Linux Containers and Virtualization: Utilizing Rust for Linux Containers - Second Edition

Mathematics should always be read with pencil and paper at the ready because, most likely, you will have to work your way through the examples and the discussion. Before attempting any problems in the section exercise sets, work through all the examples in that section.The examples are constructed to illustrate what I consider the most important aspectsof the section, and therefore, reect the procedures necessary to work most of theproblems. When reading an example, copy it down on a piece of paper and do not look at the solution in the book. Try working it, then compare your results against the solution given, and, if necessary resolve any differences. I have tried to include most of the important steps in each example, but if something is not clear you should always try—and here is where the pencil and paper come in again—to ll in the details or missing steps. This may not be easy, but it is part of the learning process.The accumulation of facts followed by the slow assimilation of understanding simplycannot be achieved without a struggle. Cover Title Copyright Preface Contents 1. Introduction to Differential Equations 1.1 Denitions and Terminology 1.2 Initial-Value Problems 1.3 Differential Equations as Mathematical Models Chapter 1 In Review 2. First-Order Differential Equations 2.1 Solution Curves Without a Solution 2.1.1 Direction Fields 2.1.2 Autonomous First-Order DEs 2.2 Separable Equations 2.3 Linear Equations 2.4 Exact Equations 2.5 Solutions by Substitutions 2.6 A Numerical Method Chapter 2 In Review 3. Modeling with First-Order Differential Equations 3.1 Linear Models 3.2 Nonlinear Models 3.3 Modeling with Systems of First-Order DEs Chapter 3 In Review 4. Higher-Order Differential Equations 4.1 Preliminary Theory—Linear Equations 4.1.1 Initial-Value and Boundary-Value Problems 4.1.2 Homogeneous Equations 4.1.3 Nonhomogeneous Equations 4.2 Reduction of Order 4.3 Homogeneous Linear Equations with Constant Coefcients 4.4 Undetermined Coefcients—Superposition Approach 4.5 Undetermined Coefcients—Annihilator Approach 4.6 Variation of Parameters 4.7 Cauchy-Euler Equations 4.8 Green’s Functions 4.8.1 Initial-Value Problems 4.8.2 Boundary-Value Problems 4.9 Solving Systems of Linear DEs byElimination 4.10 Nonlinear Differential Equations Chapter 4 In Review 5. Modeling with Higher-Order Differential Equations 5.1 Linear Models: Initial-Value Problems 5.1.1 Spring/Mass Systems: Free Undamped Motion 5.1.2 Spring/Mass Systems: Free Damped Motion 5.1.3 Spring/Mass Systems: Driven Motion 5.1.4 Series Circuit Analogue 5.2 Linear Models: Boundary-Value Problems 5.3 Nonlinear Models Chapter 5 In Review 6. Series Solutions of Linear Equations 6.1 Review of Power Series 6.2 Solutions About Ordinary Points 6.3 Solutions About Singular Points 6.4 Special Functions Chapter 6 In Review 7. The Laplace Transform 7.1 Denition of the Laplace Transform 7.2 Inverse Transforms and Transforms ofDerivatives 7.2.1 Inverse Transforms 7.2.2 Transforms of Derivatives 7.3 Operational Properties I 7.3.1 Translation on the S-Axis 7.3.2 Translation on the t-Axis 7.4 Operational Properties II 7.4.1 Derivatives of a Transform 7.4.2 Transforms of Integrals 7.4.3 Transform of a Periodic Function 7.5 The Dirac Delta Function 7.6 Systems of Linear Differential Equations Chapter 7 In Review 8. Systems of Linear First-Order Differential Equations 8.1 Preliminary Theory—Linear Systems 8.2 Homogeneous Linear Systems 8.2.1 Distinct Real Eigenvalues 8.2.2 Repeated Eigenvalues 8.2.3 Complex Eigenvalues 8.3 Nonhomogeneous Linear Systems 8.3.1 Undetermined Coefcients 8.3.2 Variation of Parameters 8.4 Matrix Exponential Chapter 8 In Review 9. Numerical Solutions of Ordinary Differential Equations 9.1 Euler Methods and Error Analysis 9.2 Runge-Kutta Methods 9.3 Multistep Methods 9.4 Higher-Order Equations and Systems 9.5 Second-Order Boundary-Value Problems Chapter 9 In Review APPENDIXES A: Integral-Defined Functions B: Matrices C: Laplace Transforms ANSWERS for Selected Odd-Numbered Problems 1. 1.1 1.2 1.3 R 2. 2.1 2.2 2.3 2.4 2.5 2.6 R 3. 3.1 3.2 3.3 R 4. 4.1 4.2 4.3 4.4 4.5 4.6 4.7 4.8 4.9 4.10 R 5. 5.1 5.2 5.3 R 6. 6.1 6.2 6.3 6.4 R 7. 7.1 7.2 7.3 7.4 7.5 7.6 R 8. 8.1 8.2 8.3 8.4 R 9. 9.1 9.2 9.3 9.4 9.5 R appA appB Index A B C D E F G H I K L M N O P Q R S T U V W Y Z