- Chapter 2
- Body forces and stress forces.
- Definition of traction.
- Calculation of traction across arbitrary plane.
- Mathematics of Cartesian tensors and vectors.
- Matrix and addition and multiplication.
- Changing coordinate systems.
- Eigenvalues, eigenvectors, and principal axes.
- Dot, cross, and dyadic products of vectors.

- Definition of stress tensor and its relationship to traction.
- Symmetry of stress tensor.
- Traction and stress on boundaries.

- Chapter 3
- Newton's second law in continuous media.
- Mass budget.
- Momentum budget.
- Open systems.
- Accelerated reference frames and inertial forces.
- Non-Cartesian coordinates.
- Lagrangian coordinates in continuum mechanics.

- Chapter 4
- Displacements of continuous media.
- Decomposition of displacements into translation, rotation, and strain.
- Rotation tensor and its dual vector.
- Strain tensor and unit extensions.
- Strain tensor and angle changes.
- Strain tensor and fractional volume change.
- Principal axis frame of strain tensor.
- Compatibility conditions on strain tensor and derivation of displacement field.
- Continuous motion and strain and rotation rates.