Math 410 Lecture Notes, Fall 2020

The following are lecture notes (pdf files) that you may download as they become available.

• Real Numbers (6 August version)
  
  1. Real Number System
  2. Sequences of Real Numbers
  3. Series of Real Numbers
  4. Sets of Real Numbers
  

• Functions and Regularity (6 August version)
  
  5. Functions, Continuity, and Limits
  6. Differentiability and Derivatives
  7. Mean-Value Theorems and Their Applications
  8. Cauchy Continuity and Uniform Continuity
  

• Riemann Integrals and Integrability (6 August version)
  
  9. Riemann Integrals
  10. Riemann Integrable Functions
  11. Relating Integration with Differentiation
  

• Uniform Convergence of Functions (6 August version)
  
  12. Sequences of Functions
  13. Series of Functions
  14. Everywhere Continuous, Nowhere Differentiable Functions
  15. Weierstrass Approximation Theorem
  

Notes on Related Topics

The following are notes (pdf files) on related topics that you may download as they become available.

• Formulas for Roots of Polynomials (11 October 2016 version)
  
  1. Introduction
  2. Formulas for Roots of Cubics and Quartics
  3. Derivations of the Quadratic Formula
  4. Derivation of the Cubic Formula
  5. Derivation of the Quartic Formula