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prob6 Tulane MATH 131
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  • Title: prob6
  • Type: Notes
  • School: Tulane
  • Course: MATH 131
  • Term: Fall

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Calculus Honors 131. Problem set 6. Due October 21. 1) Prove that 14 b, 4 0 by computing the lower and upper Riemann sums corresponding to equally spaced point on the interval [0, b]. x3 dx = 2) Compute the integral of f (x) = xp from a to b by using a partiton of the interval [a, b] of the form P = {x0 , x1 , , xn } designed in such a way that the ratio r = xi /xi 1 is constant. Observe that normally one chooses a partition with the di erence xi xi 1 constant (then we simply say that the points are spaced). equally 3) Here is another way to solve problem 2). De ne 1 b cn := 0 xp dx. Prove that 0 a xp dx = cn an+1 . Check also that 0 2a a xp dx = a (x + a)p dx. p ck . k Use the binomial theorem to check that 2p+1 cp ap+1 = 2ap+1 k even Con rm the result by mathematical induction. 4) Compute the derivative of the function x F (x) = 0 xf (t) dt. x Use the previous result to check that x 0 0 u f (t) dt 5) Find (f 1 ) (0) if f (x) = 0 du = 0 (x u)f (u) du. x [1 + sin(sin t)] dt. 1

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Path: Tulane >> MATH >> 221 Fall, 2008

Description: Quiz 1 Thurs. 1/22/04 Name: 1. Find the unit vector u which has the same direction as the vector a =< 1, 2, 3 >. |a| = 1 + 4 + 9 = 14. Hence u = 1 < 1, 2, 3 >. 14 2. Let a = 3i + 2j + k and b = i + 2j + 2k be vectors in space. Find: a. a 2b a 2...
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Path: Tulane >> MATH >> 221 Fall, 2008
Description: Name: Midterm 1 Th. 02/12/04 1. Let u =< 1, 2, 1 > and v =< 0, 1, 3 > be 2 vectors in space. Are they parallel, perpendicular, or neither? Justify your answer. cos = 5 5 uv = =2 . So the vectors are neither parallel nor perpendicular. |u|v| 3 6 1...
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Path: Tulane >> MATH >> 221 Fall, 2008
Description: Quiz 8 Thurs. 04/1/03 Name: 1. Let F (x, y, z) = (yz + y)i + (xz + x)j + (xy)k be a 3-dimensional vector eld. Is F conservative? If so, nd a potential function for it. Domain of F is simply connected. Py = z + 1 = Qx and Pz = y = Rx and Qz = x = Ry...
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Path: Tulane >> MATH >> 221 Fall, 2008
Description: 1. Let z = f (x, y). Find the slope of the tangent line, a tangent vector, a normal vector, and the equation of the tangent line at a given point. 2. TANGENT PLANES. a) Find the equation of the tangent plane (or the equation of the line perpendicular...
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Path: Tulane >> MATH >> 221 Fall, 2008
Description: Quiz 2 Thurs. 1/29/04 Name: 1. Let a = i 2j + k and b = 5i + 4k. a. Find the area of the parallelogram determined by the sides a and b. Area= |a b| = | < 8, 1, 10 > | = 64 + 1 + 100 = 165. b. Find the volume of the parallelepiped determined by...
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Path: Tulane >> MATH >> 305 Fall, 2008
Description: Math 305/605 HW #11 Due: Tuesday, April 15 To be done but not turned in: Read 34. 33 #13 34 #2(a), 3, 5, 8 To be done and TURNED IN: 33 #8(a), 10 34 #2(b), 4, 6, 11 Hint for 33 #10: Look at the solution sketch to 33 #11(c) in the back of the book ...
math305hw11.pdf
Path: Tulane >> MATH >> 605 Fall, 2008
Description: Math 305/605 HW #11 Due: Tuesday, April 15 To be done but not turned in: Read 34. 33 #13 34 #2(a), 3, 5, 8 To be done and TURNED IN: 33 #8(a), 10 34 #2(b), 4, 6, 11 Hint for 33 #10: Look at the solution sketch to 33 #11(c) in the back of the book ...
