Last modified: 22 Jul 2026 13:42
Analysis provides the rigourous, foundational underpinnings of calculus. The focus of this course is multivariable analysis, building on the single-variable theory from MA2009 Analysis I and MA2509 Analysis II. Concepts and results around multivariable differentiation are comprehensively established, laying the ground for multivariable integration in MX3535 Analysis IV.
As in Analysis I and II, abstract reasoning and proof-authoring are key skills emphasised in this course.
| Study Type | Undergraduate | Level | 3 |
|---|---|---|---|
| Term | First Term | Credit Points | 15 credits (7.5 ECTS credits) |
| Campus | Aberdeen | Sustained Study | No |
| Co-ordinators |
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Course Aims
To provide students with the basic knowledge of the modern mathematical analysis.
Main Learning Outcomes
-Understand definitions and basic concepts of real analysis (real number, limit, continuity, differential, etc.)
-Be fluent computing limits, and differentials, and manipulating elementary functions.
Course Content
-Euclidean spaces: metric structure, topology
- Functions between Euclidean spaces: limits, continuity
- Differentiability of functions between Euclidean spaces
- The chain rule, the Inverse Function Theorem, and the Implicit Function Theorem
- Applications of differentiation
Information on contact teaching time is available from the course guide.
| Assessment Type | Summative | Weighting | 70 | |
|---|---|---|---|---|
| Assessment Weeks | Feedback Weeks | |||
| Feedback |
2-hour exam worth 70% of the overall grade. |
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| Knowledge Level | Thinking Skill | Outcome |
|---|---|---|
| Conceptual | Apply | Apply knowledge of basic logic to understand and reproduce mathematical arguments. |
| Conceptual | Understand | Understand the implicit and inverse function theorems. |
| Conceptual | Understand | Understand Lagrange multipliers. |
| Conceptual | Understand | Understand differentiation in n variables, including the chain rule. |
| Conceptual | Understand | Understand basic analysis in n variables, including basic notions such as sequences and limits. |
| Factual | Remember | Be able to state the main definitions and theorems from the course. |
| Procedural | Apply | Solve problems, of varying levels of difficulty, on the material from the course. |
| Procedural | Understand | To demonstrate knowledge and understanding of proof techniques from the course. |
| Reflection | Create | Be able to give examples to illustrate the theorems from the course. |
| Assessment Type | Summative | Weighting | 15 | |
|---|---|---|---|---|
| Assessment Weeks | Feedback Weeks | |||
| Feedback |
Class Test (50 minutes, in class) worth 15% of the overall grade. |
|||
| Knowledge Level | Thinking Skill | Outcome |
|---|---|---|
| Conceptual | Apply | Apply knowledge of basic logic to understand and reproduce mathematical arguments. |
| Conceptual | Understand | Understand basic analysis in n variables, including basic notions such as sequences and limits. |
| Factual | Remember | Be able to state the main definitions and theorems from the course. |
| Procedural | Apply | Solve problems, of varying levels of difficulty, on the material from the course. |
| Procedural | Understand | To demonstrate knowledge and understanding of proof techniques from the course. |
| Reflection | Create | Be able to give examples to illustrate the theorems from the course. |
| Assessment Type | Summative | Weighting | 15 | |
|---|---|---|---|---|
| Assessment Weeks | Feedback Weeks | |||
| Feedback |
Homework worth 15% of the overall grade. |
|||
| Knowledge Level | Thinking Skill | Outcome |
|---|---|---|
| Conceptual | Apply | Apply knowledge of basic logic to understand and reproduce mathematical arguments. |
| Conceptual | Understand | Understand the implicit and inverse function theorems. |
| Conceptual | Understand | Understand basic analysis in n variables, including basic notions such as sequences and limits. |
| Conceptual | Understand | Understand differentiation in n variables, including the chain rule. |
| Factual | Remember | Be able to state the main definitions and theorems from the course. |
| Procedural | Apply | Solve problems, of varying levels of difficulty, on the material from the course. |
| Procedural | Understand | To demonstrate knowledge and understanding of proof techniques from the course. |
| Reflection | Create | Be able to give examples to illustrate the theorems from the course. |
There are no assessments for this course.
| Assessment Type | Summative | Weighting | ||
|---|---|---|---|---|
| Assessment Weeks | Feedback Weeks | |||
| Feedback |
2-hour exam. Best of (resit exam mark) or (resit exam mark with carried forward CA marks). |
|||
| Knowledge Level | Thinking Skill | Outcome |
|---|---|---|
|
|
||
| Knowledge Level | Thinking Skill | Outcome |
|---|---|---|
| Conceptual | Understand | Understand Lagrange multipliers. |
| Conceptual | Understand | Understand differentiation in n variables, including the chain rule. |
| Reflection | Create | Be able to give examples to illustrate the theorems from the course. |
| Procedural | Apply | Solve problems, of varying levels of difficulty, on the material from the course. |
| Procedural | Understand | To demonstrate knowledge and understanding of proof techniques from the course. |
| Conceptual | Understand | Understand the implicit and inverse function theorems. |
| Conceptual | Apply | Apply knowledge of basic logic to understand and reproduce mathematical arguments. |
| Factual | Remember | Be able to state the main definitions and theorems from the course. |
| Conceptual | Understand | Understand basic analysis in n variables, including basic notions such as sequences and limits. |
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