MATH 121/6.0 - Differential and Integral Calculus
Calculus is a branch of mathematics that can describe precisely how one numerical output quantity changes in response to changes in one or more numerical input quantities. This is a general two-term calculus course, starting with a revision of high-school pre-calculus, and of the basics of single-variable differentiation and integration, and then moving on to more advanced topics, such as multi-variable calculus, differential equations, and various techniques of optimization. Students can take this course with or without high-school calculus experience. The course is not intended as a pure mathematics course, and so there is more of an emphasis on techniques and applications than on formal proofs.
- Conceptual understanding and technical mastery of the following main areas of calculus and pre-calculus:
- Basics of algebra and arithmetic.
- Functions and graphs.
- Geometry and trigonometry.
- Differential equations.
- partial derivatives and vector calculus.
- An ability to apply knowledge of the topics above to solve extended problems, both abstract and applied.
- An ability to communicate and present such mathematical problem-solving skills by combining explanatory English text with mathematical equations and graphs in a coherent and comprehensible way.
In the Fall, the first “field-trip” will be an on-site “Math Movie Night” of short mathematics videos (tried informally last year, with very positive student feedback), and the second field-trip will be to the on-site Observatory Science Centre (http://www.the-observatory.org/), once the site of the former Royal Greenwich Observatory. Both field-trips will provide some problems for subsequent homework, classwork, and assessed non-exam assignments.
In the Winter, the first “field-trip” will be another on-site “Math Movie Night”, and the second field-trip will be an on-site late-evening telescopic observing session, related to astronomical mathematics. As in the Fall, both field-trips will be used as sources for homework, classwork, and assessed non-exam assignments.
There is no primary research in this course: the objective is rather to obtain a firm grasp of basic calculus and precalculus, thereby providing a solid foundation for further study in mathematics or in its application to other disciplines; however, an emphasis is put on two prerequisites for subsequent more advanced study: applying and explaining mathematics clearly, in a way that integrates explanatory text, equations, diagrams, and graphs; and moving beyond a high-school “plug and chug” approach, towards a more sophisticated awareness of what mathematics is really about. In addition, some problems considered in the coursework will be related to a historical site (the Observatory Science Centre), and the two “Math Movie Nights” will refer to some mathematical problems of historical interest.
The overall course mark is the average (rounded up to the nearest whole percent) of the Fall and Winter term percentages. Within each term (both of which have two classes per week in Weeks 1-6 and 8-12, separated by a midterm trip in Week 7), the marks breakdown is as follows: