26.T Logic;
Inequalities; Limits I <-(READ ME (PDF version in list below))
Reference: Stewart page xvi,
Handout, Stewart Appendix A,
Stewart 1.4
Keywords: Symbolic logic,
universal and existential quantifiers, implication, truth tables,
limit of a function, epsilon-delta definition
Learning Objectives: The student will be able to:
- Translate English statements involving
"for all" or "for every", "there exists",
and "if ... then" or "implies" into mathematical notation, and vice versa
- Distinguish the meanings of phrases such as the following,
and express them in mathematical notation:
- "For every epsilon there is a delta such that ... "
- "There is a delta such that for every epsilon ... "
- "There exist an epsilon and a delta such that ... "
- Solve simple inequalities, especially inequalities involving
absolute values
- State the precise definition of a limit
26.R Limits II
Reference: Stewart 1.4, 1.3, Appendix F
Keywords: Limit of a function, one-sided limits,
epsilon-delta definition, limit laws
Learning Objectives: The student will be able to:
- Explain the definition of a limit graphically
- Use the definition of a limit to prove limits in simple cases
- Use the definition of a limit to prove some of the limit laws,
such as "the limit of sum is the sum of the limits"