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Path: Tulane >> MATH >> 305 Fall, 2008
Description: Math 305/605 HW #3 Due: Friday, February 1 To be done but not turned in: Read 8. To be done and TURNED IN: 8 #1(b), 2(b), 3, 5(a), 8(b) 1 ...
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Path: Tulane >> MATH >> 605 Fall, 2008
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Path: Tulane >> MATH >> 305 Fall, 2008
Description: Math 305/605 HW #1 Due: Tuesday, January 22 To be done but not turned in: Read 1 4. 1 #3, 4, 11 2 #2, 4 3 #1, 4, 8 4 #1(b, e, h, n, v), 2(b, e, h, n, v) To 1 3 4 be done and TURNED IN: #5, 12 #3, 6 #3(b, e, h, n, v), 4(b, e, h, n, v) 1 ...
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Path: Tulane >> MATH >> 605 Fall, 2008
Description: Math 305/605 HW #1 Due: Tuesday, January 22 To be done but not turned in: Read 1 4. 1 #3, 4, 11 2 #2, 4 3 #1, 4, 8 4 #1(b, e, h, n, v), 2(b, e, h, n, v) To 1 3 4 be done and TURNED IN: #5, 12 #3, 6 #3(b, e, h, n, v), 4(b, e, h, n, v) 1 ...
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Path: Tulane >> MATH >> 305 Fall, 2008
Description: Math 305/605 HW #2 Due: Tuesday, January 29 To be done but not turned in: Read 4 7. 4 #6, 11 5 #1 6 #1, 2 Read carefully Example 1 in 8. To 4 5 7 be done and TURNED IN: #7, 14 #2 #3, 4, 5 1 ...
math305hw2.pdf
Path: Tulane >> MATH >> 605 Fall, 2008
Description: Math 305/605 HW #2 Due: Tuesday, January 29 To be done but not turned in: Read 4 7. 4 #6, 11 5 #1 6 #1, 2 Read carefully Example 1 in 8. To 4 5 7 be done and TURNED IN: #7, 14 #2 #3, 4, 5 1 ...
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Path: Tulane >> MATH >> 305 Fall, 2008
Description: Math 305/605 HW #8 Due: Tuesday, March 25 To be done but not turned in: Read 20, 28, 29, 31. 20 #1, 5, 12 28 #2(c), 7, 11 29 #1(a, c), 2 31 #1 To be done and TURNED IN: 20 #2, 6, 14 28 #2(d), 4, 14(a) 29 #1(d, e), 5 31 #2, 6 1 ...
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Path: Tulane >> MATH >> 605 Fall, 2008
Description: Math 305/605 HW #8 Due: Tuesday, March 25 To be done but not turned in: Read 20, 28, 29, 31. 20 #1, 5, 12 28 #2(c), 7, 11 29 #1(a, c), 2 31 #1 To be done and TURNED IN: 20 #2, 6, 14 28 #2(d), 4, 14(a) 29 #1(d, e), 5 31 #2, 6 1 ...
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Path: Tulane >> MATH >> 305 Fall, 2008
Description: Math 305/605 HW #5 Due: Tuesday, February 19 To be done but not turned in: Read 11, 12. 9 #15 11 #2 12 #3(a, c, e, g), 7 To be done and TURNED IN: 9 #18 10 #11(a) 11 #3 12 #3(b, d, f ), 4 Also turn in a solution to the following problem. A set S R...
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Path: Tulane >> MATH >> 605 Fall, 2008
Description: Math 305/605 HW #5 Due: Tuesday, February 19 To be done but not turned in: Read 11, 12. 9 #15 11 #2 12 #3(a, c, e, g), 7 To be done and TURNED IN: 9 #18 10 #11(a) 11 #3 12 #3(b, d, f ), 4 Also turn in a solution to the following problem. A set S R...
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Path: Tulane >> MATH >> 325 Fall, 2008
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Path: Tulane >> MATH >> 325 Fall, 2008
Description: Comments. This set of questions should help you prepare for the nal exam. I expect the nal to be similar in length and style of questions. In addition, make sure that youre comfortable with the problems and solutions from the rst two midterms. As usu...
