Module manager: Serguei Komissarov
Email: S.S.Komissarov@leeds.ac.uk
Taught: Semester 2 (Jan to Jun) View Timetable
Year running 2025/26
GCSE Mathematics or equivalent.
| MATH0111 | Elementary Diff Calculus 1 |
| MATH0212 | Elementary Integral Calculus (Version 1) |
MATH0390 and MATH0365
This module is not approved as a discovery module
This module develops mathematical skills, typically covered in A-level mathematics, which are needed for further study in a range of programmes. In particular, students will gain confidence in the fundamental tools of differentiation and integration and how these can be applied to solve real-world problems.
To teach differential and integral calculus at A-level standard.
The module introduces foundational skills in calculus and the essential theoretical background on functions and analysis to put these topics into context. As well as being able to differentiate and integrate a range of common functions applications of calculus are presented.
On successful completion of the module students will have demonstrated the understanding of
1. The role of proof in mathematics.
2. Functions of real arguments, including; the difference between defining a function and computing its values and the power series of a function.
3. Limits and continuity.
4. Infinitesimals and the derivative of a function as its instantaneous rate of change.
5. The antiderivative and indefinite integral.
6. Definite integrals and the fundamental theorem of calculus.
Skills Learning Outcomes
On successful completion of the module students will have demonstrated the following skills learning outcomes:
a. Explaining mathematics in clear, precise and logical way;
b. Using power series to find approximate values of common functions.
c. Finding limits for simple sequences and functions.
d. Differentiating common functions and applying basic rules of differentiation forto functions derived from those common functions.
e. Using differentiation for basic analysis of functions and sketching their graphs.
f. Finding integrals of simple functions using the basic rules and methods of integration.
g. Using calculus for real-life applications.
- Geometric sequence and series.
- Functions of real argument andinverse functions.
- Limits and continuity of functions.
- Exponentiation, power functions, polynomials and basics of power series. Exponential, logarithmic and trigonometric functions.
- Derivative of a function. Basic rules of differentiation. Derivatives of common functions.
- Use of differentiation for analysis of functions e.g. finding tangent lines, determining stationary points, and graph sketching.
- Antiderivatives and indefinite integrals and basic rules of integration.
- Elementary differential equations. Power-series solutions to the equations defining exponential and trigonometric functions.
- Finite-difference and differential equations in finance. Regular and continuous interest.
- Definite integrals and the Fundamental Theorem of Calculus.
Methods of assessment
The assessment details for this module will be provided at the start of the academic year
| Delivery type | Number | Length hours | Student hours |
|---|---|---|---|
| Lecture | 33 | 1 | 33 |
| Seminar | 10 | 1 | 10 |
| Private study hours | 157 | ||
| Total Contact hours | 43 | ||
| Total hours (100hr per 10 credits) | 200 | ||
Feedback on 9 regular marked problem sheets and the mid-term test. Weekly non-assessed quizzes.
Check the module area in Minerva for your reading list
Last updated: 30/04/2025
Errors, omissions, failed links etc should be notified to the Catalogue Team