MATH1200 - Calculus I (Fall)
Offerings: FALL (3-1)
Prerequisites: OAC Calculus or equivalent
Exclusions: MATH*1000, MATH*108
Calendar Description: This is a theoretical course intended primarily for students who need or expect to pursue further studies in mathematics and its applications. Topics to be included are: trigonometry including the compound angle formulas; inequalities and absolute values; limits and continuity using rigorous definitions, the derivative and various applications; Rolle's theorem and the mean value theorem for derivatives; the differential and anti-differentiation; the definite integral and various applications, the Mean-Value Theorem for integrals; the Fundamental Theorem of Calculus; logarithmic, exponential functions.
Intended Students: Majors in any of the Physical Sciences or Engineering. (Mathematics, Statistics and computing majors may be enrolled in either the BA or BSc programs.)
Objectives: This course provides a rigorous introduction to both differential calculus and elementary integral calculus. Theory is emphasized and proofs are an important part of the course.
The course proceeds from a study of trigonometric functions including the compound angle formulas, inequalities and absolute values to the formal definition of a limit. From here, we proceed to the derivative, and various derivative formulas. These are applied to related rate problems, extreme value problems, and graph sketching. The Riemann definite integral is introduced as the limit of a sum. The Fundamental Theorem of Calculus is proved. We study indefinite integration, followed by application of the definite integral to area problems. The course ends with the exponential and logarithm functions.
Representative Texts: Calculus, 5th edition, by James Stewart, published by Nelson, Canada.
MATH 1200 course notes, by Jack Weiner, REVISED September, 2003, published by the University of Guelph Bookstore.
References: The Mathematics Survival Kit, by Jack Weiner, published by Nelson, Canada.
Evaluation: Three or four tests conducted in the one hour lab assigned to the course and a two hour final exam.