Software Quality Engineering

PART I OVERVIEW AND BASICS
1 Overview
1.1 Meeting People’s Quality Expectations
1.2 Book Organization and Chapter Overview
1.3 Dependency and Suggested Usage
1.4 Reader Preparation and Background Knowledge

2 What Is Software Quality?
2.1 Quality: Perspectives and Expectations
2.2 Quality Frameworks and ISO-9126
2.3 Correctness and Defects: Definitions, Properties, and Measurements
2.4 A Historical Perspective of Quality
2.5 So, What Is Software Quality?

3 Quality Assurance
3.1 Classification: QA as Dealing with Defects
3.2 Defect Prevention
3.2.1 Education and training
3.2.2 Formal method
3.2.3 Other defect prevention techniques
3.3.1 Inspection: Direct fault detection and removal
3.3.2 Testing: Failure observation and fault removal
3.3.3 Other techniques and risk identification
3.4.1 Software fault tolerance
3.4.2 Safety assurance and failure containment
3.3 Defect Reduction
3.4 Defect Containment
3.5 Concluding Remarks

4 Quality Assurance in Context
4.1 Handling Discovered Defect During QA Activities
4.2 QA Activities in Software Processes
4.3 Verification and Validation Perspectives
4.4 Reconciling the Two Views
4.5 Concluding Remarks
Problems

5 Quality Engineering
5.1 Quality Engineering: Activities and Process
5.2 Quality Planning: Goal Setting and Strategy Formation
5.3 Quality Assessment and Improvement
5.4 Quality Engineering in Software Processes
5.5 Concluding Remarks

PART II SOFTWARETESTING
6 Testing: Concepts, Issues, and Techniques
6.1 Purposes, Activities, Processes, and Context
6.2 Questions About Testing
6.3 Functional vs. Structural Testing: What to Test?
6.4 Coverage-Based vs. Usage-Based Testing: When to Stop Testing?
6.5 Concluding Remarks








 Test Activities, Management, and Automation
7.1 Test Planning and Preparation
7.1.1 Test planning: Goals, strategies, and techniques
7.1.2 Testing models and test cases
7.1.3 Test suite preparation and management
7.1.4 Preparation of test procedure
7.2 Test Execution, Result Checking, and Measurement
7.3 Analysis and Follow-up
7.4 Activities, People, and Management
7.5 Test Automation
7.6 Concluding Remarks
Problems

8 Coverage and Usage Testing Based on Checklists and Partitions
8.1 Checklist-Based Testing and Its Limitations
8.2 Testing for Partition Coverage
8.3 Usage-Based Statistical Testing with Musa’s Operational Profiles
8.4 Constructing Operational Profiles
8.5 Case Study: OP for the Cartridge Support Software
8.6 Concluding Remarks
8.2.1 Some motivational examples
8.2.2 Partition: Concepts and definitions
8.2.3 Testing decisions and predicates for partition coverage
8.3.1 The cases for usage-based statistical testing
8.3.2 Musa OP: Basic ideas
8.3.3 Using OPs for statistical testing and other purposes
8.4.1 Generic methods and participants
8.4.2 OP development procedure: Musa-1
8.4.3 OP development procedure: Musa-2
8.5.1 Background and participants
8.5.2 OP development in five steps
8.5.3 Metrics collection, result validation, and lessons learned

9. Input Domain Partitioning and Boundary Testing
9.1 Input Domain Partitioning and Testing
9.2 Simple Domain Analysis and the Extreme Point Combination Strategy
9.3 Testing Strategies Based on Boundary Analysis
9.1.1 Basic concepts, definitions, and terminology
9.1.2 Input domain testing for partition and boundary problems
9.3.2 Other Boundary Test Strategies and Applications
9.4.1 Strong and approximate strategies
9.4.2 Other types of boundaries and extensions
9.4.3 Queuing testing as boundary testing
9.4 Weak 1 x 1 strategy
9.5 Concluding Remarks

