| CODE | MAT2212 | ||||||||
| TITLE | Analysis 2 | ||||||||
| UM LEVEL | 02 - Years 2, 3 in Modular Undergraduate Course | ||||||||
| MQF LEVEL | 5 | ||||||||
| ECTS CREDITS | 4 | ||||||||
| DEPARTMENT | Mathematics | ||||||||
| DESCRIPTION | Continuity - Limits of functions: on subsets of R and C - Continuity - Uniform continuity - Extreme Value Theorem - The intermediate value theorem - Continuous Inverse Function Theorem - Monotonic functions on intervals - Convex functions. Differentiability - Differentiability of functions on subsets of R - Algebra of derivatives and the chain rule - Rolle’s Theorem and Mean Value Theorem - Darboux’s Theorem - Classification of critical points - L’Hôpital’s rules. Study-Unit Aims: The aim of this unit is to study continuity of functions of a real or complex variable, and differentiability of functions of a real variable. Students will become acquainted with the definitions of limits of functions, and of continuity of functions, in terms of ε and δ. It will be shown that the continuous functions form an algebra that includes all the polynomials. Boundedness, maxima, minima, and uniform continuity for continuous functions on closed intervals will be investigated. Furthermore, the student will see that the derivative of a function is a limit and will have the opportunity to prove the familiar rules regarding the algebra of derivatives. Rolle’s Theorem, Mean Value Theorem, and l’Hôpital’s Theorem will also be proven during this unit and the student will have the opportunity to see various applications of these theorems. Learning Outcomes: Knowledge and understanding: At the end of this study-unit, the students will be able to apply limiting properties to describe, and prove, continuity and differentiability conditions for real and complex functions. They will also be able to prove important theorems, such as the Intermediate Value Theorem, Rolle’s Theorem and Mean Value Theorem. Skills: - This study-unit will allow the student to deal carefully with the notion of limits. - Analysis is the rigorous study of calculus, and in this unit rigorous proofs of calculus results with which the students may already be familiar, will be developed. Main Text/s and Supplementary Readings: Main Texts - Lecture notes for this course. (E. Chetcuti) - Abbott S., Understanding Analysis, Springer, 2001 - Garling D. J. H., A course in Mathematical Analysis Volume 1 Foundations and Elementary Real Analysis, Cambridge University Press 2013. Supplementary Readings: - W. Rudin, Principles of Mathematical Analysis (McGraw-Hill, Third Edition), 1976 - Spivak M., Calculus, Publish or Perish, 3rd Edition, 1994 - Bartle R. and Sherbert D., Introduction to Real Analysis, Wiley, 3rd Ed., 1999 - Apostol T., Mathematical Analysis, Addison-Wesley, 2nd Edition, 1974. |
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| ADDITIONAL NOTES | Follows from: MAT1211 Leads to: MAT2213 |
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| STUDY-UNIT TYPE | Lecture and Tutorial | ||||||||
| METHOD OF ASSESSMENT |
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| LECTURER/S | Emanuel Chetcuti |
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The University makes every effort to ensure that the published Courses Plans, Programmes of Study and Study-Unit information are complete and up-to-date at the time of publication. The University reserves the right to make changes in case errors are detected after publication.
The availability of optional units may be subject to timetabling constraints. Units not attracting a sufficient number of registrations may be withdrawn without notice. It should be noted that all the information in the description above applies to study-units available during the academic year 2025/6. It may be subject to change in subsequent years. |
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