MATH 1007 Lecture Notes - Lecture 1: Pythagorean Trigonometric Identity, Even And Odd Functions, Function Composition

• School: Carleton University
• Department: Mathematics
• Course: MATH 1007
• Professor: Minyi Huang

Document Summary

This set of notes is only for students registered in this course. Calculus = differentiation + integration: differentiation (calculating derivative of a function) Derivative is the change rate of a function: integration (the reverse process of differentiation) The position of an object having free fall. This will be answered by calculating derivatives (differentiation). An engine consumes liquid fuel with rate (l/s) according to the curve. What is the total fuel consumption in 3 seconds?this will be answered by integration ( nding the area under the curve). Example: view integration as the reverse process of differentiation: you drive from ottawa to toronto, leaving at 2pm and arrive at 7pm. Denote your mileage by the function s(t), 0 t 5: differentiation: the change rate (derivative) of s(t) is v (t) which is actually your speed at, the formal notation: ds(t) dt. = v (t: on the other hand, if you have exact speed record for the whole duration (i. e. know v (t),