Many students have difficulty in grasping the idea that the integral of a function over an interval is a number. The reason is that this number is difficult to produce by traditional methods, i.e. by antidifferentiation, and so the central idea is lost.

– Peter Lax, Past President of the American Mathematical Society

### Elementary Applied Calculus

#### Welcome to Students

- Why is calculus considered such a big deal?
- If you heard this opinion from fellow students, perhaps they might be reacting to the incredible conceptual leaps that the subject requires. More so than in previous math courses, calculus demands that you recognize the interconnections among many ideas and learn how to parse an unfamiliar type of question for the relevant skill. This very source of frustration–multiple points of view all targeting the same symbolic manipulation–gives the subject its wide applicability to everyday life! For your instructor or fellow students who "get it" at an intuitive level, such a wide applicability contributes to the subject's aesthetic appeal (hence the other source from which you might have heard the "big deal" opinion).
- What are some skills that I can take from this class?
- An
**expanded mathematical toolbox**to discuss quantities that change in response to one or more other variables. - A
**deepened mathematical appreciation**for the versatility and ubiquity of linear approximation. **Improved algebra skills**, especially in manipulating expressions and solving polynomial equations.

- An
- What do I need to succeed in this class?
**Strong time management**, dedicating at least twice as much time to study out of class as we spend together in class.**Self-knowledge**and the willingness to brush up on algebra skills that might have atrophied since your last math class.**Mental flexibility**and the ability to see problems from more than one perspective.