Section 5 Course description
Math 1560, Calculus I, is a first course in calculus, covering limits, derivatives, and integrals of functions of one variable.
We do not assume that you took calculus in high school, but we do assume that you’re familiar with algebra, functions, and trigonometry.
We’ll be dealing with all your favourite functions from high school: polynomials, logarithms, exponentials, even trigonometric functions.
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Limits tell us about the value of a function near a point. A limit is simulataneously approximate and precise. In fact, most of calculus could be described as “the art of precise approximation”
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Derivatives tell us about how a function is changing near a point. Most rates of change in the sciences, from speed to population growth, are quantified using derivatives.
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Integrals will be defined in the context of calculating area, but they also appear whenever aggregates or averages are being considered.
Both derivatives and integrals are defined using limits, and the two are related in a (possibly) surprising way.
The course will follow the order of the textbook. We cover everything, with the following exceptions:
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We do not cover Section 1.2, on the precise definition of the limit.
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Sections 4.1 (Newton’s method) and 5.5 (numerical integration) will not be covered in class, or on the tests. You will, however, be introduced to these concepts in tutorial, as part of a compute-based lab assignment.
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Section 2.2 (interpretations of the derivative) is recommended reading for conceptual understanding, but won’t be covered directly in class.
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Section 3.2 (Mean Value Theorem) will be discussed, since it is needed to explain some of the results in Chapter 3, but it won’t be assessed on homework or tests.
The remainder of the content is divided into four units:
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Unit 1: Sections 1.1, 1.3, 1.4, 1.5, 1.6, and 2.1
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Unit 2: Sections 2.3, 2.4, 2.5, 2.6, 2.7, and 3.1
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Unit 3: Sections 3.3, 3.4, 3.5, 4.2, 4.3, and 4.4
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Unit 4: Sections 4.5, 5.1, 5.2, 5.3, 5.4, and 6.1
Each unit will begin with a Readiness Assurance Process (RAT). This process is designed for you to assess whether or not you are familiar with the prerequisites needed for a unit. It takes the form of an in-class quiz with two parts: you first take the quiz individually, and then you re-take the quiz with a group.
A small part of your grade will be earned by completing each RAT, but it is participation-based. It does not depend on the score you receive on the quiz.
Each unit will end with a unit test, which will be written in the Testing Centre. The tests will consist of a short Moodle quiz (primarily multiple-choice) and one or two written-response long answer questions. You will be able to complete the written questions on the attendance sheet provided by the Testing Centre.