10 Coverage and Usage Testing Based on Finite-State Machines
and Markov Chains
10.1 Finite-State Machines and Testing
10.1.1 Overcoming limitations of simple processing models
10.1.2 FSMs: Basic concepts and examples
10.1.3 Representations of FSMs
10.2 FSM Testing: State and Transition Coverage
10.2.1 Some typical problems with systems modeled by FSMs
10.2.2 Model construction and validation
10.2.3 Testing for correct states and transitions
10.2.4 Applications and limitations
10.3 Case Study: FSM-Based Testing of Web-Based Applications
10.3.1 Characteristics of web-based applications
10.3.2 What to test: Characteristics of web problems
10.3.3 FSMs for web testing
10.4.1 Markov chains and operational profiles
10.4.2 From individual Markov chains to unified Markov models
10.4.3 UMM construction
10.4 Markov Chains and Unified Markov Models for Testing
10.5 Using UMMs for Usage-Based Statistical Testing
10.5.1 Testing based on usage frequencies in UMMs
10.5.2 Testing based on other criteria and UMM hierarchies
10.5.3 Implementation, application, and other issues
10.6 Case Study Continued: Testing Based on Web Usages
10.6.1 Usage-based web testing: Motivations and basic approach
10.6.2 Constructing UMMs for statistical web testing
10.6.3 Statistical web testing: Details and examples
10.7 Concluding Remarks

11 Control Flow, Data Dependency, and Interaction Testing
1 1.1 Basic Control Flow Testing
1 1.1.1 General concepts
1 1.1.2 Model construction
11.1.3 Path selection
1 1.1.4 Path sensitization and other activities
11.2 Loop Testing, CFT Usage, and Other Issues
1 1.2.1 Different types of loops and corresponding CFGs
11.2.2 Loop testing: Difficulties and a heuristic strategy
1 1.2.3 CFT Usage and Other Issues
1 1.3 Data Dependency and Data Flow Testing
11.3.1 Basic concepts: Operations on data and data dependencies
11.3.2 Basics of DFT and DDG
11.3.3 DDG elements and characteristics
11.3.4 Information sources and generic procedure for DDG construction
11.3.5 Building DDG indirectly
11.3.6 Dealing with loops
1 1.4 DFT Coverage and Applications
1 1.4.1 Achieving slice and other coverage
1 1.4.2 DFT: Applications and other issues
11.4.3 DFT application in synchronization testing
1 1.5 Concluding Remarks

12 Testing Techniques: Adaptation, Specialization, and Integration
12.1 Testing Sub-Phases and Applicable Testing Techniques
12.2 Specialized Test Tasks and Techniqu,es
12.3 Test Integration f
12.4 Case Study: Hierarchical Web Testing
12.5 Concluding Remarks

PART 111 QUALITY ASSURANCE BEYOND TESTING
13 Defect Prevention and Process lmpirovement
13.1 Basic Concepts and Generic Approaches
13.2 Root Cause Analysis for Defect Prevention
13.3 Education and Training for Defect Prevention
13.4 Other Techniques for Defect Prevention
13.4.1 Analysis and modeling for defect prevention
13.4.2 Technologies, standards, and methodologies for defect prevention
13.4.3 Software tools to block defect injection
13.5.1 Process selection, definition, and conformance
13.5.2 Process maturity
13.5 Focusing on Software Processes
13.5.3 Process and quality improvement
13.6 Concluding Remarks

14 Software Inspection
14.1 Basic Concepts and Generic Process
14.2 Fagan inspection
14.3 Other Inspections and Related Activities
14.3.1 Inspections of reduced scope or team size
14.3.2 Inspections of enlarged scope or team size
14.3.3 Informal desk checks, reviews, and walkthroughs
14.3.4 Code reading
14.3.5 Other formal reviews and static analyses
14.4 Defect Detection Techniques, TooYProcess Support, and Effectiveness
14.5 Concluding Remarks
Problems
15 Formal Verification
15.1 Basic Concepts: Formal Verification and Formal Specification
15.2 Formal Verification: Axiomatic Approach
15.2. I Formal logic specifications
15.2.2 Axioms
15.2.3 Axiomatic proofs and a comprehensive example
15.3.1 Weakest pre-conditions and backward chaining
15.3.2 Functional approach and symbolic execution
15.3.3 Seeking alternatives: Model checking and other approaches
15.3 Other Approaches
15.4 Applications, Effectiveness, and Integration Issues
15.5 Concluding Remarks
Problems
16 Fault Tolerance and Failure Containment
16.1 Basic Ideas and Concepts
16.2 Fault Tolerance with Recovery Blocks
16.3 Fault Tolerance with N-Version Programming
16.3.1 NVP: Basic technique and implementation
16.3.2 Ensuring version independence
16.3.3 Applying NVP ideas in other QA activities
16.4 Failure Containment: Safety Assurance and Damage Control
16.4.1 Hazard analysis using fault-trees and event-trees
16.4.2 Hazard resolution for accident prevention
16.4.3 Accident analysis and post-accident damage control
16.5.1 Modeling and analyzing heterogeneous systems
16.5.2 Prescriptive specifications foir safety
16.5 Application in Heterogeneous Systems
16.6 Concluding Remarks