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Path: Tulane >> MATH >> 325 Fall, 2008
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Path: Tulane >> MATH >> 441 Fall, 2008
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Path: Tulane >> MATH >> 441 Fall, 2008
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Path: Tulane >> MATH >> 441 Fall, 2008
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Path: Tulane >> CELL >> 413 Fall, 2008
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Path: Tulane >> CELL >> 413 Fall, 2008
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Path: Tulane >> CELL >> 413 Fall, 2008
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Path: Tulane >> CELL >> 413 Fall, 2008
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Path: Tulane >> CELL >> 413 Fall, 2008
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Path: Tulane >> CELL >> 413 Fall, 2008
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Path: Tulane >> CELL >> 413 Fall, 2008
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Path: Tulane >> CELL >> 413 Fall, 2008
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Path: Tulane >> CELL >> 413 Fall, 2008
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Path: Tulane >> CELL >> 413 Fall, 2008
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Path: Tulane >> CELL >> 413 Fall, 2008
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Path: Tulane >> CELL >> 413 Fall, 2008
Description: ...
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Path: Tulane >> CELL >> 413 Fall, 2008
Description: Cleavage Cell Division Cell Cycle Control Morula Compaction Blastocyst Hatching Implantation Decidual Reaction Early Cell Lineages Inner Cell Mass Trophoblasts (Extra-embryonic) Anomalies Cleavage Cleavage Blastomere Equal Asynchronous 40 hours...
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Path: Tulane >> CELL >> 413 Fall, 2008
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Path: Tulane >> CELL >> 413 Fall, 2008
Description: Skeletal Development Multiple Cellular Origins 1 - Paraxial Mesoderm Somite, Sclerotome Axial Skeleton (e.g. vertebra) 2 - Lateral Plate Mesoderm Appendicular Skeleton (e.g. limb) 3 - Neural Crest Head Skeleton Established as 1 - Hyaline Cartilage ...
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Path: Tulane >> CELL >> 413 Fall, 2008
Description: Gastrulation - Cell Lineages Blastocyst Embryo pole Inner cell mass (embryoblast) Blastocoel Outer cell mass (trophoblast) abembryonic pole Day 6 Blastocyst adheres to endometrium at embryo pole Trophoblast proliferation production of hCG (maintai...
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Path: Tulane >> CELL >> 413 Fall, 2008
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Path: Tulane >> EBIO >> 101 Fall, 2008
Description: BIOLOGY 101 Diversity of Life Syllabus Fall 2008 Instructor: Dr. Bryan J. Sigel Office Hours: Boggs 401, TBA or by appointment Phone number: (504) 247-1580 E-mail: bsigel@tulane.edu Class Meetings: Monday, Wednesday, and Friday at 2:00, Richardson...
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Path: Tulane >> EBIO >> 111 Fall, 2008
Description: BIOLOGY 101 Diversity of Life Syllabus Fall 2008 Instructor: Dr. Bryan J. Sigel Office Hours: Boggs 401, TBA or by appointment Phone number: (504) 247-1580 E-mail: bsigel@tulane.edu Class Meetings: Monday, Wednesday, and Friday at 2:00, Richardson...
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Path: Tulane >> REAL >> 232 Fall, 2008
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Path: Tulane >> EENS >> 113 Fall, 2008
Description: EENS 113- 01, 02, 07 Spring 2007 EENS-113 CLASS PARTICIPATION / HOMEWORK 01, 02, 07 Instructor 1/22 1/29 2/5 2/12 2/26 3/5 ERIKA L. GONZALEZ S ID # 1 2 3 4 5 6 1 0661 100 0 100 100 100 100 2 0668 100 100 100 100 100 100 3 0910 100 100 100 100 100 100...
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Path: Tulane >> EENS >> 113 Fall, 2008
Description: HYDROLOGIC (WATER CYCLE) Water is in constant circulation powered by sunlight solar energy Reservoir Oceans Ice Caps and Glaciers Groundwater Lakes Soil Moisture Atmosphere Streams and Rivers Biosphere PROBLEMS Volume (Km x 10,000,000) 3 Percent ...
