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

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Location Call Number Status Location Service Notes
Engineering Library - Stacks TA347.D45 K35 2018 Browse related items Request

    Details

    Subject(s)
    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.
    ISBN
    • 9781498798815 (hardcover : acid-free paper)
    • 1498798810 (hardcover : acid-free paper)
    LCCN
    2017016364
    OCLC
    982654393
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