Unit information: Foundations and Applications of Calculus in 2026/27

Please note: Programme and unit information may change as the relevant academic field develops. We may also make changes to the structure of programmes and assessments to improve the student experience.

Unit name Foundations and Applications of Calculus
Unit code LANG00058
Credit points 20
Level of study QCA-3
Teaching block(s) Teaching Block 4 (weeks 1-24)
Unit director Mr. Tim Walker
Open unit status Not open
Units you must take before you take this one (pre-requisite units)

IELTS: minimum 5.5 overall; minimum 5.0 in Speaking, Listening, Reading and Writing components, or equivalent. 

Students should have the appropriate qualifications in Mathematics at the equivalent of QCA level 2

Units you must take alongside this one (co-requisite units)

None

Units you may not take alongside this one

None

School/department Centre for Academic Language and Development
Faculty Faculty of Arts

Unit Information

Foundations and Application of Calculus is an engaging and illuminating unit that contains the fundamental building blocks to develop a solid comprehension of the meaning and application of calculus. No prior knowledge of calculus is assumed, which allows a comprehensive journey through common functions and their graphical representations leading to the essential understanding and application of techniques for differentiation and integration. By the end of the unit, you will be confident with single variable calculus and be aware of the use of differential equations. By working collaboratively to solve complex problems, you will then be ready to learn undergraduate techniques in calculus within Mathematics, Computer Science, and related degrees at the University of Bristol.

Your learning on this unit

An overview of content

Foundations and Applications of Calculus covers:

  • Key algebraic manipulation and skills.
  • Common functions and equations and their graphical representations.
  • Understanding calculus and exploring important techniques and uses.
  • Introduction to differential equations.

How will students, personally, be different as a result of the unit

You will consolidate and extend on level 2 mathematical ideas in addition to exploring level 3 mathematics concepts. Learning will be a mixture of guided independent study, assessment for learning, and collaborative tasks designed to encourage community, belonging, and the development of individual and teamwork study skills. Teaching and learning will provide diverse opportunities to build your confidence to contribute in workshops and effectively act on feedback which are key skills for success in undergraduate degrees. You will be given insights into their future study at the University of Bristol by suggested further study (extension tasks) relevant to programmes in the schools of Mathematics and Computer Science.

Learning Outcomes

On successful completion of the unit, students will be able to:

  1. Manipulate expressions using algebraic techniques.
  2. Recognise, manipulate, and solve with important functions and their graphs.
  3. Use calculus to describe and analyse change and summations of a function using advanced algebraic and numerical methods.
  4. Use common techniques to solve differential equations.

How you will learn

Learning is facilitated in weekly classroom sessions involving a combination of teacher-led input, and practical, workshop-style exercises. In addition to activities in class, appropriate e-learning technologies will be used for self-assessment as well as further self-study.

How you will be assessed

Tasks which help you learn and prepare you for summative tasks (formative): 

Regular progress quizzes and exam practice questions with formative feedback (0%, not required for credit). 

Tasks which count towards your unit mark (summative): 

  • Written examination (30%) [ILOs 1, 2, 3] 
  • Written examination (70%) [ILOs 1, 2, 3, 4] 

When assessment does not go to plan 

Any student registered on the International Foundation Programme will be offered a conditional place on an undergraduate degree at the University of Bristol. Students must meet the entry requirements to be admitted onto an undergraduate degree at the University of Bristol. Different degree programmes may have different entry requirements. The IFP Board will review the mark profiles of all students who are close to attaining the entry requirements but are outside the previously agreed near miss criteria and may agree to admit them to a degree programme. If not admitted, students may be offered a further opportunity (i.e. two attempts in total) to meet the entry requirements for their intended degree programme at the University of Bristol by re-taking a relevant assessment. Marks are not capped for this purpose. If a student is absent or their performance in assessment is significantly affected due to exceptional circumstances, they may re-take the relevant assessment at the next appropriate time, without penalty.

Resources

If this unit has a Resource List, you will normally find a link to it in the Blackboard area for the unit. Sometimes there will be a separate link for each weekly topic.

If you are unable to access a list through Blackboard, you can also find it via the Resource Lists homepage. Search for the list by the unit name or code (e.g. LANG00058).

How much time the unit requires
Each credit equates to 10 hours of total student input. For example a 20 credit unit will take you 200 hours of study to complete. Your total learning time is made up of contact time, directed learning tasks, independent learning and assessment activity.

See the University Workload statement relating to this unit for more information.

Assessment
The assessment methods listed in this unit specification are designed to enable students to demonstrate the named learning outcomes (LOs). Where a disability prevents a student from undertaking a specific method of assessment, schools will make reasonable adjustments to support a student to demonstrate the LO by an alternative method or with additional resources.

The Board of Examiners will consider all cases where students have failed or not completed the assessments required for credit. The Board considers each student's outcomes across all the units which contribute to each year's programme of study. For appropriate assessments, if you have self-certificated your absence, you will normally be required to complete it the next time it runs (for assessments at the end of TB1 and TB2 this is usually in the next re-assessment period).
The Board of Examiners will take into account any exceptional circumstances and operates within the Regulations and Code of Practice for Taught Programmes.