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Differential equations for engineers : the essentials / by David V. Kalbaugh.
Author
Kalbaugh, David V.
[Browse]
Format
Book
Language
English
Published/Created
Boca Raton, FL : CRC Press, Taylor & Francis Group, [2018]
Description
xvii, 433 pages ; 26 cm
Availability
Available Online
Taylor & Francis eBooks Complete
SCI-TECHnetBASE
Copies in the Library
Location
Call Number
Status
Location Service
Notes
Engineering Library - Stacks
TA347.D45 K35 2018
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Details
Subject(s)
Differential equations
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Engineering mathematics
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Bibliographic references
Includes bibliographical references and index.
Contents
Machine generated contents note: ch. 1 Introduction
1.1. Foundations
1.1.1. Arithmetic
1.1.2. Algebra
1.1.2.1. Quadratic Equations
1.1.2.2. Higher-Order Polynomial Equations
1.1.2.3. Systems of Simultaneous Linear Equations
1.1.2.4. Logarithms and Exponentials
1.1.3. Trigonometry
1.1.4. Differential Calculus
1.1.4.1. Derivative
1.1.4.2. Rules of Differentiation
1.1.4.3. Infinite Series
1.1.5. Integral Calculus
1.1.5.1. Change of Variable
1.1.5.2. Integration by Parts
1.1.6. Transitioning to First-Order Ordinary Differential Equations
1.2. Classes of Differential Equations
1.3. A Few Other Things
1.4. Summary
Solved Problems
Problems to Solve
Word Problems
Challenge Problems
ch. 2 First-Order Linear Ordinary Differential Equations
2.1. First-Order Linear Homogeneous Ordinary Differential Equations
2.1.1. Example: RC Circuit
2.1.2. Time-Varying Equations and Justification of Separation of Variables Procedure
2.2. First-Order Linear Nonhomogeneous Ordinary Differential Equations
2.2.1. Integrating Factor
2.2.2. Kernel and Convolution
2.2.3. System Viewpoint
2.3. System Stability
2.4. Summary
ch. 3 First-Order Nonlinear Ordinary Differential Equations
3.1. Nonlinear Separable Ordinary Differential Equations
3.1.1. Example: Sounding Rocket Trajectory
3.1.1.1. Maximum Speed Going Up
3.1.1.2. Maximum Altitude
3.1.1.3. Maximum Speed Coming Down
3.2. Possibility of Transforming Nonlinear Equations into Linear Ones
3.3. Successive Approximations for almost Linear Systems
3.4. Summary
Computing Projects: Phase 1
ch. 4 Existence, Uniqueness, and Qualitative Analysis
4.1. Motivation
4.2. Successive Approximations (General Form)
4.2.1. Successive Approximations Example
4.3. Existence and Uniqueness Theorem
4.3.1. Lipschitz Condition
4.3.2. Statement of the Existence and Uniqueness Theorem
4.3.3. Successive Approximations Converge to a Solution
4.4. Qualitative Analysis
4.5. Stability Revisited
4.6. Local Solutions
4.7. Summary
ch. 5 Second-Order Linear Ordinary Differential Equations
5.1. Second-Order Linear Time-Invariant Homogeneous Ordinary Differential Equations
5.1.1. Two Real Roots
5.1.2. Repeated Roots
5.1.3. Complex Conjugate Roots
5.1.4. Under-, Over-, and Critically Damped Systems
5.1.5. Stability of Second-Order Systems
5.2. Fundamental Solutions
5.3. Second-Order Linear Nonhomogeneous Ordinary Differential Equations
5.3.1. Example: Automobile Cruise Control
5.3.2. Variation of Parameters (Kernel) Method
5.3.3. Undetermined Coefficients Method
5.3.3.1. Steady-State Solutions
5.3.3.2. Example: RLC Circuit with Sine-Wave Source
5.3.3.3. Resonance with a Sine-Wave Source
5.3.3.4. Resonance with a Periodic Input Other than a Sine Wave
5.3.3.5. Satisfying Initial Conditions Using the Undetermined Coefficients Method
5.3.3.6. Limitations of the Undetermined Coefficients Method
5.4. Existence and Uniqueness of Solutions to Second-Order Linear Ordinary Differential Equations
5.5. Summary
ch. 6 Higher-Order Linear Ordinary Differential Equations
6.1. Example: Satellite Orbit Decay
6.2. Higher-Order Homogeneous Linear Equations
6.3. Higher-Order Nonhomogeneous Linear Equations
6.3.1. Variation of Parameters (Kernel) Method
6.3.2. Undetermined Coefficients Method
