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    Numerical methods for engineers / Steven C. Chapra, Berger chair in computing and engineering, Tufts University, Raymond P. Canale, professor emeritus of civil engineering, University of Michigan.

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    • Title:Numerical methods for engineers / Steven C. Chapra, Berger chair in computing and engineering, Tufts University, Raymond P. Canale, professor emeritus of civil engineering, University of Michigan.
    •    
    • Author/Creator:Chapra, Steven C.
    • Other Contributors/Collections:Canale, Raymond P.
    • Published/Created:New York, NY : McGraw-Hill Education, [2015]

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    • Library of Congress Subjects:Engineering mathematics--Data processing.
      Numerical calculations--Data processing.
      Microcomputers--Programming.
    • Edition:Seventh edition.
    • Description:xvi, 970 pages : illustrations ; 24 cm
    • Summary:"The seventh edition of Chapra and Canale's Numerical Methods for Engineers retains the instructional techniques that have made the text so successful. Numerous new or revised problems are drawn from actual engineering practice. The expanded breadth of engineering disciplines covered is especially evident in these exercises, which now cover such areas as biotechnology and biomedical engineering. Excellent new examples and case studies span all areas of engineering giving students a broad exposure to various fields in engineering." -- Provided by publisher.
    • Notes:Includes bibliographical references (pages 954-956) and index.
    • ISBN:9780073397924 (alk. paper)
      007339792X (alk. paper)
    • Contents:Machine generated contents note: pt. ONE MODELING, COMPUTERS, AND ERROR ANALYSIS
      Pt1.1. Motivation
      Pt1.2. Mathematical Background
      Pt1.3. Orientation
      ch. 1 Mathematical Modeling and Engineering Problem Solving
      1.1. Simple Mathematical Model
      1.2. Conservation Laws and Engineering
      Problems
      ch. 2 Programming and Software
      2.1. Packages and Programming
      2.2. Structured Programming
      2.3. Modular Programming
      2.4. Excel
      2.5. MATLAB
      2.6. Mathcad
      2.7. Other Languages and Libraries
      Problems
      ch. 3 Approximations and Round-Off Errors
      3.1. Significant Figures
      3.2. Accuracy and Precision
      3.3. Error Definitions
      3.4. Round-Off Errors
      Problems
      ch. 4 Truncation Errors and the Taylor Series
      4.1. Taylor Series
      4.2. Error Propagation
      4.3. Total Numerical Error
      4.4. Blunders, Formulation Errors, and Data Uncertainty
      Problems
      Epilogue: Part One
      Pt1.4. Trade-Offs
      Pt1.5. Important Relationships and Formulas
      Pt1.6. Advanced Methods and Additional References
      pt. TWO ROOTS OF EQUATIONS
      Pt2.1. Motivation
      Pt2.2. Mathematical Background
      Pt2.3. Orientation
      ch. 5 Bracketing Methods
      5.1. Graphical Methods
      5.2. Bisection Method
      5.3. False-Position Method
      5.4. Incremental Searches and Determining Initial Guesses
      Problems
      ch. 6 Open Methods
      6.1. Simple Fixed-Point Iteration
      6.2. Newton-Raphson Method
      6.3. Secant Method
      6.4. Brent's Method
      6.5. Multiple Roots
      6.6. Systems of Nonlinear Equations
      Problems
      ch. 7 Roots of Polynomials
      7.1. Polynomials in Engineering and Science
      7.2. Computing with Polynomials
      7.3. Conventional Methods
      7.4. Muller's Method
      7.5. Bairstow's Method
      7.6. Other Methods
      7.7. Root Location with Software Packages
      Problems
      ch. 8 Case Studies: Roots of Equations
      8.1. Ideal and Nonideal Gas Laws (Chemical/Bio Engineering)
      8.2. Greenhouse Gases and Rainwater (Civil/Environmental Engineering)
      8.3. Design of an Electric Circuit (Electrical Engineering)
      8.4. Pipe Friction (Mechanical/Aerospace Engineering)
      Problems
      Epilogue: Part Two
      Pt2.4. Trade-Offs
      Pt2.5. Important Relationships And Formulas
