Table of Engineering Applications
| Topic | Example or Section |
| Controls | |
| State-Space Models | Section 10.2.2 |
| Transfer Function Models | Section 10.2.3 |
| Model Connections – Closed-Loop Systems and System Response | Section 10.3 |
| PID Control System | Example 10.1 |
| Root Locus | Section 10.4.1 |
| Bode Plot | Section 10.4.2 |
| Nichols Plot | Section 10.4.3 |
| Engineering Mathematics | |
| Evaluating a Fourier Series | Example 2.1 |
| Convergence of a Series | Example 2.2 |
| Summing a Double Series | Example 2.3 |
| Solution of a System of Equations | Example 2.4 |
| Secant Method | Example 3.14 |
| Solution of a System of Equations | Example 4.2 |
| Radius of Curvature | Example 4.10 |
| Euler–Lagrange Equation | Example 4.11 |
| Fourier Coefficients | Example 4.13 |
| Cauchy Integral Formula | Example 4.18 |
| System of First-Order Equations and the Matrix Exponential | Example 4.23 |
| Laplace Transform Solution of an Inhomogeneous Differential Equation #1 | Example 4.29 |
| Laplace Transform Solution of an Inhomogeneous Differential Equation #2 | Example 4.31 |
| Limit Using Assumptions | Example 4.4 |
| Perturbation Solution #1 | Example 4.7 |
| Perturbation Solution #2 | Example 4.8 |
| Poincare Plot | Example 5.11 |
| Nonlinear Ordinary Differential Equation | Example 5.12 |
| Second-Order Differential Equation: Periodic Inhomogeneous Term | Example 5.15 |
| Interpolation Function from Some Data | Example 5.24 |
| Function’s Parameters for a Fit to Some Data | Example 5.25 |
| Parametric Solution to a Nonlinear Differential Equation | Example 5.26 |
| Fluid Mechanics | |
| Flow Around a Cylinder | Example 6.6 |
| Air Entrainment by Liquid Jets | Example 5.14 |
| Flow Around an Ellipse | Example 7.6 |
| Laminar Flow in Horizontal Cylindrical Pipes | Section 11.5.1 |
| Flow in Three Reservoirs | Section 11.5.2 |
| Pressure Coefficient of a Joukowski Airfoil | Section 11.6.1 |
| Surface Profile in Nonuniform Flow in Open Channels | Section 11.6.2 |
| Heat Transfer | |
| Heat Conduction in a Slab | Example 5.13 |
| One-Dimensional Transient Heat Diffusion in Solids | Section 11.2.1 |
| Heat Transfer in Concentric Spheres: Ablation of a Tumor | Section 11.2.2 |
| Heat Flow Through Fins | Section 11.2.3 |
| Natural Convection Along Heated Plates | Section 11.3 |
| View Factor Between Two Parallel Rectangular Surfaces | Section 11.4 |
| Kinematics | |
| Four-Bar Linkage | Example 7.7 |
| Signal Processing | |
| Spectral Analysis of a Sine Wave | Example 5.27 |
| Spectral Analysis of a Sine Wave of Finite Duration | Example 5.28 |
| Cross-Correlation of a Signal with Noise | Example 5.29 |
| Sum of Two Sinusoidal Signals | Example 7.2 |
| Steerable Sonar/Radar Array | Example 7.3 |
| Effects of Filters on Sinusoidal Signals | Example 10.2 |
| Effects of Windows on Spectral Analysis | Example 10.3 |
| Spectrum Averaging | Example 10.4 |
| Aliasing | Example 10.5 |
| Statistics | |
| Histograms | Example 9.1 |
| Whisker Plot | Section 9.1.5 |
| Confidence Intervals | Section 9.2.4 |
| Hypothesis Testing | Section 9.2.5 |
| Simple Linear Regression | Section 9.3.1 |
| Multiple Linear Regression | Section 9.3.2 |
| Nonlinear Regression Analysis | Section 9.4 |
| Two-Factor ANOVA | Example 9.2 |
| Four-Factor Factorial Analysis | Example 9.3 |
| Structures | |
| Analysis of Beams | Example 4.20 |
| Deformation of a Timoshenko Beam | Example 4.21 |
| Beam with a Concentrated Load | Example 5.4 |
| Beam with an Overhang | Example 5.5 |
| Beam with Abrupt Change in Properties | Example 5.6 |
| Deflection of a Uniformly Loaded Solid Circular Plate | Example 5.16 |
| von Mises Stress in a Stretched Plate with a Hole | Example 7.4 |
| Analysis of Beams | Example 7.5 |
| Vibrations | |
| Natural Frequencies of a Three Degrees-of-Freedom System | Example 2.5 |
| Natural Frequency Coefficient of a Two Degrees-of-Freedom System | Example 3.5 |
| Natural Frequencies of Beams | Example 4.5 |
| Peak Amplitude Response of a Single Degree-of-Freedom System | Example 4.9 |
| Response of a Two Degrees-of-Freedom System | Example 4.30 |
| Two Degrees-of-Freedom System Revisited | Example 5.7 |
| Particle Impact Damper | Example 5.8 |
| Change in Period of a Nonlinear System | Example 5.9 |
| Single Degree-of-Freedom System | Example 5.10 |
| Natural Frequencies of a Beam Clamped at Both Ends | Example 5.20 |
| Mode Shape of a Circular Membrane | Example 6.10 |
| Periodic Force on a Single Degree-of-Freedom System | Section 8.2.1 |
| Squeeze Film Damping and Viscous Fluid Damping | Section 8.2.2 |
| Electrostatic Attraction | Section 8.2.3 |
| Single Degree-of-Freedom System Energy Harvester | Section 8.2.4 |
| Response to Harmonic Excitation: Amplitude Response Functions | Section 8.3.2 |
| Enhanced Energy Harvester | Section 8.3.3 |
| Natural Frequencies and Mode Shapes of a Cantilever Beam with In-Span Attachments | Section 8.4.1 |
| Effects of Electrostatic Force on Natural Frequency and Stability of a Beam | Section 8.4.2 |
| Response of a Cantilever Beam with an In-span Attachment to an Impulse Force | Section 8.4.3 |
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