17 Comparing Quality Assurance Techniques and Activities
17.1 General Questions: Cost, Benefit, and Environment
17.2 Applicability to Different Environments
17.3 Effectiveness Comparison
17.3.1 Defect perspective
17.3.2 Problem types
17.3.3 Defect level and pervasiveness
17.3.4 Result interpretation and constructive information
17.4 Cost Comparison
17.5 Comparison Summary and Recommendations

PART IV QUANTIFIABLE QUALITY IMPROVEMENT
18 Feedback Loop and Activities for Quantifiable Quality Improvement
18.1 QA Monitoring and Measurement
18.1.1 Direct vs. indirect quality measurements
18.1.2 Direct quality measurements Result and defect measurements
18.1.3 Indirect quality measurements: Environmental, product internal,and activity measurements
18.2 Immediate Follow-up Actions and Feedback
18.3 Analyses and Follow-up Actions
18.3.1 Analyses for product release decisions
18.3.2 Analyses for other project management decisions
18.3.3 Other feedback and follow-up actions
18.4.1 Feedback loop: Implementation and integration
18.4.2 A refined quality engineering, process
18.4.3 Tool support: Strategy, implementation, and integration
18.4 Implementation, Integration, and Tool Support
18.5 Concluding Remarks

19 Quality Models and Measurements
19.1 Models for Quality Assessment
19.2 Generalized Models
19.3 Product-Specific Models
19.4 Model Comparison and Interconnections
19.5 Data Requirements and Measurement
19.6 Selecting Measurements and Models
19.7 Concluding Remarks

20 Defect Classification and Analysis
20.1 General Types of Defect Analyses
20.1.1 Defect distribution analysis
20.1.2 Defect trend analysis and defect dynamics model
20.1.3 Defect causal analysis
20.2.1 ODC concepts
20.2.2 Defect classification using ODC: A comprehensive example
20.2.3 Adapting ODC to analyze web errors
20.3. I One-way analysis: Analyzing a single defect attribute
20.3.2 Two-way and multi-way analysis: Examining cross-interactions
20.2 Defect Classification and ODC
20.3 Defect Analysis for Classified Data
20.4 Concluding Remarks

21 Risk Identification for Quantifiable Quality Improvement
21.1 Basic Ideas and Concepts
21.2 Traditional Statistical Analysis Techniques
21.3 New Techniques for Risk Identification
2 1.3.1 Principal component and discriminant analyses
2 1.3.2 Artificial neural networks and learning algorithms
21.3.3 Data partitions and tree-based modeling
21.3.4 Pattern matching and optimal set reduction
2 1.4 Comparisons and Integration
2 1.5 Risk Identification for Classified Defect Data
2 1.6 Concluding Remarks

22 Software Reliability Engineering
22.1 SRE: Basic Concepts and General Approaches
22.2 Large Software Systems and Reliability Analyses
22.3 Reliability Snapshots Using IDRMs
22.4 Longer-Term Reliability Analyses Using SRGMs TBRMs for Reliability Analysis and Improvement
22.5.1 Constructing and using TBRMs
22.5.2 TBRM Applications
22.5.3 TBRM’s impacts on reliability improvement Implementation and Software Tool Support

Link:
http://cramitin.net/s8tsa7jl8tjg

http://cramitin.net/ksmo31wxqrwp

http://cramitin.net/u8emtanj93f0

new Link
Part 1 :
http://www.4shared.com/rar/aRzmGWcH/Software_Quality_Engineeringpa.html
Part 2 :
http://www.4shared.com/rar/LDtFSgCc/Software_Quality_Engineeringpa.html
Part 3 :
http://www.4shared.com/rar/sshHoRjn/Software_Quality_Engineeringpa.html

Read more...

CNC Part Programming Commands

Download

Read more...