      Pt2.6. Advanced Methods And Additional References
      pt. THREE LINEAR ALGEBRAIC EQUATIONS
      Pt3.1. Motivation
      Pt3.2. Mathematical Background
      Pt3.3. Orientation
      ch. 9 Gauss Elimination
      9.1. Solving Small Numbers of Equations
      9.2. Naive Gauss Elimination
      9.3. Pitfalls of Elimination Methods
      9.4. Techniques for Improving Solutions
      9.5. Complex Systems
      9.6. Nonlinear Systems of Equations
      9.7. Gauss-Jordan
      9.8. Summary
      Problems
      ch. 10 LU Decomposition and Matrix Inversion
      10.1. LU Decomposition
      10.2. Matrix Inverse
      10.3. Error Analysis and System Condition
      Problems
      ch. 11 Special Matrices and Gauss-Seidel
      11.1. Special Matrices
      11.2. Gauss-Seidel
      11.3. Linear Algebraic Equations with Software Packages
      Problems
      ch. 12 Case Studies: Linear Algebraic Equations
      12.1. Steady-State Analysis of a System of Reactors (Chemical/Bio Engineering)
      12.2. Analysis of a Statically Determinate Truss (Civil/Environmental Engineering)
      12.3. Currents and Voltages in Resistor Circuits (Electrical Engineering)
      12.4. Spring-Mass Systems (Mechanical/Aerospace Engineering)
      Problems
      Epilogue: Part Three
      Pt3.4. Trade-Offs
      Pt3.5. Important Relationships and Formulas
      Pt3.6. Advanced Methods and Additional References
      pt. FOUR OPTIMIZATION
      Pt4.1. Motivation
      Pt4.2. Mathematical Background
      Pt4.3. Orientation
      ch. 13 One-Dimensional Unconstrained Optimization
      13.1. Golden-Section Search
      13.2. Parabolic Interpolation
      13.3. Newton's Method
      13.4. Brent's Method
      Problems
      ch. 14 Multidimensional Unconstrained Optimization
      14.1. Direct Methods
      14.2. Gradient Methods
      Problems
      ch. 15 Constrained Optimization
      15.1. Linear Programming
      15.2. Nonlinear Constrained Optimization
      15.3. Optimization with Software Packages
      Problems
      ch. 16 Case Studies: Optimization
      16.1. Least-Cost Design of a Tank (Chemical/Bio Engineering)
      16.2. Least-Cost Treatment of Wastewater (Civil/Environmental Engineering)
      16.3. Maximum Power Transfer for a Circuit (Electrical Engineering)
      16.4. Equilibrium and Minimum Potential Energy (Mechanical/Aerospace Engineering)
      Problems
      Epilogue: Part Four
      Pt4.4. Trade-Offs
      Pt4.5. Additional References
      pt. FIVE CURVE FITTING
      Pt5.1. Motivation
      Pt5.2. Mathematical Background
      Pt5.3. Orientation
      ch. 17 Least-Squares Regression
      17.1. Linear Regression
      17.2. Polynomial Regression
      17.3. Multiple Linear Regression
      17.4. General Linear Least Squares
      17.5. Nonlinear Regression
      Problems
      ch. 18 Interpolation
      18.1. Newton's Divided-Difference Interpolating Polynomials
      18.2. Lagrange Interpolating Polynomials
      18.3. Coefficients of an Interpolating Polynomial
      18.4. Inverse Interpolation
      18.5. Additional Comments
      18.6. Spline Interpolation
      18.7. Multidimensional Interpolation
      Problems
      ch. 19 Fourier Approximation
      19.1. Curve Fitting with Sinusoidal Functions
      19.2. Continuous Fourier Series
      19.3. Frequency and Time Domains
      19.4. Fourier Integral and Transform
      19.5. Discrete Fourier Transform (DFT)
      19.6. Fast Fourier Transform (FFT)
      19.7. Power Spectrum
      19.8. Curve Fitting with Software Packages
      Problems
      ch. 20 Case Studies: Curve Fitting
      20.1. Linear Regression and Population Models (Chemical/Bio Engineering)
      20.2. Use of Splines to Estimate Heat Transfer (Civil/Environmental Engineering)
      20.3. Fourier Analysis (Electrical Engineering)
      20.4. Analysis of Experimental Data (Mechanical/Aerospace Engineering)
      Problems
      Epilogue: Part Five
      Pt5.4. Trade-Offs
      Pt5.5. Important Relationships and Formulas
      Pt5.6. Advanced Methods and Additional References
      pt. SIX NUMERICAL DIFFERENTATION AND INTEGRATION
      Pt6.1. Motivation
      Pt6.2. Mathematical Background
