## NATS1180 Mathematics for Scientists

### 10 creditsClass Size: 180

Module manager: Marcelo P de Miranda
Email: m.miranda@leeds.ac.uk

Taught: Semester 1 (Sep to Jan) View Timetable

Year running 2024/25

### Pre-requisite qualifications

GCSE Mathematics (or equivalent)

Module replaces

CHEM1181 NATS1380 NATS2380

This module is not approved as a discovery module

### Module summary

Mathematical knowledge and skills are essential for the successful training of scientists and important for the professional life of scientists. This module will be taken by science students who do not have grade B or above in A’level mathematics (or equivalent); its aim will be to raise the mathematical competence of the students to that base level.

### Objectives

On completion of this module, students should have gained confidence and proficiency in a set of mathematical manipulations appropriate to the study of science and be able to apply these to scientific problems.

The topics of study will be discussed in lectures and extensively practiced via problem solving in workshops and coursework.

Learning outcomes
On successful completion of the module students will have demonstrated the following learning outcomes:

1. Perform basic algebraic manipulations and calculations, including applications of basic (polynomial, trigonometric, exponential, logarithmic) functions.
2. Rearrange and solve linear or quadratic equations as well as pairs of simultaneous linear equations.
3. Represent functions graphically and retrieve quantitative information from plots of functions.
4. Differentiate basic functions and simple combinations of these functions.
5. Use differentiation to find rates of change and extrema of basic functions.
6. Integrate basic functions and simple combinations of these functions.
7. Use integration to find the areas under curves and the cumulative changes associated with basic functions.
8. Solve simple, separable first order differential equations and identify or check solutions for boundary (or initial) value problems.

Skills Learning Outcomes
On successful completion of the module students will have demonstrated the following skills learning outcomes:

9. Work-Ready - Core Literacies: Display mathematical skills and apply mathematics in the context of everyday situations.
10. Work-Ready - Problem solving & analytical skills

### Syllabus

Functions, including polynomial, trigonometric, exponential, and logarithmic functions.

Differentiation of functions and relation between derivatives and slopes or rates of change. Higher and partial derivatives. Use of differentiation to locate minima, maxima and inflection points of functions. Full differentials.

Definite and indefinite integration of functions. Relation between integrals, areas under curves, and cumulative change.

Differential equations and boundary or initial value problems. Their relevance, and solution of simple cases.

Methods of Assessment

We are currently refreshing our modules to make sure students have the best possible experience. Full assessment details for this module are not available before the start of the academic year, at which time details of the assessment(s) will be provided.

Assessment for this module will consist of;

1 x Coursework
1 x In-person open-note exam

### Teaching methods

 Delivery type Number Length hours Student hours Workshop 11 1.00 11.00 Lectures 11 1.00 11.00 Independent online learning hours 12.00 Private study hours 66.00 Total Contact hours 22.00 Total hours (100hr per 10 credits) 100.00

### Opportunities for Formative Feedback

Workshops (problem solving, face-to-face, weekly during teaching weeks, 1 hour)
Online tests (students answers marked, and correct answers shown, at every attempt)