Elemen Differensial Panjang, Luas, Volume

Slides:



Advertisements
Similar presentations
U2 L8 Chain and Quotient Rule CHAIN & QUOTIENT RULE
Advertisements

Konversi Sistem Koordinat
Robot Modeling and the Forward Kinematic Solution
Trigonometry Review Find sin(  /4) = cos(  /4) = tan(  /4) = Find sin(  /4) = cos(  /4) = tan(  /4) = csc(  /4) = sec(  /4) = cot(  /4) = csc(
Polar Differentiation. Let r = f( θ ) and ( x,y) is the rectangular representation of the point having the polar representation ( r, θ ) Then x = f( θ.
Section 2.9 Linear Approximations and Differentials Math 1231: Single-Variable Calculus.
MAT Math. Tools II Tangent Plane and Normal Suppose the scalar field  =  ( x, y, z, t) at time t o, the level surfaces are given by  ( x, y,
Tic-Tac-Toe Using the Graphing Calculator for Derivatives.
Sec. 4.5: Integration by Substitution. T HEOREM 4.12 Antidifferentiation of a Composite Function Let g be a function whose range is an interval I, and.
Matakuliah : Kalkulus-1
1 Mathematical Methods Physics 313 Professor Lee Carkner Lecture 22.
Chem Ch 22/#2 Today’s To Do List l Maxwell Relations l Natural Independent Variables.
For each point (x,y,z) in R3, the cylindrical coordinates (r,,z) are defined by the polar coordinates r and  (for x and y) together with z. Example Find.
Lecture 24 CSE 331 Oct 30, Homework stuff Please turn in your HW 6 Graded HW 5 and HW 7 at the END of the lecture.
Warm-up Problems Solve the IVP . Give the largest interval over which the solution is defined.
Find the period of the function y = 4 sin x
Coordinate Systems.
3D Geometric Transformation Point in 3D space –Position (x, y, z) –Color (r, g, b) –Normal (Nx, Ny, Nz) Homogenous Coordinates –Position (x,y,z,w) –Usually.
Darryl Michael/GE CRD Fields and Waves Lesson 2.1 VECTORS and VECTOR CALCULUS.
Vector calculus 1)Differential length, area and volume
CHAPTER Continuity Integration by Parts The formula for integration by parts  f (x) g’(x) dx = f (x) g(x) -  g(x) f’(x) dx. Substitution Rule that.
Integration by parts Product Rule:. Integration by parts Let dv be the most complicated part of the original integrand that fits a basic integration Rule.
Da Nang-03/2014 Natural Science Department – Duy Tan University Lecturer: Ho Xuan Binh Triple Integrals in Cylindrical Coordinates In this section, we.
Prof. David R. Jackson ECE Dept. Fall 2014 Notes 6 ECE 2317 Applied Electricity and Magnetism Notes prepared by the EM Group University of Houston 1.
Lesson 3-11 Linear Approximations and Differentials.
Triple Integrals in Cylindrical and Spherical Coordinates
Chapter 5: Double and Triple Integrals I. Review Q1 & Q2 from preclass Ch. 5- Double and Triple Integrals > Review.
CHAPTER Continuity Implicit Differentiation.
3.1 Definition of the Derivative & Graphing the Derivative
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.
Dr. Hugh Blanton ENTC 3331 Dr. Blanton - ENTC Orthogonal Coordinate Systems 2 Fields and Waves VECTORS and VECTOR CALCULUS.
Dr. Omar Al Jadaan Assistant Professor – Computer Science & Mathematics General Education Department Mathematics.
Separable Differential Equations
Linear approximation and differentials (Section 2.9)
Sec 6.3 Separation of Variables (Homogeneous Equations) Read Intro p.423 To test if a function is homogeneous, replace each variable in the equation by.
A b c d Main Integral Formulas for Computing Areas The Independent Variable is x The Independent Variable is y This is a dx integral This is a dy integral.
