# Review of Fundamental Topics

Below are the links to videos that review important fundamental topics in civil and environmental engineering. You can access the entire course playlists or each video individually. Each video includes a brief review of the topic, provides worked-out examples, and ends with self-practice questions. We hope you find these videos useful.

### Mathematics

- Matrix Operations (multiplication, addition, subtraction, transpose, determinant)
- Systems of Linear Equations (algebra)
- Polynomial Functions
- Derivatives/Integrals (relationships between the functions, area of the curve, slope)
- Numerical Integration
- Improper Integrals
- Applications of Integration
- Differential Equations (Basics and first order)
- Differential Equations (homogenous ODEs)
- Differential Equations (non-homogeneous ODEs)
- Trigonometry/Geometry (sin/cos, right triangles, similar triangles)
- Linear interpolation

### Statics

- Forces, External versus Internal Forces, Sign Convention
- Moment of a Force and Couple Moment
- Supports and Calculation of Reactive Forces
- Free Body Diagrams (draw few examples of free body diagrams)
- 2D Equilibrium (mention 3D, forces and moments)
- Truss Analysis I (zero-force members, method of joints)
- Truss Analysis II (method of sections)
- Resultants of Distributed Loads (concept and show the most common practical applications)
- Shear Forces and Bending Moments, Relationship Among Lateral Load, Shear Force, and Bending Moment
- Calculation of Internal forces (N, V, M) at a Point
- Construction of Shear Force and Bending Moment Diagrams: Functions
- Construction of Shear Force and Bending Moment Diagrams: Graphical
- Centroids of Areas, Centroids of Composite Sections
- Second Moment of the Area (moment of inertia) and Radius of Gyration
- Application of Parallel Axis Theorem to Calculate Moments of Inertia of Composite Sections

### Mechanics of Materials

**Mechanics of Materials Playlist**

- Definitions of Strain and Stress
- Stress-Strain Diagram and Mechanical Properties of Materials, Linear Elastic vs. Inelastic Behavior, Ductile vs Brittle Behavior
- Hooke's law, Poisson's ratio
- Stresses Calculation in a Beam: Axial (a bit of background, formula, example)
- Stresses Calculation in a Beam: Bending (a bit of background, formula, example)
- Stresses Calculation in a Beam: Shear (a bit of background, formula, example)
- Stresses Calculation in a Beam: Torsion (a bit of background, formula, example)
- Plane-Stress Transformation, Principal Stress (background, Mohr circle)
- Calculating Deflection of a Statically Determinate Structure: Double Integration
- Calculating deflection of a Statically Determinate Structure: Conjugate beam
- Calculating Deflection of a Statically Determinate Structure: Virtual work