A comprehensive, classroom-tested set of notes developed as a course text for undergraduate students, covering core topics in mathematical modeling, calculus, linear algebra, differential equations, and probability.
These notes emphasize conceptual understanding, mathematical structure, and connections between theory and real-world systems.
This text integrates multiple areas of mathematics commonly used in modeling:
- Calculus and techniques of integration
- Differential equations and dynamical systems
- Linear algebra (including eigenvalues and linear transformations)
- Probability and stochastic processes
- Applications to physical and real-world systems
The material is presented with a balance of rigor and accessibility, including proofs where appropriate and a strong focus on intuition and modeling.
The notes include:
- Structured chapters with clear progression of topics
- Worked examples and explanations
- Problem sets for each section
- Selected solutions
- Appendices covering supporting material (complex numbers, series, etc.)
These notes were developed for classroom use and have been refined across multiple course offerings.
The goal is to provide students with:
- a coherent mathematical foundation
- exposure to modeling techniques
- the ability to connect abstract concepts with applications
- Prioritize clarity over excessive formalism
- Introduce rigor where it enhances understanding
- Emphasize connections between different areas of mathematics
- Support problem-solving and independent learning
The document was written in LaTeX and developed as part of an undergraduate mathematics curriculum.
CC BY-NC 4.0