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Path: Tulane >> EENS >> 113 Fall, 2008
Description: STRUCTURAL GEOLOGY Last Updated October 23, 2003 STRUCTURAL GEOLOGY STRUCTURAL GEOLOGY -Study of the form, arrangement and internal structure of rocks. -Study of the 3-D configuration of bedrock units GEOLOGIC MAP GEOLOGIC BLOCK DIAGRAM GEOLOGIC CR...
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Path: Tulane >> EENS >> 113 Fall, 2008
Description: TOPOGRAPHIC MAPS MAP 2-D REPRESENTATION OF THE EARTHS SURFACE TOPOGRAPHIC MAP A graphic representation of the 3-D configuration of the earths surface. This is it shows elevations (third dimension). It provides a plane view of the land (the perspectiv...
SEDIMENTARY-ROCKS-2.pdf
Path: Tulane >> EENS >> 113 Fall, 2008
Description: SEDIMENTARY ROCKS Sedimentary rocks are classified based on their TEXTURE and COMPOSITION TEXTURE. Is the geometrical arrangement of the constituents of a rock (SIZE, SHAPE and MUTUAL RELATIONSHIPS OF PARTICLES). Based on their composition there are...
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Path: Tulane >> EENS >> 113 Fall, 2008
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Path: Tulane >> EENS >> 113 Fall, 2008
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Path: Tulane >> EENS >> 113 Fall, 2008
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SEDIMENTARY-ROCKS-1.pdf
Path: Tulane >> EENS >> 113 Fall, 2008
Description: SEDIMENTARY ROCKS SEDIMENTARY ROCKS Sedimentary rocks are formed near or at the surface of the earth. They are derived from preexisting source rocks. They are composed by sediments, this is material that has been weathered, transported and deposited...
studyguide-sp07.pdf
Path: Tulane >> EENS >> 113 Fall, 2008
Description: SPRING 2007 PHYSICAL GEOLOGY LAB SECTIONS 01, 02 and 07 FINAL EXAM STUDY GUIDE TOPOGRAPHIC MAP READING. [50 %] (LABORATORY 9) Scales (Verbal, graphic or bar, R.F. or fractional), and scale conversion. Map Coordinates and orientation (Latitude and...
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Path: Tulane >> EENS >> 113 Fall, 2008
Description: Tulane Earth glass (6-6.5), brass yellow, may have striated faces (aka \"fool\'s gold\"), black...
MINERALS-1.pdf
Path: Tulane >> EENS >> 113 Fall, 2008
Description: 1/6 MINERALS PHYSICAL PROPERTIES OF MINERALS The Study of rocks allows geologist to understand the history of the Earth. Most Rocks are aggregates of minerals. One must therefore, be able to identify minerals, which are components of common rocks. M...
VOLCANOES-1.pdf
Path: Tulane >> EENS >> 113 Fall, 2008
Description: VOLCANOES, EARTHQUAKES AND PLATE TECTONICS September 29, 2003 VOLCANOES, EARTHQUAKES AND PLATE TECTONICS VOLCANIC LANDFORMS VOLCANO. A vent through which magma, ash, and gases erupt, or the structure built around a vent by such eruption. VOLCANO TYP...
structural-geology-practice exercise-sp06.pdf
Path: Tulane >> EENS >> 113 Fall, 2008
Description: Name _ EENS 113-_ 1. For the following geologic maps. A. Indicate with the appropriate symbols the strike and dip of each of the formations. B. In the space provided sketch a geologic cross-section oriented as indicated by the profile line. C. Name t...
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Path: Tulane >> EENS >> 204 Fall, 2008
Description: EQ Case Histories EENS 204 Tulane University Natural Disasters Prof. Stephen A. Nelson Earthquake Case Histories This page last updated on 21-Jan-2004 Earthquake Case Histories For this lecture we will watch a video entitled \"Killer Quake\", produce...
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Path: Tulane >> EENS >> 605 Fall, 2008
Description: EQ Case Histories EENS 204 Tulane University Natural Disasters Prof. Stephen A. Nelson Earthquake Case Histories This page last updated on 21-Jan-2004 Earthquake Case Histories For this lecture we will watch a video entitled \"Killer Quake\", produce...
