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Table of Contents:
1. First-Order Differential Equations 2. Mathematical Models and Numerical Methods 3. Linear Equations of Higher Order 4. Introduction to Systems of Differential Equations 5. Linear Systems of Differential Equations 6. Nonlinear Systems and Phenomena 7. Laplace Transform Methods 8. Power Series Methods 9. Fourier Series Methods and Partial Differential Equations 10. Eigenvalue Methods and Boundary Value Problems Language: English Design of Fluid Thermal Systems SI Edition 4th Edition by William S Janna solution manual differential equations and boundary value problems computing and modeling 5th edition pdf
1.1 Differential Equations and Mathematical Models
1.2 Integrals as General and Particular Solutions
1.3 Slope Fields and Solution Curves
1.4 Separable Equations and Applications
1.5 Linear First-Order Equations
1.6 Substitution Methods and Exact Equations
2.1 Population Models
2.2 Equilibrium Solutions and Stability
2.3 Acceleration—Velocity Models
2.4 Numerical Approximation: Euler’s Method
2.5 A Closer Look at the Euler Method
2.6 The Runge—Kutta Method
3.1 Introduction: Second-Order Linear Equations
3.2 General Solutions of Linear Equations
3.3 Homogeneous Equations with Constant Coefficients
3.4 Mechanical Vibrations
3.5 Nonhomogeneous Equations and Undetermined Coefficients
3.6 Forced Oscillations and Resonance
3.7 Electrical Circuits
3.8 Endpoint Problems and Eigenvalues
4.1 First-Order Systems and Applications
4.2 The Method of Elimination
4.3 Numerical Methods for Systems
5.1 Matrices and Linear Systems
5.2 The Eigenvalue Method for Homogeneous Systems
5.3 A Gallery of Solution Curves of Linear Systems
5.4 Second-Order Systems and Mechanical Applications
5.5 Multiple Eigenvalue Solutions
5.6 Matrix Exponentials and Linear Systems
5.7 Nonhomogeneous Linear Systems
6.1 Stability and the Phase Plane
6.2 Linear and Almost Linear Systems
6.3 Ecological Models: Predators and Competitors
6.4 Nonlinear Mechanical Systems
6.5 Chaos in Dynamical Systems
7.1 Laplace Transforms and Inverse Transforms
7.2 Transformation of Initial Value Problems
7.3 Translation and Partial Fractions
7.4 Derivatives, Integrals, and Products of Transforms
7.5 Periodic and Piecewise Continuous Input Functions
7.6 Impulses and Delta Functions
8.1 Introduction and Review of PowerSeries
8.2 Series Solutions Near Ordinary Points
8.3 Regular Singular Points
8.4 Method of Frobenius: The Exceptional Cases
8.5 Bessel’s Equation
8.6 Applications of Bessel Functions
9.1 Periodic Functions and Trigonometric Series
9.2 General Fourier Series and Convergence
9.3 Fourier Sine and Cosine Series
9.4 Applications of Fourier Series
9.5 Heat Conduction and Separation of Variables
9.6 Vibrating Strings and the One-Dimensional Wave Equation
9.7 Steady-State Temperature and Laplace’s Equation
10.1 Sturm—Liouville Problems and Eigenfunction Expansions
10.2 Applications of Eigenfunction Series
10.3 Steady Periodic Solutions and Natural Frequencies
10.4 Cylindrical Coordinate Problems
10.5 Higher-Dimensional Phenomena
ISBN-10: 0321796985
ISBN-13: 978-0321796981
ISBN-13: 9780321796981
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