Engineering Homework Help

Textbook: https://technicalbookspdf.com/download/2019/10/181019/Advanced%20Engineering%20Mathematics%20Sixth%20Edition%20by%20Dennis%20G.%20Zill.pdf

Chapter 3: Higher-Order Differential Equations

3.1 Theory of Linear Equations 106

3.1.1 Initial-Value and Boundary-Value Problems 106

3.1.2 Homogeneous Equations 108

3.1.3 Nonhomogeneous Equations 113

3.2 Reduction of Order 117

3.3 Homogeneous Linear Equations with Constant Coefficients 120

3.4 Undetermined Coefficients 127

3.5 Variation of Parameters 136

3.6 Cauchy–Euler Equations 141

3.7 Nonlinear Equations 147

3.8 Linear Models: Initial-Value Problems 151

3.8.1 Spring/Mass Systems: Free Undamped Motion 

3.8.2 Spring/Mass Systems: Free Damped Motion 155

3.8.3 Spring/Mass Systems: Driven Motion 158

3.8.4 Series Circuit Analogue 161

3.9 Linear Models: Boundary-Value Problems 167

3.10 Green’s Functions 177

3.10.1 Initial-Value Problems 177

3.10.2 Boundary-Value Problems 183

3.11 Nonlinear Models 187

3.12 Solving Systems of Linear Equations 196 Chapter 3 in Review 203

Chapter 8: Matrices

8.1 Matrix Algebra 368

8.2 Systems of Linear Algebraic Equations 376

8.3 Rank of a Matrix 389

8.4 Determinants 393

8.5 Properties of Determinants 399

8.6 Inverse of a Matrix 405

8.6.1 Finding the Inverse 405

8.6.2 Using the Inverse to Solve Systems 411

8.7 Cramer’s Rule 415

8.8 The Eigenvalue Problem 418

8.9 Powers of Matrices 426

8.10 Orthogonal Matrices