Mathematical Studies
MA211: Calculus I (5 ECTS)
This is a continuation of first year Calculus, dealing with more advanced topics. Further techniques of integration, reduction formulas, volumes of revolution. Introduction to Hyperbolic functions and their inverses. Series and convergence. Improper Integrals. Some differential equations.
Taught in Semester(s) 1. Examined in Semester(s) 1.
Workload: 100 hours (24 Lecture hours, 12 Tutorial hours, 64 Self study hours).
Module Learning Outcomes.
On successful completion of this module the learner should be able to:
- Solve some definite integrals via reduction formulas.
- Calculate volumes of revolution in straightforward instances.
- State the definition of the hyperbolic functions and their inverses and properties of these functions.
- Define the notion of limit of a sequence and be able to apply the comparison, ratio and root tests, and the integral test for convergence of series.
- Evaluate improper integrals and so-called p-integrals.
- Solve linear 1st and 2nd order differential equations.
Indicative Content
This course continues the study of Calculus of one variable in more advances topics. The topics include further integration in the form of reduction formulas and calculating volumes of revolution. An introduction to hyperbolic functions, their graphs. Properties of Sinh, Cosh, Tanh and their inverse functions, derivatives and integrals thereof. An introduction to sequences and series. The notion of convergence of a series and tests for convergence of series. Improper integrals and how to evaluate them. Elementary 1st and 2nd order differential equations.
Module Resources
- Calculus: A Complete Course. 5th edition. Robert A. Adams, Addison Wesley.
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