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Path: Tulane >> EENS >> 204 Fall, 2008
Description: Mass Wasting Processes EENS 204 Tulane University Natural Disasters Prof. Stephen A. Nelson Mass-Wasting and Mass-Wasting Processes This page last updated on 16-Oct-2007 Mass-Wasting and its Human Impacts Mass-Wasting is defined as the down slope...
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Path: Tulane >> EENS >> 605 Fall, 2008
Description: Mass Wasting Processes EENS 204 Tulane University Natural Disasters Prof. Stephen A. Nelson Mass-Wasting and Mass-Wasting Processes This page last updated on 16-Oct-2007 Mass-Wasting and its Human Impacts Mass-Wasting is defined as the down slope...
FS065-97_map.pdf
Path: Tulane >> EENS >> 204 Fall, 2008
Description: , , , , , , , , Tacoma , , , , , Lake Tapps , , Puyallup , , , Sumner ,, , Orting , , , Graham nd , , Sou , get u Federal P , Way , PP @ , PPPPPPP @ , PP P @ @ , , , ,Auburn , , , , , , , Enumclaw , , , , Buckley Wilkeson Wh it e R ive r Green...
FS065-97_map.pdf
Path: Tulane >> EENS >> 605 Fall, 2008
Description: , , , , , , , , Tacoma , , , , , Lake Tapps , , Puyallup , , , Sumner ,, , Orting , , , Graham nd , , Sou , get u Federal P , Way , PP @ , PPPPPPP @ , PP P @ @ , , , ,Auburn , , , , , , , Enumclaw , , , , Buckley Wilkeson Wh it e R ive r Green...
tropical_cyclones.pdf
Path: Tulane >> EENS >> 204 Fall, 2008
Description: Exceptional Weather - Tropical Cyclones EENS 204 Tulane University Natural Disasters Prof. Stephen A. Nelson Exceptional Weather - Tropical Cyclones This document last updated on 05-Nov-2007 Exceptional Weather We have already discussed the facto...
tropical_cyclones.pdf
Path: Tulane >> EENS >> 605 Fall, 2008
Description: Exceptional Weather - Tropical Cyclones EENS 204 Tulane University Natural Disasters Prof. Stephen A. Nelson Exceptional Weather - Tropical Cyclones This document last updated on 05-Nov-2007 Exceptional Weather We have already discussed the facto...
tornadoes.pdf
Path: Tulane >> EENS >> 204 Fall, 2008
Description: Exceptional Weather - Tornadoes Page 1 of 9 EENS 204 Tulane University Natural Disasters Prof. Stephen A. Nelson Exceptional Weather - Thunderstorms, Tornadoes, Nor\'easters, & Drought This document last updated on 03-Nov-2008 Thunderstorms Thund...
tornadoes.pdf
Path: Tulane >> EENS >> 605 Fall, 2008
Description: Exceptional Weather - Tornadoes Page 1 of 9 EENS 204 Tulane University Natural Disasters Prof. Stephen A. Nelson Exceptional Weather - Thunderstorms, Tornadoes, Nor\'easters, & Drought This document last updated on 03-Nov-2008 Thunderstorms Thund...
struct&materials.pdf
Path: Tulane >> EENS >> 204 Fall, 2008
Description: Earth Struct & Materials Page 1 of 17 EENS 204 Tulane University Natural Disasters Prof. Stephen A. Nelson Earth Structure, Materials, Systems, and Cycles This page last updated on 16-Jan-2006 The Earth in the Solar System The Solar System The E...
struct&materials.pdf
Path: Tulane >> EENS >> 605 Fall, 2008
Description: Earth Struct & Materials Page 1 of 17 EENS 204 Tulane University Natural Disasters Prof. Stephen A. Nelson Earth Structure, Materials, Systems, and Cycles This page last updated on 16-Jan-2006 The Earth in the Solar System The Solar System The E...
605syllabus_fall2008_revised.pdf
Path: Tulane >> EENS >> 204 Fall, 2008
Description: Syllabus EENS 204 Revised EENS 605 Natural Disasters Revised Syllabus Fall 2008 Instructor: Dr. Stephen A. Nelson Office Hours - MWF 1:00 - 4:00 PM, Room 208, Blessey Hall, e-mail - snelson@tulane.edu Office Phone 862-3194 Required Textbook: Natu...

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