Sequences, Series, and Limits Chapter 1. Sequences Chapter 2. Series Chapter 3. Limits of Functions Part II. Qualitative Properties of Continuous and Differentiable Functions Chapter 4. Continuity Chapter 5. Differentiability Part III. Applications to Convex Functions and Optimization Chapter 6. Convex Functions Chapter 7. Inequalities and Extremum Problems Part IV. Antiderivatives, Riemann Integrability, and Applications Chapter 8. Antiderivatives Chapter 9. Riemann Integrability Chapter 10. Applications of the Integral Calculus Appendix A. Basic Elements of Set Theory Appendix B. Topology of the Real Line