9*pi/2])

Example2 Circle in a plane Graph the curve traced by the vector function

Example3 Curve of Intersection Find the vector function that describes the curve C of the intersection of the plane.and the paraboloid

Derivative of Vector Function