Chapter 15 - WordPress.com...Suppose that a region G in the uv-plane is transformed one-to-one into...

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Chapter 15 Multiple Integrals Ch 15.8: Substitutions in Multiple Integral

Transcript of Chapter 15 - WordPress.com...Suppose that a region G in the uv-plane is transformed one-to-one into...

Page 1: Chapter 15 - WordPress.com...Suppose that a region G in the uv-plane is transformed one-to-one into the region R in the xy-plane by equations of the form — g(u, v), Y = h(u, v),

Chapter 15Multiple Integrals

Ch 15.8: Substitutions in Multiple Integral

Page 2: Chapter 15 - WordPress.com...Suppose that a region G in the uv-plane is transformed one-to-one into the region R in the xy-plane by equations of the form — g(u, v), Y = h(u, v),

Substitutions in Double Integrals

Page 3: Chapter 15 - WordPress.com...Suppose that a region G in the uv-plane is transformed one-to-one into the region R in the xy-plane by equations of the form — g(u, v), Y = h(u, v),
Page 4: Chapter 15 - WordPress.com...Suppose that a region G in the uv-plane is transformed one-to-one into the region R in the xy-plane by equations of the form — g(u, v), Y = h(u, v),
Page 5: Chapter 15 - WordPress.com...Suppose that a region G in the uv-plane is transformed one-to-one into the region R in the xy-plane by equations of the form — g(u, v), Y = h(u, v),
Page 6: Chapter 15 - WordPress.com...Suppose that a region G in the uv-plane is transformed one-to-one into the region R in the xy-plane by equations of the form — g(u, v), Y = h(u, v),
Page 7: Chapter 15 - WordPress.com...Suppose that a region G in the uv-plane is transformed one-to-one into the region R in the xy-plane by equations of the form — g(u, v), Y = h(u, v),
Page 8: Chapter 15 - WordPress.com...Suppose that a region G in the uv-plane is transformed one-to-one into the region R in the xy-plane by equations of the form — g(u, v), Y = h(u, v),
Page 9: Chapter 15 - WordPress.com...Suppose that a region G in the uv-plane is transformed one-to-one into the region R in the xy-plane by equations of the form — g(u, v), Y = h(u, v),
Page 10: Chapter 15 - WordPress.com...Suppose that a region G in the uv-plane is transformed one-to-one into the region R in the xy-plane by equations of the form — g(u, v), Y = h(u, v),
Page 11: Chapter 15 - WordPress.com...Suppose that a region G in the uv-plane is transformed one-to-one into the region R in the xy-plane by equations of the form — g(u, v), Y = h(u, v),
Page 12: Chapter 15 - WordPress.com...Suppose that a region G in the uv-plane is transformed one-to-one into the region R in the xy-plane by equations of the form — g(u, v), Y = h(u, v),
Page 13: Chapter 15 - WordPress.com...Suppose that a region G in the uv-plane is transformed one-to-one into the region R in the xy-plane by equations of the form — g(u, v), Y = h(u, v),
Page 14: Chapter 15 - WordPress.com...Suppose that a region G in the uv-plane is transformed one-to-one into the region R in the xy-plane by equations of the form — g(u, v), Y = h(u, v),
Page 15: Chapter 15 - WordPress.com...Suppose that a region G in the uv-plane is transformed one-to-one into the region R in the xy-plane by equations of the form — g(u, v), Y = h(u, v),

Substitutions in Triple Integrals

Page 16: Chapter 15 - WordPress.com...Suppose that a region G in the uv-plane is transformed one-to-one into the region R in the xy-plane by equations of the form — g(u, v), Y = h(u, v),
Page 17: Chapter 15 - WordPress.com...Suppose that a region G in the uv-plane is transformed one-to-one into the region R in the xy-plane by equations of the form — g(u, v), Y = h(u, v),
Page 18: Chapter 15 - WordPress.com...Suppose that a region G in the uv-plane is transformed one-to-one into the region R in the xy-plane by equations of the form — g(u, v), Y = h(u, v),
Page 19: Chapter 15 - WordPress.com...Suppose that a region G in the uv-plane is transformed one-to-one into the region R in the xy-plane by equations of the form — g(u, v), Y = h(u, v),
Page 20: Chapter 15 - WordPress.com...Suppose that a region G in the uv-plane is transformed one-to-one into the region R in the xy-plane by equations of the form — g(u, v), Y = h(u, v),
Page 21: Chapter 15 - WordPress.com...Suppose that a region G in the uv-plane is transformed one-to-one into the region R in the xy-plane by equations of the form — g(u, v), Y = h(u, v),
Page 22: Chapter 15 - WordPress.com...Suppose that a region G in the uv-plane is transformed one-to-one into the region R in the xy-plane by equations of the form — g(u, v), Y = h(u, v),
Page 23: Chapter 15 - WordPress.com...Suppose that a region G in the uv-plane is transformed one-to-one into the region R in the xy-plane by equations of the form — g(u, v), Y = h(u, v),

Exercises:Exercises:4,6,14

Homework: 2,4,5,7,13,18


G ANNEX G Abbreviations - Home Page | National ... · G ANNEX G Abbreviations ... Food & Nutrition Service FNS ... Region 1 F1 Forest Service - Region 2 F2 Forest Service - Region

G ANNEX G Abbreviations - Home Page | National ... · G ANNEX G Abbreviations ... Food & Nutrition Service FNS ... Region 1 F1 Forest Service - Region 2 F2 Forest Service - Region

Definition 6.1.7 Dual Graph G* of a Plane Graph: (1)A plane graph whose vertices corresponding to the faces of G. (2)The edges of G* corresponds to the.

