Las ecuaciones diferenciales ordinarias constituyen el modelo matemático de numerosos fenómenos físicos y problemas de índole técnico. Esto hace que su conocimiento sea imprescindible para los estudiantes de Ciencias e Ingeniería.
Ecuaciones Diferenciales Elementales integra la teoría subyacente, los procedimientos de solución y los aspectos numéricos/computacionalesde las Ecuaciones Diferenciales en una forma perfecta. Por ejemplo, cada vez que un nuevo tipo de problema se presenta (por ejemplo, ecuaciones de primer orden, ecuaciones de orden superior, sistemas de ecuaciones diferenciales, etc), el texto comienza con la básica de existencia y unicidad teoría.
Esto proporciona al alumno el marco necesario para comprender y resolver ecuaciones diferenciales. Teoría se presenta como un simple como sea posible con un énfasis en cómo usarla. La tabla de contenido es amplio y permite una mayor flexibilidad para los instructores.
1.1 Examples of Differential Equations
1.2 Direction Fields2: FIRST ORDER DIFFERENTIAL EQUATIONS
2.1 Introduction
2.2 First Order Linear Differential Equations
2.3 Introduction to Mathematical Models
2.4 Population Dynamics and Radioactive Decay
2.5 First Order Nonlinear Differential Equations
2.6 Separable First Order Equations
2.7 Exact Differential Equations
2.8 The Logistic Population Model
2.9 Applications to Mechanics
2.10 Euler’s Method
3:SECOND AND HIGHER ORDER LINEAR DIFFERENTIAL EQUATIONS
3.1 Introduction
3.2 The General Solution of Homogeneous Equations
3.3 Constant Coefficient Homogeneous Equations
3.4 Real Repeated Roots; Reduction of Order
3.5 Complex Roots
3.6 Unforced Mechanical Vibrations
3.7 The General Solution of a Linear Nonhomogeneous Equation
3.8 The Method of Undetermined Coefficients
3.9 The Method of Variation of Parameters
3.10 Forced Mechanical Vibrations, Electrical Networks, and Resonance
3.11 Higher Order Linear Homogeneous Differential Equations
3.12 Higher Order Homogeneous Constant Coefficient Differential Equations
3.13 Higher Order Linear Nonhomogeneous Differential Equations
4: FIRST ORDER LINEAR SYSTEMS
4.1 Introduction
4.2 Existence and Uniqueness
4.3 Homogeneous Linear Systems
4.4 Constant Coefficient Homogeneous Systems and the Eigenvalue Problem
4.5 Real Eigenvalues and the Phase Plane
4.6 Complex Eigenvalues
4.7 Repeated Eigenvalues
4.8 Nonhomogeneous Linear Systems
4.9 Numerical Methods for Systems of Differential Equations
4.10 The Exponential Matrix and Diagonalization
5: LAPLACE TRANSFORMS
5.1 Introduction
5.2 Laplace Transform Pairs
5.3 The Method of Partial Fractions
5.4 Laplace Transforms of Periodic Functions and System Transfer Functions
5.5 Solving Systems of Differential Equations
5.6 Convolution
5.7 The Delta Function and Impulse Response
6: NONLINEAR SYSTEMS
6.1 Introduction
6.2 Equilibrium Solutions and Direction Fields
6.3 Conservative Systems
6.4 Stability
6.5 Linearization and the Local Picture
6.6 Two-Dimensional Linear Systems
6.7 Predator-Prey Population Models
7: NUMERICAL METHODS
7.1 Euler’s Method, Heun’s Method, the Modified Euler’s Method
7.2 Taylor Series Methods
7.3 Runge-Kutta Methods
8: SERIES SOLUTION OF DIFFERENTIAL EQUATIONS
8.1 Introduction
8.2 Series Solutions near an Ordinary Point
8.3 The Euler Equation
8.4 Solutions Near a Regular Singular Point and the Method of Frobenius
8.5 The Method of Frobenius Continued; Special Cases and a Summary
Autor/es: L. Johnson / W. Kohler
Edición: 2da Edición
ISBN: 0321290445
Tipo: Solucionario
Formato: PDF
Idioma: Inglés
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