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Book Cover
E-RESOURCE
Author Greenberg, Michael D., 1935-

Title Foundations of Applied Mathematics.

Published New York : Dover Publications, 2013.
©2013.

Copies

Location Call No. Status
 UniM INTERNET resource    AVAILABLE
Physical description 1 online resource (1398 pages)
polychrome rdacc
Contents Cover -- Fourier and Laplace Transform Tables, Inside Front Cover -- Title Page -- Copyright Page -- Dedication -- Contents -- Preface -- Part I Real Variable Theory -- Chapter 1 The Important Limit Processes -- 1.1. Functions and Functionals -- 1.2. Limits, Continuity, and Uniform Continuity -- 1.3. Differentiation -- 1.4. Integration -- 1.5. Asymptotic Notation and the "Big Oh" -- 1.6. Numerical Integration -- 1.7. Differentiation of Integrals Containing a Parameter -- Leibnitz's Rule -- Exercises -- Chapter 2 Infinite Series -- 2.1. Sequences and Series -- Fundamentals and Tests for Convergence -- 2.2. Series with Terms of Mixed Sign -- 2.3. Series with Terms That Are Functions -- Power Series -- 2.4. Taylor Series -- 2.5. That's All Very Nice, But How Do We Sum the Series? Acceleration Techniques -- *2.6. Asymptotic Expansions -- Exercises -- Chapter 3 Singular Integrals -- 3.1. Choice of Summability Criteria -- Convergence and Cauchy Principal Value -- 3.2. Tests for Convergence -- 3.3. The Gamma Function -- 3.4. Evaluation of Singular Integrals -- Exercises -- Chapter 4 Interchange of Limit Processes and the Delta Function -- 4.1. Theorems on Limit Interchange -- 4.2. The Delta Function and Generalized Functions -- Exercises -- Chapter 5 Fourier Series and the Fourier Integral -- 5.1. The Fourier Series of f(x) -- 5.2. Pointwise Convergence of the Series -- 5.3. Termwise Integration and Differentiation of Fourier Series -- 5.4. Variations : Periods Other than 2π, and Finite Interval -- 5.5. Infinite Period -- the Fourier Integral -- Exercises -- Chapter 6 Fourier and Laplace Transforms -- 6.1. The Fourier Transform -- 6.2. The Laplace Transform -- 6.3. Other Transforms -- Exercises -- Chapter 7 Functions of Several Variables -- 7.1. Chain Differentiation -- 7.2. Taylor Series in Two or More Variables -- Exercises.
Chapter 8 Vectors, Surfaces, and Volumes -- 8.1. Vectors and Elementary Operations -- 8.2. Coordinate Systems, Base Vectors, and Components -- 8.3. Angular Velocity of a Rigid Body -- 8.4. Curvilinear Coordinate Representation of Surfaces -- 8.5. Curvilinear Coordinate Representation of Volumes -- Exercises -- Chapter 9 Vector Field Theory -- 9.1. Line Integrals -- 9.2. The Curves, Surfaces, and Regions Under Consideration -- 9.3. Divergence, Gradient, and Curl -- 9.4. The Divergence Theorem -- 9.5. Stokes' Theorem -- 9.6. Irrotational and Solenoidal Fields -- 9.7. Noncartesian Systems -- 9.8. Fluid Mechanics -- Irrotational Flow -- 9.9. The Gravitational Potential -- Exercises -- Chapter 10 The Calculus of Variations -- 10.1. Functions of One or More Variables -- 10.2. Constraints -- Lagrange Multipliers -- 10.3. Functionals and the Calculus of Variations -- 10.4. Two or More Dependent Variables -- Hamilton's Principle -- 10.5. Two or More Independent Variables -- Vibrating Strings and Membranes -- 10.6. The Ritz Method -- 10.7. Optimal Control -- Exercises -- Additional References for Part I -- Part II Complex Variables -- Chapter 11 Complex Numbers -- 11.1. The Algebra of Complex Numbers -- 11.2. The Complex Plane -- Exercises -- Chapter 12 Functions of a Complex Variable -- 12.1. Basic Notions -- 12.2. Differentiation and the Cauchy-Riemann Conditions for Analyticity -- 12.3. Harmonic Functions -- 12.4. Some Elementary Functions and Their Singularities -- 12.5. Multivaluedness and the Need for Branch Cuts -- Exercises -- Chapter 13 Integration, Cauchy's Theorem, and the Cauchy Integral Formula -- 13.1. Integration in the Complex Plane -- 13.2. Bounds on Contour Integrals -- 13.3. Cauchy's Theorem -- 13.4. An Important Little Integral -- 13.5. The Cauchy Integral Formula -- Exercises -- Chapter 14 Taylor and Laurent Series -- 14.1. Complex Series.