CE STATICS Dr. Mustafa Y. Al-Mandil Department of Civil Engineering Center of Gravity & Centroid Method of Weighted average x y z W1W1 W4W4 W3W3.
Proper Time LL 2 Section 3. An inertial frame with some clocks moving in arbitrary manner. X Y v(t) Our frame, our clock.
1 Vector Calculus. Copyright © 2007 Oxford University Press Elements of Electromagnetics Fourth Edition Sadiku2 Figure 3.1 Differential elements in the.
CE STATICS Dr. Mustafa Y. Al-Mandil Department of Civil Engineering Centroid of Area Centroid of Volume x z y y x dV dA.
Differential Equations. Up until now we have always solved equations that are static. Eg 2x +3 = 8 or 4x 3 -5x 2 = 0 However, nothing in the world about.
FdM 1 Electromagnetism First-year course on Integral types © Frits F.M. de Mul.
Four dimensional current vector Section 28. For convenience, we often consider a distribution of point charges to be a continuous distribution of charge.
CHAPTER Continuity Fundamental Theorem of Calculus In this lecture you will learn the most important relation between derivatives and areas (definite.
Transformations in 3D Lecture 17 Mon, Oct 6, 2003.
3.9 Differentials Let y = f(x) represent a function that is differentiable in an open interval containing x. The differential of x (denoted by dx) is any.
School of EECS, SNU Photonic Systems Laboratory Generalized Coordinate Systems 박현희 Photonic Systems Laboratory School of EE, Seoul National.
BELL RINGER. MULTIPLYING A MONOMIAL BY A POLYNOMIAL.
 Remember than any percent is a part of 100.
Slide Presentations for ECE 329, Introduction to Electromagnetic Fields, to supplement “Elements of Engineering Electromagnetics, Sixth Edition” by Nannapaneni.
1.3 Integral Calculus Line, Surface, Volume Integrals.
Gauss ® Divergence òòD.ds = òòò r dv ® Ñ.D = r(r)
Linear approximation and differentials (Section 3.9)
1.  Materi 1 Macam-macam sistem koordinat - Sistem loordinat Kartesian - Sitem koordinat silinder - Sistem koordinat Bola  Materi 2 Transformasi koordinat.
Problem of the Day (Calculator Allowed)
Edward C. Jordan Memorial Offering of the First Course under the Indo-US Inter-University Collaborative Initiative in Higher Education and Research: Electromagnetics.
V 1. Conservation of Mass dz dy dx
Lesson 13-3: Determinants & Cramer’s Rule
Change of Variables In 2-D,
Lecture 22 CSE 331 Oct 23, 2017.
Lecture 24 CSE 331 Oct 29, 2012.
Describing Motion in 3-D (and 2-D) §3.4–3.5.
Linear approximation and differentials (Section 3.9)
Lecture 26 CSE 331 Nov 1, 2010.
Systems of Linear Equations: Determinants
Single-Source Shortest Path & Minimum Spanning Trees
Integration and the Logarithmic Function
Partial Derivatives Chain Rule
Translation in Homogeneous Coordinates
Lecture 24 CSE 331 Oct 29, 2018.
Presentation transcript:

Elemen Differensial Panjang, Luas, Volume Pertemuan ke-4

Sistem koordinat Cartesian P1(x, y, z) P2(x + x, y + y, z + z) Panjang differensial dl dl = dx ax + dy ay + dz az Luas differensial dsx = dy dz ax dsy = dx dz ay dsz = dx dy az Volume differensial dv = dx dy dz

Sistem koordinat silinder P1(, , z) P2( + ,  + , z + z) Panjang differensial dl dl = d a +  d a + dz az Luas differensial ds =  d dz a ds = d dz a dsz =  d d az Volume differensial dv =  d d dz

Sistem koordinat bola P1(r, , ) P2(r + r,  + ,  + ) Panjang differensial dl dl = dr ar + r d a + r sin  d a Luas differensial dsr = r2 sin  d d ar ds = r sin  dr d a ds = r dr d a Volume differensial dv = r2 sin  dr d d

END