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Section
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Topic
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Page
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Chapter 15
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Matrix Computing and Subroutine Libraries
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197
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15.1
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Problem 1: Many Simultaneous Linear Equations
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197
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15.2
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Problem 1, Formulation: Linear into Matrix Equations
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198
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15.3
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Problem 2: Simple
but Unsolvable Statics
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198
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15.4
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Problem 2: Theory, Statics
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199
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15.5
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Problem 2, Formulation: Nonlinear Simultaneous Equations
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200
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15.6
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Theory: Matrix Problems
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201
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15.6.1
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Classes of Matrix Problems
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201
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15.7
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Method: Matrix Computing
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204
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15.8
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Implementation:Using Scientific Libraries
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207
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15.9
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Implementation: Determining Available Libraries
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209
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15.9.1
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Determining Contents of a Library
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210
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15.9.2
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Determining the Needed Routine
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210
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15.9.3
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Implementation: Calling
LAPACK
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9.5
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15.9.4
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Calling LAPACK from C
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212
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15.9.5
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Calling LAPACK Fortran from C
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213
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15.9.6
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C Compiling Calling Fortran
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214
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15.10
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Extension: More Netlib Libraries
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214
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15.10.1
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SLATEC's
Common Math Library
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215
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15.11
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Exercises: Testing Matrix Calls
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216
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15.12
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Implementation: LAPACK Short Contents
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218
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15.13
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Implementation: Netlib Short Contents
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221
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15.14
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Implementation: SLATEC Short Contents
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222
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Chapter 16
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Bound States in Momentum Space
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231
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16.1
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Problem: Bound States in Nonlocal Potentials
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231
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16.2
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Theory: k-Space Schroedinger Equation
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232
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16.3
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Method: Reducing Integral to Linear Equations
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233
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16.4
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Model: The Delta-Shell Potential
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235
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16.5
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Implementation: Binding Energies, bound.c
(.f)
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236
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16.6
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Exploration: Wave Function
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237
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Chapter 17
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Quantum Scattering via Integral Equations (O)
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239
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17.1
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Problem: Quantum Scattering in k Space
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239
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17.2
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Theory, Lippmann-Schwinger Equation
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240
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17.3
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Theory, Mathematics: Singular Integrals
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241
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17.3.1
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Numerical Principal Values
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242
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17.4
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Method: Converting Integral to Matrix Equations
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243
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17.4.1
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Solution via Inversion or Elimination
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245
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17.4.2
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Solving i epsilon Integral Equations (O)
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245
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17.5
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Implementation: Delta-Shell Potential, scatt.f
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246
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17.6
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Exploration: Scattering Wave Function
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248
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Chapter 18
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Computing Hardware Basics: Memory and CPU
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249
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18.1
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Problem: Speeding Up Your Program
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249
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18.2
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Theory: Components of a High-Performance Computer
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250
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18.2.1
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Memory Hierarchy
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250
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18.2.2
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The Central Processing Unit
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254
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18.2.3
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CPU Design: RISC
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254
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18.2.4
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CPU Design: Vector Processing
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255
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18.2.5
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Virtual Memory
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256
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18.3
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Method: Programming for Virtual Memory
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256
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18.4
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Implementation: Good and Bad Virtual Memory Use
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257
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18.5
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Method: Programming for Data Cache
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258
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18.6
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Implementation 1: Cache Misses
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260
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18.7
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Implementation 2: Cache Misses
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260
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18.8
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Implementation 3: Large Matrix Multiplication
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261
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Chapter 19
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High-Performance Computing: Profiling and Tuning
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263
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19.1
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Problem: Effect of Hardware on Performance
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263
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19.2
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Method: Tabulating Speedups
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263
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19.3
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Implementation 1: Baseline Program, tune.f
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264
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19.4
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Method: Profiling
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265
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19.5
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Implementation 2: Basic Optimization, tune1.f
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266
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19.6
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Implementation 2: Vector Tuning, tune2.f
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269
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19.7
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Implementation 3: Vector Code on RISC, tune3.f
|
270
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19.8
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Implementation 4: Superscalar Tuning, tune4.f
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271
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19.9
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Assessment
|
273
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|
Chapter 20
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Parallel Computing and PVM
|
275
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|
20.1
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Problem: Speeding Up Your Program
|
275
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20.2
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Theory: Parallel Semantics
|
276
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20.2.1
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Parallel Instruction and Data Streams
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276
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20.2.2
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Granularity
|
277
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20.2.3
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Parallel
Performance
|
277
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20.3
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Method: Multitasking Programming
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278
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20.3.1
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Method: Multitask Organization
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278
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20.4
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Method: Distributed Memory Programming
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279
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20.5
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Implementation: PVM
Bug Populations
|
280
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20.5.1
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The Plan
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280
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Chapter 21
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Object-Oriented Programming: Kinematics (O)
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283
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21.1
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Problem: Superposition of Motions
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283
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21.2
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Theory: Object-Oriented Programming
|
284
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|
21.2.1
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OOP Fundamentals
|
284
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21.3
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Theory: Newton's Laws, Equation Of Motion
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285
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21.4
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OOP Method: Class Structure
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285
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21.5
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Implementation: Uniform 1-D Motion, unim1d.cpp
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286
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21.5.1
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Uniform Motion In 1-D, Class Um1D
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287
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21.5.2
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Implementation: Uniform Motion In 2-D, Child Um2D, unimot2d.cpp
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288
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21.5.3
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Class Um2D: Uniform Motion In 2-D
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289
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21.5.4
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Implementation: Projectile Motion, Child Accm2D, accm2d.cpp
|
291
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|
21.5.5
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Accelerated Motion in Two Directions
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293
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21.6
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Assessment: Exploration, shms.cpp
|
295
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|
Chapter 22
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Thermodynamic Simulations: The Ising Model
|
297
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22.1
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Problem: Hot Magnets
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297
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22.2
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Theory: Statistical Mechanics
|
297
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22.3
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Model: An Ising Chain
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299
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22.4
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Solution, Analytic
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301
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22.5
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Solution, Numerical: The Metropolis Algorithm
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301
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|
22.6
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Implementation, Metropolis Algorithm, ising.f
(.c)
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304
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|
22.7
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Assessment: Approach to Thermal Equilibrium
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305
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|
22.8
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Assessment: Thermodynamic Properties
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305
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|
22.9
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Exploration: Beyond Nearest Neighbors
|
307
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|
22.10
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Exploration:
2-D and 3-D Ising Simulations (SUHEP)
|
307
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|
Chapter 23
|
Functional Integration on Quantum Paths (O)
|
309
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|
23.1
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Problem: Relation of Quantum to Classical Trajectories
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309
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|
23.2
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Theory: Feynman's Spacetime Propagation
|
309
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23.3
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Method, Analytic: The Bound-State Wave Function
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312
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23.4
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Method, Numerical: Path Integration on a Lattice
|
314
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|
23.5
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Method: Lattice Computation of Propagators
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316
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|
23.6
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Implementation: Lattice Programming, qmc.f
(.c)
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319
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|
23.7
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Assessment and Exploration
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321
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