The following files are PDF documents created in Word, with figures created in PowerPoint. Beyond the basic notes on mathematics there are two main themes: structural analysis and probabilistic analysis. This means that the notes are meant to provide support for the structural analysis courses CIVL 332 and CIVL 435, and the probabilistic course CIVL 518.

- MATHEMATICS
- Notation
- Fractions
- Functions
- Calculus
- Quadrature
- Combinations
- Series Expansions
- Complex Analysis
- Nonlinear Equations
- Differential Equations
- Vectors and Geometry
- Matrices and Linear Algebra

- SOLID MECHANICS
- Stress and Strain
- 3D Elasticity Theory
- Stress Transformations
- Stress-based Failure Criteria

- PLANE TRUSSES AND FRAMES
- Symbols
- Idealization of Structures and Loads
- Assumptions, Theories, Methods
- Stability and Indeterminacy
- Forces in Determinate Structures
- Moment-Area Method
- Conjugate Beam Method
- Unit Virtual Load Method
- Flexibility Method
- Slope Deflection Method
- Moment Distribution Method
- Stiffness Method
- Influence Lines
- Approximate Methods
- Elasto-plastic Analysis

- STRUCTURAL BOUNDARY VALUE PROBLEMS
- Truss Members
- Euler-Bernoulli Beams
- Timoshenko Beams
- St Venant Torsion
- Warping Torsion
- Beams with Axial Force
- Beams on Elastic Foundation
- Lateral Torsional Buckling
- 2D Continuum Problems
- Kirchhoff and Mindlin Plates
- Curved Beams and Arches

- STRUCTURAL INITIAL VALUE PROBLEMS
- SDOF Oscillators
- Oscillating Strings and Beams
- Oscillating Plates
- MDOF Dynamics

- ENERGY METHODS
- Virtual Work and Variational Principles
- Calculus of Variations
- Work and Energy Expressions

- COMPUTATIONAL STRUCTURAL ANALYSIS
- Computational Stiffness Method
- Finite Element Fundamentals
- Inelastic and Dynamic Analysis
- Response Sensitivity Analysis
- The Truss Element
- The Linear Frame Element
- The Displacement-based Nonlinear Frame Element
- The Force-based Nonlinear Frame Element
- The CST Element
- The Q4 Element
- The M4 Element

- BASIC PROBABILISTIC ANALYSIS
- Uncertainty and Risk
- Set Theory
- Probability Theory

- PROBABILISTIC MODELS
- Discrete Random Variables
- Continuous Random Variables
- Extreme Value Models
- Multivariate Distribution Models
- Linear Regression Models
- Logistic Regression Models
- Damage Accumulation Models
- Size Effect Models
- Fragility Models
- Bayesian Network Models
- Bayesian Hierarchical Models
- Bernoulli Sequences
- Poisson Point Processes
- Poisson Pulse Processes
- Continuous Stochastic Processes
- Discounting Models

- PROBABILISTIC METHODS
- Analysis of Functions
- Probability Transformations
- Reliability Analysis
- MVFOSM
- FORM
- SORM
- Sampling
- System Reliability
- Load Combination
- Stochastic Dynamics
- Stochastic Fatigue

- DECISIONS UNDER UNCERTAINTY
- How Humans Make Decisions
- Calibration to Past Practice
- Calibration to Target Safety
- Expected Cost Theory
- Expected Utility Theory
- Prospect Theory
- LQI and SWTP
- Decision Trees

- OPTIMIZATION
- Downhill Simplex Algorithm
- Directional Line Search Algorithm
- Bisection Algorithm
- 1D Newton-Raphson Algorithm
- Secant Algorithm
- Golden Section Algorithm

- LINEAR ALGEBRA
- Cholesky Decomposition
- LU Decomposition
- Determinant and Matrix Inversion
- Decomposition and Substitution

- TECHNICAL WRITING
- Why Write Well
- Good Habits of Technical Writing
- Grammar
- Mini Dictionary