1. 課程大綱 OUTLINE Line Integrals （曲線積分） Surface Integral （曲面積分） 2.

Slides:



Advertisements
Similar presentations
Average Value and the 2 nd Fundamental Theorem. What is the area under the curve between 0 and 2? f(x)
Advertisements

© 2010 Pearson Education, Inc. All rights reserved.
Another Application: Arc Length (3/3/06) What is the length of a given arc? More specifically, given the function f (x), how long is the curve of f as.
Subspaces, Basis, Dimension, Rank
Hexagonal Pyramid cut at an angle #1
Let c (t) = (t 2 + 1, t 3 − 4t). Find: (a) An equation of the tangent line at t = 3 (b) The points where the tangent is horizontal. ` ` `
Section 11.4 Areas and Lengths in Polar Coordinates.
Fundamental Theorems of Calculus 6.4. The First (second?) Fundamental Theorem of Calculus If f is continuous on, then the function has a derivative at.
Advance Calculus Diyako Ghaderyan 1 Contents:  Applications of Definite Integrals  Transcendental Functions  Techniques of Integration.
Section 5.3 – The Definite Integral
3.6 Perpendiculars and Distance
Areas of Circles and Sectors
4.4c 2nd Fundamental Theorem of Calculus. Second Fundamental Theorem: 1. Derivative of an integral.
Chapter 8 – Further Applications of Integration
4.4 The Fundamental Theorem of Calculus
SECTION 5.4 The Fundamental Theorem of Calculus. Basically, (definite) integration and differentiation are inverse operations.
CHAPTER Continuity Fundamental Theorem of Calculus In this lecture you will learn the most important relation between derivatives and areas (definite.
CHAPTER Continuity Arc Length Arc Length Formula: If a smooth curve with parametric equations x = f (t), y = g(t), a  t  b, is traversed exactly.
Advance Calculus Diyako Ghaderyan 1 Contents:  Applications of Definite Integrals  Transcendental Functions  Techniques of Integration.
Main Menu Salas, Hille, Etgen Calculus: One and Several Variables Copyright 2003 © John Wiley & Sons, Inc. All rights reserved. Line Integrals a. Definition.
Calculus, 8/E by Howard Anton, Irl Bivens, and Stephen Davis Copyright © 2005 by John Wiley & Sons, Inc. All rights reserved (p. 443) First Area.
Copyright © 2011 Pearson Education, Inc. Publishing as Pearson Addison-Wesley. Chapter 5 Integration.
Chapter 12 Vector-Valued Functions. Copyright © Houghton Mifflin Company. All rights reserved.12-2 Definition of Vector-Valued Function.
Chapter 8 – Further Applications of Integration
5.3 Definite Integrals and Antiderivatives. What you’ll learn about Properties of Definite Integrals Average Value of a Function Mean Value Theorem for.
Chapter Seven Applications of Integration. Copyright © Houghton Mifflin Company. All rights reserved. 7 | 2 Figure 7.1.
Erik Jonsson School of Engineering and Computer Science FEARLESS Engineering ENGR 3300 – 505 Advanced Engineering Mathematics
11-4 Angle Measures and Segment Lengths Learning Target: I can find angle measures and segment lengths. Goal 2.03.
10.3 Parametric Arc Length & Area of a Surface of Revolution.
(MTH 250) Lecture 19 Calculus. Previous Lecture’s Summary Definite integrals Fundamental theorem of calculus Mean value theorem for integrals Fundamental.
7.4 Day 2 Surface Area Greg Kelly, Hanford High School, Richland, Washington(Photo not taken by Vickie Kelly)
The Fundamental Theorem of Similarity. The FTS I 5 II Find the scale factor (ratio of similitude):
Arc Length & Surfaces of Revolution (7.4)
Hexagonal Pyramid cut at an angle #1
1.3 Integral Calculus Line, Surface, Volume Integrals.
Definition (p. 866).
4.4 The Fundamental Theorem of Calculus
Chapter 5 Integrals.
Warm Up Chapter 4.4 The Fundamental Theorem of Calculus
Thursday, November 08, 2018Thursday, November 08, 2018
Use Part 1 of the Fundamental Theorem of Calculus to find the derivative of the function. {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.
Use Part 1 of the Fundamental Theorem of Calculus to find the derivative of the function. {image}
Use Simpson's Rule with n = 10 to estimate the length of the arc of the twisted cubic {image} , from the origin to the point (3, 9, 27)
Notes Over Pythagorean Theorem
Arc Length and Surfaces of Revolution
Wednesday, December 05, 2018Wednesday, December 05, 2018
Warm Up Chapter 4.4 The Fundamental Theorem of Calculus
Chapter 5 Integration Copyright © 2011 Pearson Education, Inc. Publishing as Pearson Addison-Wesley.
Useful results from chapter 3
Chapter 2 Section 1.
Warm Up Chapter 4.4 The Fundamental Theorem of Calculus
Determining Chord Length
The Fundamental Theorem of Calculus
Calculus II (MAT 146) Dr. Day Friday, February 23, 2018
Definite Integrals and Antiderivatives
Chapter 2 Section 1.
Calculate Length of Arcs
Warm Up Find the distance between the two points
Central Angles and Arc Length
True or False: The exact length of the parametric curve {image} is {image}
Definite Integrals & Antiderivatives
8.1 Arc Length.
Areas of Plane Figures 11-6 Arc Lengths and Areas of Sectors
Chapter 17: Line Integrals and Surface Integrals
True or False: The exact length of the parametric curve {image} is {image}
Calculus II (MAT 146) Dr. Day Monday, February 26, 2018
Chapter 5 Integration.
Applications of Integration
Section 9.1 Arc Length and Surface Area I
Presentation transcript:

1

課程大綱 OUTLINE Line Integrals （曲線積分） Surface Integral （曲面積分） 2

LINE INTEGRALS - 平面曲線段長 3

LINE INTEGRALS - THE LINE INTEGRAL 4

5

6

7

8

9

LINE INTEGRALS - LINE INTEGRAL WITH RESPECT TO ARC LENGTH 10

LINE INTEGRALS - LINE INTEGRAL WITH RESPECT TO ARC LENGTH 11

LINE INTEGRALS - LINE INTEGRAL WITH RESPECT TO ARC LENGTH 12

LINE INTEGRALS - LINE INTEGRAL WITH RESPECT TO ARC LENGTH 13

LINE INTEGRALS - LINE INTEGRAL WITH RESPECT TO ARC LENGTH 14

LINE INTEGRALS - LINE INTEGRAL WITH RESPECT TO ARC LENGTH 15

LINE INTEGRALS - 兩類曲線積分的關聯 16

LINE INTEGRALS - 兩類曲線積分的關聯 17

LINE INTEGRALS - 兩類曲線積分的關聯 18

LINE INTEGRALS - THE FUNDAMENTAL THEOREM FOR LINE INTEGRALS 19

LINE INTEGRALS - THE FUNDAMENTAL THEOREM FOR LINE INTEGRALS 20

SURFACE INTEGRAL 曲面積分 - THE AREA OF A SURFACE 21

SURFACE INTEGRAL 曲面積分 - THE AREA OF A SURFACE 22

SURFACE INTEGRAL 曲面積分 - SURFACE INTEGRALS 23

SURFACE INTEGRAL 曲面積分 - SURFACE INTEGRALS 24

SURFACE INTEGRAL 曲面積分 - SURFACE INTEGRALS 25

Feedback: Privacy Policy Feedback
Do Not Sell My Personal Information
About project: SlidePlayer Terms of Service

© 2024 SlidePlayer.com. Inc. All rights reserved.