Automating Manufacturing System

PREFACE
Designing software for control systems is difficult. Experienced controls engineers
have learned many techniques that allow them to solve problems. This book was written to
present methods for designing controls software using Programmable Logic Controllers
(PLCs). It is my personal hope that by employing the knowledge in the book that you will
be able to quickly write controls programs that work as expected (and avoid having to
learn by costly mistakes.)

This book has been designed for students with some knowledge of technology,
including limited electricity, who wish to learn the discipline of practical control system
design on commonly used hardware. To this end the book will use the Allen Bradley ControlLogix
processors to allow depth. Although the chapters will focus on specific hardware,
the techniques are portable to other PLCs. Whenever possible the IEC 61131
programming standards will be used to help in the use of other PLCs.

In some cases the material will build upon the content found in a linear controls
course. But, a heavy emphasis is placed on discrete control systems.

Total 839 pages 6 mb

Download

Read more...

First Course in Finite Elements

Preface
This book is written to be an undergraduate and introductory graduate level textbook, depending on whether the more advanced topics appearing at the end of each chapter are covered.

Without the advanced topics, the book is of a level readily comprehensible by junior and senior undergraduate students in science and engineering.With theadvanced topics included, thebookcan serve as the textbook for the first course in finite elements at the graduate level. The text material evolved from over 50 years of combined teaching experience by the authors of graduate and undergraduate finite element courses.

The book focuses on the formulation and application of the finite element method. It differs from other elementary finite element textbooks in the following three aspects:
1. It is introductory andself-contained.Only a modest background in mathematics and physics is needed,all of which is covered in engineering and science curricula in the firsttwo years. Furthermore,many of the specific topics in mathematics, such as matrix algebra, some topics in differential equations, and mechanics and physics, such as conservation laws and constitutive equations, are reviewed prior to their application.
2. It is generic. While most introductory finite element textbooks are application specific, e.g. focusing on linear elasticity, the finite element method in this book is formulated as a general purpose numerical procedure for solving engineering problems governed by partial differential equations. The methodology for obtaining weak forms for the governing equations, a crucial step in the development and understanding of finite elements, is carefully developed. Consequently, students from various engineering and science disciplines will benefit equally from the exposition of the subject.
3. It isa hands-on experience.Thebookintegrates finite element theory, finite element code development and the application of commercial software package. Finite element code development is introduced throughMATLAB exercises and aMATLAB program, whereas ABAQUS is used for demonstrating the use of commercial finite element software.
The material in the book can be covered in a single semester and a meaningful course can be constructed from a subset of the chapters in this book for a one-quarter course. The course material is organized in three chronological units of about one month each: (1) finite elements for one-dimensional problems; (2) finite elements for scalar field problems in two dimensions and (3)finite elements for vectorfield problems in two dimensions and beams. In each case, the weak form is developed, shape functions are described and these ingredients are synthesized to obtain the finite element equations. Moreover, in a web-base chapter, the application of general purpose finite element software using ABAQUS is given for linear heat conduction and elasticity.
Each chapter contains a comprehensive set of homework problems, some of which require programming with MATLAB. Each book comes with an accompanying ABAQUS Student Edition CD, and MATLAB finite element programs can be downloaded from the accompanying website hosted by John Wiley&Sons:www.wileyeurope/college/Fish. Atutorial for theABAQUSexample problems, written by ABAQUS staff, is also included in the book.

Depending on the interests and background of the students, three tracks have been developed:
1. Broad Science and Engineering (SciEng) track
2. Advanced (Advanced) track
3. Structural Mechanics (StrucMech) track
The SciEng track is intended for a broad audience of students in science and engineering. It is aimed at presenting FEM as a versatile tool for solving engineering design problems and as a tool for scientific discovery. Students who have successfully completed this track should be able to appreciate and apply the finite element method for the types of problems described in the book, but more importantly, the SciEng track equips them with a set of skills that will allow them to understand and develop the method for a variety of problems that have not been explicitly addressed in the book. This is our recommended track.

The Advanced track is intended for graduate students as well as undergraduate students with a strong focus on applied mathematics, who are less concerned with specialized applications, such as beams and trusses, but rather with a more detailed exposition of the method. Although detailed convergence proofs in multidimensions are left out, the Advanced track is an excellent stepping stone for students interested in a comprehensive mathematical analysis of the method.
The StrucMech track is intended for students in Civil, Mechanical and Aerospace Engineering whose main interests are in structural and solid mechanics. Specialized topics, such as trusses, beams and energy based principles, are emphasized in this track, while sections dealing with topics other than solid mechanics in multidimensions are classified as optional.

