Nguồn ngoài

Differential Equations for Engineers

A one semester first course on differential equations, aimed at engineering students. Prerequisite for the course is the basic calculus sequence.

Differential Equations Mathematics

Tác giả: Jiří Lebl
Nhà xuất bản: Oklahoma State University
Nguồn: LibreTexts
Giấy phép: CC BY-SA
Ngôn ngữ: EN
Danh mục: Khoa học cơ bản

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0: Introduction
0.1: Notes About These Notes
0.2: Introduction to Differential Equations
0.3: Classification of Differential Equations
0.E: Introduction (Exercises)
1: First order ODEs
1.1: Integrals as solutions
1.2: Slope fields
1.3: Separable Equations
1.4: Linear equations and the integrating factor
1.5: Substitution
1.6: Autonomous equations
1.7: Numerical methods: Eulers method
1.8: Exact Equations
1.9: First Order Linear PDE
1.E: First order ODEs (Exercises)
2: Higher order linear ODEs
2.1: Second order linear ODEs
2.2: Constant coefficient second order linear ODEs
2.3: Higher order linear ODEs
2.4: Mechanical Vibrations
2.5: Nonhomogeneous Equations
2.6: Forced Oscillations and Resonance
2.E: Higher order linear ODEs (Exercises)
3: Systems of ODEs
3.1: Introduction to Systems of ODEs
3.2: Matrices and linear systems
3.3: Linear systems of ODEs
3.4: Eigenvalue Method
3.5: Two dimensional systems and their vector fields
3.6: Second order systems and applications
3.7: Multiple Eigenvalues
3.8: Matrix exponentials
3.9: Nonhomogeneous systems
3.E: Systems of ODEs (Exercises)
4: Fourier series and PDEs
4.01: Boundary value problems
4.02: The trigonometric series
4.03: More on the Fourier series
4.04: Sine and cosine series
4.05: Applications of Fourier series
4.06: PDEs separation of variables and the heat equation
4.07: One dimensional wave equation
4.08: DAlembert solution of the wave equation
4.09: Steady state temperature and the Laplacian
4.10: Dirichlet Problem in the Circle and the Poisson Kernel
4.E: Fourier Series and PDEs (Exercises)
5: Eigenvalue problems
5.1: Sturm-Liouville problems
5.2: Application of Eigenfunction Series
5.3: Steady Periodic Solutions
5.E: Eigenvalue Problems (Exercises)
6: The Laplace Transform
6.1: The Laplace Transform
6.2: Transforms of derivatives and ODEs
6.3: Convolution
6.4: Dirac Delta and Impulse Response
6.5: Solving PDEs with the Laplace Transform
6.E: The Laplace Transform (Exercises)
7: Power series methods
7.1: Power Series
7.2: Series Solutions of Linear Second Order ODEs
7.3: Singular Points and the Method of Frobenius
7.E: Power series methods (Exercises)
8: Nonlinear Systems
8.1: Linearization critical points and equilibria
8.2: Stability and classication of isolated critical points
8.3: Applications of Nonlinear Systems
8.4: Limit cycles
8.5: Chaos
8.E: Nonlinear Equations (Exercises)
Appendix A: Linear Algebra
A.1: Vectors Mappings and Matrices
A.2: Matrix Algebra
A.3: Elimination
A.4: Subspaces Dimension and The Kernel
A.5: Inner Product and Projections
A.6: Determinant
A.E: Linear Algebra (Exercises)
Appendix B: Table of Laplace Transforms