      Pt6.3. Orientation
      ch. 21 Newton-Cotes Integration Formulas
      21.1. Trapezoidal Rule
      21.2. Simpson's Rules
      21.3. Integration with Unequal Segments
      21.4. Open Integration Formulas
      21.5. Multiple Integrals
      Problems
      ch. 22 Integration of Equations
      22.1. Newton-Cotes Algorithms for Equations
      22.2. Romberg Integration
      22.3. Adaptive Quadrature
      22.4. Gauss Quadrature
      22.5. Improper Integrals
      Problems
      ch. 23 Numerical Differentiation
      23.1. High-Accuracy Differentiation Formulas
      23.2. Richardson Extrapolation
      23.3. Derivatives of Unequally Spaced Data
      23.4. Derivatives and Integrals for Data with Errors
      23.5. Partial Derivatives
      23.6. Numerical Integration/Differentiation with Software Packages
      Problems
      ch. 24 Case Studies: Numerical Integration and Differentiation
      24.1. Integration to Determine the Total Quantity of Heat (Chemical/Bio Engineering)
      24.2. Effective Force on the Mast of a Racing Sailboat (Civil/Environmental Engineering)
      24.3. Root-Mean-Square Current by Numerical Integration (Electrical Engineering)
      24.4. Numerical Integration to Compute Work (Mechanical/Aerospace Engineering)
      Problems
      Epilogue: Part Six
      Pt6.4. Trade-Offs
      Pt6.5. Important Relationships and Formulas
      Pt6.6. Advanced Methods and Additional References
      pt. SEVEN ORDINARY DIFFERENTIAL EQUATIONS
      Pt7.1. Motivation
      Pt7.2. Mathematical Background
      Pt7.3. Orientation
      ch. 25 Runge-Kutta Methods
      25.1. Euler's Method
      25.2. Improvements of Euler's Method
      25.3. Runge-Kutta Methods
      25.4. Systems of Equations
      25.5. Adaptive Runge-Kutta Methods
      Problems
      ch. 26 Stiffness and Multistep Methods
      26.1. Stiffness
      26.2. Multistep Methods
      Problems
      ch. 27 Boundary-Value and Eigenvalue Problems
      27.1. General Methods for Boundary-Value Problems
      27.2. Eigenvalue Problems
      27.3. Odes and Eigenvalues with Software Packages
      Problems
      ch. 28 Case Studies: Ordinary Differential Equations
      28.1. Using ODEs to Analyze the Transient Response of a Reactor (Chemical/Bio Engineering)
      28.2. Predator-Prey Models and Chaos (Civil/Environmental Engineering)
      28.3. Simulating Transient Current for an Electric Circuit (Electrical Engineering)
      28.4. Swinging Pendulum (Mechanical/Aerospace Engineering)
      Problems
      Epilogue: Part Seven
      Pt7.4. Trade-Offs
      Pt7.5. Important Relationships and Formulas
      Pt7.6. Advanced Methods and Additional References
      pt. EIGHT PARTIAL DIFFERENTIAL EQUATIONS
      Pt8.1. Motivation
      Pt8.2. Orientation
      ch. 29 Finite Difference: Elliptic Equations
      29.1. Laplace Equation
      29.2. Solution Technique
      29.3. Boundary Conditions
      29.4. Control-Volume Approach
      29.5. Software to Solve Elliptic Equations
      Problems
      ch. 30 Finite Difference: Parabolic Equations
      30.1. Heat-Conduction Equation
      30.2. Explicit Methods
      30.3. Simple Implicit Method
      30.4. Crank-Nicolson Method
      30.5. Parabolic Equations in Two Spatial Dimensions
      Problems
      ch. 31 Finite-Element Method
      31.1. General Approach
      Contents note continued: 31.2. Finite-Element Application in One Dimension
      31.3. Two-Dimensional Problems
      31.4. Solving PDEs with Software Packages
      Problems
      ch. 32 Case Studies: Partial Differential Equations
      32.1. One-Dimensional Mass Balance of a Reactor (Chemical/Bio Engineering)
      32.2. Deflections of a Plate (Civil/Environmental Engineering)
      32.3. Two-Dimensional Electrostatic Field Problems (Electrical Engineering)
      32.4. Finite-Element Solution of a Series of Springs (Mechanical/Aerospace Engineering)
      Problems
      Epilogue: Part Eight
      Pt8.3. Trade-Offs
      Pt8.4. Important Relationships And Formulas
      Pt8.5. Advanced Methods And Additional References.
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