1 Introduction 1
1.1 Background 1
1.2 Applications of Finite elements 7
References 9
2 Direct Approach for Discrete Systems 11
2.1 Describing the Behavior of a Single Bar Element 11
2.2 Equations for a System 15
2.2.1 Equations for Assembly 18
2.2.2 Boundary Conditions and System Solution 20
2.3 Applications to Other Linear Systems 24
2.4 Two-Dimensional Truss Systems 27
2.5 Transformation Law 30
2.6 Three-Dimensional Truss Systems 35
References 36
Problems 37
3 Strong andWeak Forms for One-Dimensional Problems 41
3.1 The Strong Form in One-Dimensional Problems 42
3.1.1 The Strong Form for an Axially Loaded Elastic Bar 42
3.1.2 The Strong Form for Heat Conduction in One Dimension 44
3.1.3 Diffusion in One Dimension 46
3.2 TheWeak Form in One Dimension 47
3.3 Continuity 50
3.4 The Equivalence Between theWeak and Strong Forms 51
3.5 One-Dimensional Stress Analysis with Arbitrary Boundary Conditions 58
3.5.1 Strong Form for One-Dimensional Stress Analysis 58
3.5.2 Weak Form for One-Dimensional Stress Analysis 59

3.6 One-Dimensional Heat Conduction with Arbitrary
Boundary Conditions 60
3.6.1 Strong Form for Heat Conduction in One Dimension
with Arbitrary Boundary Conditions 60
3.6.2 Weak Form for Heat Conduction in One Dimension
with Arbitrary Boundary Conditions 61
3.7 Two-Point Boundary Value Problem with
Generalized Boundary Conditions 62
3.7.1 Strong Form for Two-Point Boundary Value Problems
with Generalized Boundary Conditions 62
3.7.2 Weak Form for Two-Point Boundary Value Problems
with Generalized Boundary Conditions 63
3.8 Advection–Diffusion 64
3.8.1 Strong Form of Advection–Diffusion Equation 65
3.8.2 Weak Form of Advection–Diffusion Equation 66
3.9 Minimum Potential Energy 67
3.10 Integrability 71
References 72
Problems 72
4 Approximation of Trial Solutions,Weight Functions
and Gauss Quadrature for One-Dimensional Problems 77
4.1 Two-Node Linear Element 79
4.2 Quadratic One-Dimensional Element 81
4.3 Direct Construction of Shape Functions in One Dimension 82
4.4 Approximation of theWeight Functions 84
4.5 Global Approximation and Continuity 84
4.6 Gauss Quadrature 85
Reference 90
Problems 90
5 Finite Element Formulation for One-Dimensional Problems 93
5.1 Development of Discrete Equation: Simple Case 93
5.2 Element Matrices for Two-Node Element 97
5.3 Application to Heat Conduction and Diffusion Problems 99
5.4 Development of Discrete Equations for Arbitrary Boundary
Conditions 105
5.5 Two-Point Boundary Value Problem with
Generalized Boundary Conditions 111
5.6 Convergence of the FEM 113
5.6.1 Convergence by Numerical Experiments 115
5.6.2 Convergence by Analysis 118
5.7 FEM for Advection–Diffusion Equation 120
References 122
Problems 123
6 Strong andWeak Forms for Multidimensional
Scalar Field Problems 131
6.1 Divergence Theorem and Green’s Formula 133
6.2 Strong Form 139
6.3 Weak Form 142
6.4 The Equivalence BetweenWeak and Strong Forms 144
6.5 Generalization to Three-Dimensional Problems 145
6.6 Strong andWeak Forms of Scalar Steady-State
Advection–Diffusion in Two Dimensions 146
References 148
Problems 148
7 Approximations of Trial Solutions,Weight Functions and
Gauss Quadrature for Multidimensional Problems 151
7.1 Completeness and Continuity 152
7.2 Three-Node Triangular Element 154
7.2.1 Global Approximation and Continuity 157
7.2.2 Higher Order Triangular Elements 159
7.2.3 Derivatives of Shape Functions for the
Three-Node Triangular Element 160
7.3 Four-Node Rectangular Elements 161
7.4 Four-Node Quadrilateral Element 164
7.4.1 Continuity of Isoparametric Elements 166
7.4.2 Derivatives of Isoparametric Shape Functions 166
