calculus iii: section 12 - shippensburg universitywebspace.ship.edu/deensley/m213/sec12_5.pdf ·...

Calculus III: Section 12.5 Professor Ensley Ship Math September 12, 2011 Professor Ensley (Ship Math) Calculus III: Section 12.5 September 12, 2011 1/5

Upload: voxuyen

Post on 03-May-2018

224 views

Category:

Documents

6 download

Report

Download

Embed Size (px):

TRANSCRIPT

Page 1: Calculus III: Section 12 - Shippensburg Universitywebspace.ship.edu/deensley/m213/sec12_5.pdf · Equation of a plane Equation of a plane Professor Ensley (Ship Math) Calculus III:

Calculus III: Section 12.5

Professor Ensley

Ship Math

September 12, 2011

Professor Ensley (Ship Math) Calculus III: Section 12.5 September 12, 2011 1 / 5

Equation of a plane

Professor Ensley (Ship Math) Calculus III: Section 12.5 September 12, 2011 2 / 5

Equation of a plane

Professor Ensley (Ship Math) Calculus III: Section 12.5 September 12, 2011 2 / 5

Equation of a plane

Example. Show that any two points P and Q on the plane

6x − 3y + 2z = 12, the vector−→PQ is perpendicular to the vector

〈6,−3, 2〉.

Professor Ensley (Ship Math) Calculus III: Section 12.5 September 12, 2011 2 / 5

Page 5: Calculus III: Section 12 - Shippensburg Universitywebspace.ship.edu/deensley/m213/sec12_5.pdf · Equation of a plane Equation of a plane Professor Ensley (Ship Math) Calculus III:

Parallel planes

Professor Ensley (Ship Math) Calculus III: Section 12.5 September 12, 2011 3 / 5

Page 6: Calculus III: Section 12 - Shippensburg Universitywebspace.ship.edu/deensley/m213/sec12_5.pdf · Equation of a plane Equation of a plane Professor Ensley (Ship Math) Calculus III:

Finding a plane determined by three points

Example. Find the equation of the plane determined by the three points(5, 1, 1), (1, 1, 2), and (2, 1, 1).

Professor Ensley (Ship Math) Calculus III: Section 12.5 September 12, 2011 4 / 5

Page 7: Calculus III: Section 12 - Shippensburg Universitywebspace.ship.edu/deensley/m213/sec12_5.pdf · Equation of a plane Equation of a plane Professor Ensley (Ship Math) Calculus III:

Trace of a plane

Professor Ensley (Ship Math) Calculus III: Section 12.5 September 12, 2011 5 / 5

THE BOUNDARY INTEGRAL EQUATION METHOD IN PLANE … › ... › S0002-9939-1995-1301017-3.pdfTHE BOUNDARY INTEGRAL EQUATION METHOD IN PLANE ELASTICITY CHRISTIAN CONSTANDA (Communicated

EQUATION OF MOTION USING FRACTIONAL CALCULUS by …

BS-1201 Differential equation and Integral Calculus · 2020. 1. 8. · of differential equation, Exact differential equation, Linear differential equation and equation reducible to

FILTER EQUATION BY FRACTIONAL CALCULUS

Calculus IIhandouts).pdf · 2017-06-02 · 1-Introduction VU Sign of co-ordinates in different octants First of all note that the equation x=0 represents a plane in the 3d space and

Calculus: Integrals, Area, and Volume - Math Plane€¦ · Calculus: Integrals, Area, and Volume Notes, Examples, Formulas, and Practice Test (with solutions) Topics include definite

The Basics of Physics with Calculus & Systems of …Calculus+Made... · Differential Calculus ... This is actually very easy! The entire equation is linear and looks like y = mx +

CH.7. PLANE LINEAR ELASTICITY - mmc.rmee.upc.edummc.rmee.upc.edu/documents/Slides/MASTER 2017-2018... · Ch.7. Plane Linear Elasticity . 7.2 Plane Stress ... Cauchy’s Equation of

Two Dimensional Problems in Elasticity2-D problems in elasticity Plane stress and plane strain problems Stress compatibility equation Airy’s stress function and equation Polynomial

Regularity of the p-Poisson equation in the plane E ... · Keywords: non-linear equation, quasiregular mapping, variational problem 1 Introduction In the plane, the theory of many

Vectors: planes. The plane Normal equation of the plane

Calculus on the complex plane C

MA261-A Calculus III 2006 Fall Homework 8 Solutions …hhaosu/Teaching/0607FCalcIII/06FMA261...5 tangent plane equation in textbook page 796, the normal vector of the tangent plane

Planes in Space. z x y Equation of a Plane z x y

The pantograph equation in quantum calculus

PH 1020 PHYSICS - IImanianvs/PH102-1.pdf · • Displacement current density • Maxwell’s equation for electromagnetic field • Derivation wave equation – Plane wave solution

VECTORS IN COMPONENT FORM - Uplift Education · PLANE EQUATION Vector equation of a plane N = + +µ A plane is completely determined by two intersecting lines, what can be translated

SCALE CALCULUS AND THE SCHRODINGER˜ EQUATION

Modelling the landing of a plane in a calculus labgalia.fc.uaslp.mx/~jvallejo/Morante-Vallejo-web.pdfModelling the landing of a plane in a calculus lab Antonio Morante and Jos´e A

Maths SL Revision - Wikispacesispmath.wikispaces.com/file/view/Calculus+-+A.pdf · Calculus – Maths SL 1. Find the equation of the normal to the curve with equation y = x3 + 1 at

Calculus 2 Lecture Notes, Section 9.1faculty.madisoncollege.edu/kmirus/20092010B/804232… · Web viewTitle Calculus 2 Lecture Notes, Section 9.1 Subject Plane Curves and Parametric

Wave-equation migration with dithered plane waves

The Boltzmann equation for plane Couette flow

Summer Reading AP Calculus - mpsri.net · Summer Reading AP Calculus Page 4 2017 Equations for Circles in the Plane Circle is the set of points in a plane whose distance from a fixed

Helmholtz Equation - NIUnicadd.niu.edu/~piot/phys_630/Lesson2.pdf · The paraxial Helmholtz equation • Start with Helmholtz equation • Consider the wave which is a plane wave

Calculus: Integrals, Area, and Volume - Math Plane

Honors Calculus I Chapter P: Prerequisites Section P.1: Lines in the Plane

4. INTERSECTIONS OF PLANES IMain Topics A Equation of a ... · 4. INTERSECTIONS OF PLANES IMain Topics A Equation of a plane BPole to a plane using cross-products CIntersection of

02 Lines in the Plane - Contemporary Calculus

Intro. Light Propagation in Free Space Helmholtz Equation 1-D Propagation Plane waves

The Stress Equilibrium Equation - padtinc.comMAE 323: Chapter 4 Plane Stress and Plane Strain 2011 Alex Grishin MAE 323 Chapter 4 3 The Stress Equilibrium Equation The stress tensor

ANALYTICAL GEOMETRY (3D) AND INTEGRAL · PDF fileANALYTICAL GEOMETRY (3D) AND INTEGRAL CALCULUS UNIT I Standard equation of a plane ... Shanti Narayan, Differential & Integral Calculus

Stress-Strain Equation Plane Stress and Plane Strain Equations

Uniform plane wave equation

The Vector Equation of a Plane