## MATH0370 Introduction to Applied Mathematics 2

### 10 creditsClass Size: 155

Taught: Semester 2 (Jan to Jun) View Timetable

Year running 2022/23

### Pre-requisite qualifications

MATH0111 and MATH0360, or equivalent

### Co-requisites

 MATH0212 Elementary Integral Calculus (Version 1)

### This module is mutually exclusive with

 LUBS1260 Mathematics for Economics and Business 1 LUBS1270 Statistics for Economics and Business 1 LUBS1280 Mathematical Economics

This module is not approved as a discovery module

### Module summary

Except on extremely large or on extremely small scales, all motion is governed by Newton's Laws, which give the relationship F = ma between force, mass and acceleration. Using many worked examples, we shall show how to apply these laws to simple models of the real world and we shall introduce the very fundamental and important concepts of linear momentum and energy.

### Objectives

To develop a basic understanding of Newton's Laws and their applications in simple examples of dynamics, and to introduce the concepts of linear momentum and energy.

On completion of this module, students should be able to:
(a) apply vector models, learnt in MATH 0360, to models of mechanical problems in both 1-D and 2-D motion;
(b) formulate and solve both static and dynamic problems of particle mechanics;
(c) solve problems based on Newton's Laws via principles of Work, Energy and Momentum.

### Syllabus

- Kinematics: 1-D motion with constant acceleration
- Time-dependent vectors and their differentiation and integration
- 2-D motion
- Relative velocity
- Projectiles
- Circular motion
- Kinetics: Forces
- Systems in equilibrium
- Forces and motion
- Newton's Laws
- Separated body diagrams
- Dynamic friction
- Horizontal and vertical circular motion
- Work and energy
- Conservative forces
- Conservation of energy
- Impulse and momentum
- Conservation of momentum
- Collisions.

### Teaching methods

 Delivery type Number Length hours Student hours Lecture 33 1.00 33.00 Private study hours 67.00 Total Contact hours 33.00 Total hours (100hr per 10 credits) 100.00

### Private study

Studying and revising of course material.
Completing of assignments and assessments.

Example classes will be covered in the lectures.

### Opportunities for Formative Feedback

Regular problem solving assignments

!!! In order to pass the module, students must pass the examination. !!!

### Methods of assessment

Coursework
 Assessment type Notes % of formal assessment In-course Assessment . 15.00 Total percentage (Assessment Coursework) 15.00

There is no resit available for the coursework component of this module. If the module is failed, the coursework mark will be carried forward and added to the resit exam mark with the same weighting as listed above.

Exams
 Exam type Exam duration % of formal assessment Open Book exam 2 hr 00 mins 85.00 Total percentage (Assessment Exams) 85.00

Normally resits will be assessed by the same methodology as the first attempt, unless otherwise stated