7.5 Higher Order Quadrilateral Elements 168
7.6 Triangular Coordinates 172
7.6.1 Linear Triangular Element 172
7.6.2 Isoparametric Triangular Elements 174
7.6.3 Cubic Element 175
7.6.4 Triangular Elements by Collapsing Quadrilateral Elements 176
7.7 Completeness of Isoparametric Elements 177
7.8 Gauss Quadrature in Two Dimensions 178
7.8.1 Integration Over Quadrilateral Elements 179
7.8.2 Integration Over Triangular Elements 180
7.9 Three-Dimensional Elements 181
7.9.1 Hexahedral Elements 181
7.9.2 Tetrahedral Elements 183
References 185
Problems 186
8 Finite Element Formulation for Multidimensional
Scalar Field Problems 189
8.1 Finite Element Formulation for Two-Dimensional
Heat Conduction Problems 189
8.2 Verification and Validation 201
8.3 Advection–Diffusion Equation 207
References 209
Problems 209
9 Finite Element Formulation for Vector Field Problems – Linear Elasticity 215
9.1 Linear Elasticity 215
9.1.1 Kinematics 217
9.1.2 Stress and Traction 219
9.1.3 Equilibrium 220
9.1.4 Constitutive Equation 222
9.2 Strong andWeak Forms 223
9.3 Finite Element Discretization 225
9.4 Three-Node Triangular Element 228
9.4.1 Element Body Force Matrix 229
9.4.2 Boundary Force Matrix 230
9.5 Generalization of Boundary Conditions 231
9.6 Discussion 239
9.7 Linear Elasticity Equations in Three Dimensions 240
Problems 241
10 Finite Element Formulation for Beams 249
10.1 Governing Equations of the Beam 249
10.1.1 Kinematics of Beam 249
10.1.2 Stress–Strain Law 252
10.1.3 Equilibrium 253
10.1.4 Boundary Conditions 254
10.2 Strong Form toWeak Form 255
10.2.1 Weak Form to Strong Form 257
10.3 Finite Element Discretization 258
10.3.1 Trial Solution andWeight Function Approximations 258
10.3.2 Discrete Equations 260
10.4 Theorem of Minimum Potential Energy 261
10.5 Remarks on Shell Elements 265
Reference 269
Problems 269
11 Commercial Finite Element Program ABAQUS Tutorials 275
11.1 Introduction 275
11.1.1 Steady-State Heat Flow Example 275
11.2 Preliminaries 275
11.3 Creating a Part 276
11.4 Creating a Material Definition 278
11.5 Defining and Assigning Section Properties 279
11.6 Assembling the Model 280
11.7 Configuring the Analysis 280
11.8 Applying a Boundary Condition and a Load to the Model 280
11.9 Meshing the Model 282
11.10 Creating and Submitting an Analysis Job 284
11.11 Viewing the Analysis Results 284
11.12 Solving the Problem Using Quadrilaterals 284
11.13 Refining the Mesh 285
11.13.1 Bending of a Short Cantilever Beam 287
11.14 Copying the Model 287
11.15 Modifying the Material Definition 287
11.16 Configuring the Analysis 287
11.17 Applying a Boundary Condition and a Load to
the Model 288
11.18 Meshing the Model 289
11.19 Creating and Submitting an Analysis Job 290
11.20 Viewing the Analysis Results 290
11.20.1 Plate with a Hole in Tension 290
11.21 Creating a New Model 292
11.22 Creating a Part 292
11.23 Creating a Material Definition 293
11.24 Defining and Assigning Section Properties 294
11.25 Assembling the Model 295
11.26 Configuring the Analysis 295
11.27 Applying a Boundary Condition and a Load to the Model 295
11.28 Meshing the Model 297
11.29 Creating and Submitting an Analysis Job 298
11.30 Viewing the Analysis Results 299
11.31 Refining the Mesh 299
Appendix 303
A.1 Rotation of Coordinate System in Three Dimensions 303
A.2 Scalar Product Theorem 304
A.3 Taylor’s Formula with Remainder and the Mean Value Theorem 304
A.4 Green’s Theorem 305
A.5 Point Force (Source) 307
A.6 Static Condensation 308
A.7 Solution Methods 309
Direct Solvers 310
Iterative Solvers 310
Conditioning 311
References 312
Problem 312
Index 313

Total 344 pages 6.3 mb
Download

Read more...