textbook-theory · English
Difference Equations to Differential Equations — Section 2.4: Continuous Functions
Section 2.4 of Dan Sloughter's open calculus text covers the definition and properties of continuous functions, including continuity at a point, one-sided continuity, and continuity on open and closed intervals. The section proves continuity of polynomials, rational functions, algebraic functions, and trigonometric functions, and establishes that compositions of continuous functions are continuous. Worked examples and problem sets illustrate removable discontinuities and piecewise-defined functions.
continuitylimitscalculusreal analysis