14.2. Taylor Series -- 14.3. Laurent Series -- 14.4. Classification of Isolated Singularities -- Exercises -- Chapter 15 The Residue Theorem and Contour Integration -- 15.1. The Residue Theorem -- 15.2. The Calculation of Residues -- 15.3. Applications -- 15.4. Cauchy Principal Value -- Exercises -- Chapter 16 Conformai Mapping -- 16.1. The Fundamental Problem -- 16.2. Conformality -- 16.3. The Bilinear Transformation and Applications -- Exercises -- Additional References for Part II -- Part III Linear Analysis -- Chapter 17 Linear Spaces -- 17.1. Introduction -- Extension to n tuples -- 17.2. The Definition of an Abstract Vector Space -- Introducing a Norm and Inner Product -- 17.3. Linear Dependence, Dimension, and Bases -- 17.4. Function Space -- *17.5. Continuity of the Inner Product -- Exercises -- Chapter 18 Linear Operators -- 18.1. Some Definitions -- 18.2. Operator Algebra -- 18.3. Further Discussion of Matrices -- 18.4. The Adjoint Operator -- Exercises -- Chapter 19 The Linear Equation Lx = c -- 19.1. Introduction -- 19.2. Existence and Uniqueness -- 19.3. The Inverse Operator L- 1 -- The Inverse of a Matrix -- *Inverse of I + M where M is Small -- the Neumann Series -- Exercises -- Chapter 20 The Eigenvalue Problem Lx = λx -- 20.1. Statement of the Eigenvalue Problem -- 20.2. Some Eigenhunts -- 20.3. The Sturm-Liouville Theory -- 20.4. Additional Discussion for the Matrix Case -- The Inertia Tensor -- 20.5. The Inhomogeneous Problem Lx = c -- 20.6. Eigen Bounds and Estimates -- Exercises -- Additional References for Part III -- Part IV Ordinary Differential Equations -- Chapter 21 First-Order Equations -- 21.1. Standard Methods of Solution -- Variables Separable -- Homogeneous of Degree Zero -- Exact Differentials and Integrating Factors -- 21.2. The Questions of Existence and Uniqueness -- Exercises -- Chapter 22 Higher-Order Systems.
*22.1. Nonlinear Case -- Existence and Uniqueness -- 22.2. The Linear Equation -- Some Theory -- 22.3. The Linear Equation -- Some Methods of Solution -- 22.4. Series Solution -- Bessel and Legendre Functions -- 22.5. The Method of Green's Functions -- 22.6. Some Nonlinear Problems and Techniques -- Nonlinear Algebraic Equations -- Application to Nonlinear Differential Equations -- Exercises -- Chapter 23 Qualitative Methods -- The Phase Plane -- 23.1. The Phase Plane and Some Simple Examples -- 23.2. Singular Points -- 23.3. Additional Examples -- Exercises -- Chapter 24 Quantitative Methods -- 24.1. The Methods of Taylor and Euler -- 24.2. Improvements: Midpoint Rule and Runge-Kutta -- 24.3. Stability -- 24.4. Application to Higher-Order Systems -- 24.5. Boundary Value Problems -- *Invariant Imbedding -- 24.6. The Method of Weighted Residuals -- 24.7. The Finite-Element Method -- Exercises -- Chapter 25 Perturbation Techniques -- 25.1. Introduction -- the Regular Case -- 25.2. Singular Perturbations: Straining Methods -- 25.3. Singular Perturbations: Boundary Layer Methods -- Exercises -- Additional References for Part IV -- Part V Partial Differential Equations -- Chapter 26 Separation of Variables and Transform Methods -- 26.1. Introduction -- 26.2. Some Background -- the Sturm-Liouville Theory -- 26.3. The Diffusion Equation -- 26.4. The Wave Equation -- 26.5. The Laplace Equation -- Exercises -- Chapter 27 Classification and the Method of Characteristics -- 27.1. Characteristics and Classification -- 27.2. The Hyperbolic Case -- 27.3. Reduction of Aϕxx + 2Bϕxy + Cϕyy = F to Normal Form -- 27.4. Comparison of Hyperbolic, Elliptic, and Parabolic Systems -- Summary -- Exercises -- Chapter 28 Green's Functions and Perturbation Techniques -- 28.1. The Green's Function Approach -- 28.2. Perturbation Methods -- Exercises.
Chapter 29 Finite-Difference Methods -- 29.1. The Heat Equation -- An Explicit Method and Its Convergence and Stability -- 29.2. The Heat Equation -- Implicit Methods -- 29.3. Hyperbolic and Elliptic Problems -- Exercises -- Additional References for Part V -- Survey-Type References -- Answers to Selected Exercises -- Index -- Some Frequently Needed Formulas, Inside Back Cover.
Summary Classic text/reference suitable for undergraduate and graduate engineering students. Topics include real variable theory, complex variables, linear analysis, partial and ordinary differential equations, and other subjects. Includes answers to selected exercises. 1978 edition.
Notes Description based on publisher supplied metadata and other sources.
Local Note Electronic reproduction. Ann Arbor, Michigan : ProQuest Ebook Central, 2018. Available via World Wide Web. Access may be limited to ProQuest Ebook Central affiliated libraries.
Subject Mathematics.
Applied.
Electronic books.
ISBN 9780486782188 (electronic bk.)
9780486492797