EPH 1100: Analytical Tools for Economics & Political Science
Fall 2026 · University of Austin (UATX)
Course Description
This course introduces the mathematical tools used throughout the economics and political science courses offered by the Center for Economics, Politics and History: functions, derivatives, optimization, linear algebra, multivariable and constrained optimization, comparative statics, and integration. Each tool is applied to an economic or political problem.
The primary reading is the class notes, one set per session. Each set of notes references the relevant chapters in Hoy et al. (2022), Mathematics for Economics (optional).
Schedule & Readings
| Class | Topic | Readings |
|---|---|---|
| 1 | Introduction to Analytical Tools | Notes · Hoy et al., Ch. 1.1–2.2 |
| 2 | Functions and Economic Relationships | Notes · Hoy et al., §2.4 |
| 3 | Limits, Continuity, and Tangent Lines | Notes · Hoy et al., §4.1–4.2, §5.1 |
| 4 | Derivatives and Differentiation Rules | Notes · Hoy et al., §5.2–5.4 |
| 5 | Differentials and Basic Applications of Derivatives | Notes · Hoy et al., §5.2, §5.4 |
| 6 | Second Derivatives, Concavity, and Convexity | Notes · Hoy et al., §5.5 |
| 7 | Optimization: Finding Maxima and Minima | Notes · Hoy et al., §6.1–6.2 |
| 8 | Review | |
| 9 | Midterm Exam | |
| 10 | Linear Algebra: Vectors and Matrices | Notes · Hoy et al., §7.3, §8.1–8.2 |
| 11 | Linear Algebra: Solving Systems and Determinants | Notes · Hoy et al., §7.1, §9.1 |
| 12 | Multivariable Functions: Partial Derivatives and the Total Differential | Notes · Hoy et al., §11.1–11.3 |
| 13 | Unconstrained Optimization: First-Order Conditions | Notes · Hoy et al., §12.1 |
| 14 | Unconstrained Optimization: Second-Order Conditions and the Hessian | Notes · Hoy et al., §11.5, §12.2 |
| 15 | Constrained Optimization: The Lagrangian Method | Notes · Hoy et al., §13.1–13.2 |
| 16 | Constrained Optimization: Applications | Notes · Hoy et al., §13.1, §13.4 |
| 17 | Comparative Statics and the Implicit Function Theorem | Notes · Hoy et al., §11.4, §14.1–14.2 |
| 18 | The Envelope Theorem | Notes · Hoy et al., §14.2–14.3 |
| 19 | Integration | Notes forthcoming |
| 20 | Review | |
| 21 | Final Exam |