6.4. Existence and Uniqueness
6.5. Stability of Higher-Order Systems
6.6. Summary
Computing Projects: Phase 2
ch. 7 Laplace Transforms
7.1. Preliminaries
7.2. Introducing the Laplace Transform
7.3. Laplace Transforms of Some Common Functions
7.4. Laplace Transforms of Derivatives
7.5. Laplace Transforms in Homogeneous Ordinary Differential Equations
7.6. Laplace Transforms in Nonhomogeneous Ordinary Differential Equations
7.6.1. General Solution Using Laplace Transforms
7.6.2. Laplace Transform of a Convolution
7.6.3. Differential Equations with Impulsive and Discontinuous Inputs
7.6.3.1. Defining the Dirac Delta Function
7.6.3.2. Ordinary Differential Equations with Impulsive Inputs
7.6.3.3. Ordinary Differential Equations with Discontinuous Inputs
7.6.4. Initial and Final Value Theorems
7.6.5. Ordinary Differential Equations with Periodic Inputs
7.6.5.1. Response to a Periodic Input
7.6.5.2. Resonance with a Nonsinusoidal Periodic Input
7.7. Summary
ch. 8 Systems of First-Order Ordinary Differential Equations
8.1. Preliminaries
8.2. Existence and Uniqueness
8.3. Numerical Integration Methods
8.3.1. Euler Method
8.3.2. Runge
Kutta Method
8.3.3. Comparing Accuracy of Euler and Runge
Kutta Methods
8.3.4. Variable Step Size
8.3.5. Other Numerical Integration Algorithms
8.4. Review of Matrix Algebra
8.5. Linear Systems in State Space Format
8.5.1. Homogeneous Linear Time-Invariant Systems
8.5.1.1. Real, Distinct Eigenvalues: Heat Transfer Example
8.5.1.2. Complex Eigenvalues: Electric Circuit Example
8.5.1.3. Complex Eigenvalues: Aircraft Dynamics Example
8.5.1.4. Repeated Eigenvalues
8.5.1.5. State Transition Matrix
8.5.1.6. Linear System Stability in State Space
8.5.1.7. Coordinate Systems: Road Vehicle Dynamics
8.5.1.8. Coordinate Systems: A General Analytic Approach
8.5.1.9. A System Viewpoint on Coordinate Systems
8.5.2. Nonhomogeneous Linear Systems
8.5.2.1. Matrix Kernel Method
8.5.2.2. Matrix Laplace Transform Method
8.5.2.3. Matrix Undetermined Coefficients Method
8.5.2.4. Worth of the Three Methods, in Summary
8.6. A Brief Look at N-Dimensional Nonlinear Systems
8.6.1. Equilibrium Points
8.6.2. Stability
8.6.3. Imposition of Limits
8.6.4. Uniquely Nonlinear Dynamics
8.6.5. Mathematical Modeling Tools for Nonlinear Systems
8.7. Summary
ch.
9 Partial Differential Equations
9.1. Heat Equation
9.1.1. Heat Equation in Initial Value Problems
9.1.1.1. Heat Equation in an Example Initial Value Problem
9.1.1.2. Existence and Uniqueness of Solutions to Parabolic Partial Differential Equations in Initial Value Problems
9.1.2. Heat Equation in Boundary Value Problems
9.2. Wave Equation and Power Series Solutions
9.2.1. Wave Equation in Initial Value Problems
9.2.1.1. Traveling Plane Wave
9.2.1.2. Traveling Wave in Spherical Coordinates
9.2.2. Wave Equation in Boundary Value Problems
9.2.2.1. Derivation of the Wave Equation for a Taut Membrane
9.2.2.2. Solving the Wave Equation in a Boundary Value Problem in Cylindrical Coordinates
9.2.3. Power Series Solutions: An Introduction
9.2.4. Bessel Equations and Bessel Functions
9.2.4.1. Bessel Functions of the First Kind
9.2.4.2. Bessel Functions of the Second Kind
9.2.5. Power Series Solutions: Another Example
9.2.6. Power Series Solutions: Some General Rules
9.2.6.1. A Few Definitions
9.2.6.2. Some General Rules
9.2.6.3. Special Cases
9.3. Laplace's Equation
9.3.1. Laplace's Equation Example in Spherical Coordinates
9.4. Beam Equation
9.4.1. Deriving the Beam Equation
9.4.2. Beam Equation in a Boundary Value Problem
9.4.3. Orthogonality of the Beam Equation Eigenfunctions
9.4.4. Nonhomogenous Boundary Value Problems
9.4.5. Other Geometries
9.5. Summary
Challenge Problems.
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ISBN
9781498798815 (hardcover : acid-free paper)
1498798810 (hardcover : acid-free paper)
LCCN
2017016364
OCLC
982654393
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Differential Equations for Engineers : The Essentials / David V. Kalbaugh.
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