Definition 6.1.7 Dual Graph G* of a Plane Graph: (1)A plane graph whose vertices corresponding to the faces of G. (2)The edges of G* corresponds to the.

E2E Migration Strategies Towards 5G: Long-term Migration ... · which 5G RAN nodes, i.e., generation nodeB g(NB) handles joint data plane (DP)/user plane (UP) and control plane (CP)

E2E Migration Strategies Towards 5G: Long-term Migration ... · which 5G RAN nodes, i.e., generation nodeB g(NB) handles joint data plane (DP)/user plane (UP) and control plane (CP)

Phase plane analysis G. Ferrari Trecatesisdin.unipv.it/.../ails/files/2-Phase_plane_handout.pdf · 2015. 10. 29. · Nonlinear systems Phase plane analysis G. Ferrari Trecate Dipartimento

Phase plane analysis G. Ferrari Trecatesisdin.unipv.it/.../ails/files/2-Phase_plane_handout.pdf · 2015. 10. 29. · Nonlinear systems Phase plane analysis G. Ferrari Trecate Dipartimento

12. COORDINATE GEOMETRY...12. COORDINATE GEOMETRY THE CARTESIAN PLANE We recall from our study of plane geometry that a plane is a two-dimensional region. We now wish to describe the

12. COORDINATE GEOMETRY...12. COORDINATE GEOMETRY THE CARTESIAN PLANE We recall from our study of plane geometry that a plane is a two-dimensional region. We now wish to describe the

Area of a Plane Region - Home - Math - The University of … Area of Plane Region 2 A = The area between a curve, f(x), and the x-axis from x=a to x=b is found by EX 1 Find the area

Area of a Plane Region - Home - Math - The University of … Area of Plane Region 2 A = The area between a curve, f(x), and the x-axis from x=a to x=b is found by EX 1 Find the area

Answers to Homework 23 point possible Plane QUXT, plant QUVR Plane TSRQ, plane TSWX Plane XTQU, plane XTSW Plane VWXU, plane VWSR 2 points each.

Answers to Homework 23 point possible Plane QUXT, plant QUVR Plane TSRQ, plane TSWX Plane XTQU, plane XTSW Plane VWXU, plane VWSR 2 points each.

Multi-region GMPLS control and data plane integration

Multi-region GMPLS control and data plane integration

Hostin g District and Region Events

Hostin g District and Region Events

Virtual SmartZone – Data Plane · PDF fileAP Control / M an g em nt Data Centralized Data Plane Deployment ... L09-vSZD-BW10 • Virtual Data Plane Bandwidth Upgrade - 1 instance

Virtual SmartZone – Data Plane · PDF fileAP Control / M an g em nt Data Centralized Data Plane Deployment ... L09-vSZD-BW10 • Virtual Data Plane Bandwidth Upgrade - 1 instance

Estrategias conceptos semana 1 plane g e

Estrategias conceptos semana 1 plane g e

Integral Equations - Mathematica +1 lies in the plane z=+kê2 and one at potential -1 is in the plane z=-kê2, both in the region r

Integral Equations - Mathematica +1 lies in the plane z=+kê2 and one at potential -1 is in the plane z=-kê2, both in the region r

Region G Collegiate Meeting

Region G Collegiate Meeting

Plane graphs and planar graphs. Part 1kostochk/math412-1/412Lec5.pdfA face of a plane graph (G;’) is aconnected componentof R2 ’(V(G)[E(G)). Thelength, ‘(Fi), of aface Fi in

Plane graphs and planar graphs. Part 1kostochk/math412-1/412Lec5.pdfA face of a plane graph (G;’) is aconnected componentof R2 ’(V(G)[E(G)). Thelength, ‘(Fi), of aface Fi in

1060 |||| CHAPTER 16 VECTOR CALCULUS - UFSCmtm.ufsc.br/~saeger/st_16_4-9(-5).pdf · 2012-12-06 · A plane lamina with constant density occupies a region in the -plane bounded by

1060 |||| CHAPTER 16 VECTOR CALCULUS - UFSCmtm.ufsc.br/~saeger/st_16_4-9(-5).pdf · 2012-12-06 · A plane lamina with constant density occupies a region in the -plane bounded by

Algebra - White Plains Middle School...A linear inequality describes a region of a coordinate plane called a half-plane. All points in the region are solutions of the linear inequality.

Algebra - White Plains Middle School...A linear inequality describes a region of a coordinate plane called a half-plane. All points in the region are solutions of the linear inequality.

Math 374 Graphs. Topics Cartesian Plane Methods of Graphing Intercept Slope Scale First Quadrant Inequality Graphs Region.

Math 374 Graphs. Topics Cartesian Plane Methods of Graphing Intercept Slope Scale First Quadrant Inequality Graphs Region.

North Country Region - nysbroadband.ny.gov · North Country Region Capital Region Southern Tier Region Western NY Region ... No rt hGeb us G en sFa l Germantown Shelter Island Ir

North Country Region - nysbroadband.ny.gov · North Country Region Capital Region Southern Tier Region Western NY Region ... No rt hGeb us G en sFa l Germantown Shelter Island Ir

Chapter 13-1 S13€¦ · Stretching and Bending Vibrations in CH2 Unit S y nnrnetric In plane Out Of plane YSU A ntisynnn.etric In plane Out Of plane Stretch in g: Bending: 13.25

Chapter 13-1 S13€¦ · Stretching and Bending Vibrations in CH2 Unit S y nnrnetric In plane Out Of plane YSU A ntisynnn.etric In plane Out Of plane Stretch in g: Bending: 13.25

6036: Area of a Plane Region

6036: Area of a Plane Region