Undergraduate Course: Further Analysis and Several Variable Calculus (MATH08082)
Course Outline
| School | School of Mathematics |
College | College of Science and Engineering |
| Credit level (Normal year taken) | SCQF Level 8 (Year 2 Undergraduate) |
Availability | Available to all students |
| SCQF Credits | 20 |
ECTS Credits | 10 |
| Summary | This is a second course in Mathematical Analysis together with Calculus in Several Variables. It follows on directly from Introduction to Mathematical Analysis. A rigorous introduction to integration in one real variable is followed by a study of differential and then integral calculus in several variables, and the analysis underpinning these topics. The language of linear algebra is used to facilitate the development of calculus in several real variables. A strong emphasis will be placed on calculational aspects and geometrical context. |
| Course description |
This is a second course in mathematical analysis, together with calculus in several variables, which aims to bring students to an understanding of and theoretical and practical proficiency in integration and differentiation.
The section on single variable integration will follow the structure of Introduction to Mathematical Analysis, with a strong emphasis on both rigorous treatment of the concepts and calculus skills. The following sections introduce fundamentally new ideas in several variable calculus, and will have more emphasis on conceptual understanding, calculation, and applications, underpinned by rigorous theory where appropriate.
Summary of student experience: you will be seeing rigorous integration for the first time, and then, building on the notions from Introduction to Mathematical Analysis, see how to develop differential and integral calculus in several variables with an eye to practice and intuition, as well as theory, including mastery of calculations in multivariable calculus. Following on from the prerequisite courses, you will further develop your mathematical communication and problem-solving skills.
|
Entry Requirements (not applicable to Visiting Students)
| Pre-requisites |
|
Co-requisites | |
| Prohibited Combinations | |
Other requirements | Due to limitations on class sizes, students will only be enrolled on this course if it is specifically referenced in their DPT. |
Information for Visiting Students
| Pre-requisites | Visiting students are advised to check that they have studied the material covered in the syllabus of each prerequisite course before enrolling. |
| High Demand Course? |
Yes |
Course Delivery Information
| Not being delivered |
Learning Outcomes
On completion of this course, the student will be able to:
- Apply mathematical knowledge and understanding to discuss and rigorously explore topics and solve standard problems in integration of functions of a single variable, using appropriate definitions and results, applying sound logical reasoning, leading to carefully explained, coherent, well-reasoned and precise arguments expressed in appropriate mathematical language in written form.
- Demonstrate conceptual and practical understanding of limits of sequences and of functions, of continuous functions and their properties, and of differentiation of scalar and vector-valued functions defined on Rn, including gradient and divergence of vector fields, with geometrical interpretations where appropriate, the Jacobian matrix of partial derivatives as the matrix representation of the derivative, critical points and their application to extremal problems.
- Demonstrate a conceptual, theoretical and practical understanding of integration of functions of several variables, and of Stokes¿ theorem and the divergence theorem as the higher-dimensional Fundamental Theorem of Calculus, including facility with double and triple integrals, polar coordinates, line and surface integrals, and their associated geometrical setting, and to solve standard unseen problems without explicit prompting.
- Work, collaboratively and individually, to discuss, explore and apply the ideas and methods of the course, to consolidate understanding, develop geometrical intuition, and in order to approach and attempt problems that may be longer, may extend the taught material, may involve combining different ideas, and may be open-ended.
- Learn topics in analysis and multivariable calculus from a variety of sources, including through active, critical, and careful reading, and making judicious use of different learning resources.
|
Additional Information
| Graduate Attributes and Skills |
Not entered |
| Keywords | Integration,several variables,limits,continuity,differentiation |
Contacts
| Course organiser | |
Course secretary | |
|
|
University Homepage