# ENG2012 : Engineering Mathematics II and Statistical Data Analysis

• Offered for Year: 2021/22
• Module Leader(s): Professor Yuri Sergeev
• Lecturer: Dr David Swailes, Dr Cristiano Villa, Dr John Appleby
• Owning School: Mathematics, Statistics and Physics
• Teaching Location: Newcastle City Campus
##### Semesters
 Semester 1 Credit Value: 10 Semester 2 Credit Value: 10 ECTS Credits: 10

#### Aims

Mathematics: to extend students' knowledge, understanding and application of analytical methods required in Mechanical Engineering. The course covers methods for solving differential equations, theory and applications of vector analysis and various infinite series.
To develop students' ability to solve mechanical engineering problems.
Statistics: to provide students with a fundamental understanding of the basic statistical techniques (summary statistics, probability distributions, interval estimation and regression analysis) routinely used in the engineering industries.

#### Outline Of Syllabus

Mathematics:
Differential Equations and Series:
- the Laplace transform and its application to solving ordinary differential equations
- Fourier series
- partial differential equations with applications
Vectors analysis:
- vector methods and their applications
- scalar and vector fields - grad, div, curl and potential fields
- surface and volume integrals
- divergence theorem and applications to transport processes
- application to fluid mechanics: material derivative, continuity and Euler's equations
Mathematical modelling: for solving mechanical engineering problems

Statistics:
Introduction: descriptive statistics
Probability: continuous distributions, normal distribution
Statistical interference: sampling distributions and confidence intervals - one sample problems (mean, standard deviation, paired comparisons) and two sample problems (comparison of means, ratio of variances)
Regression analysis

#### Teaching Methods

##### Teaching Activities
Category Activity Number Length Student Hours Comment
Scheduled Learning And Teaching ActivitiesLecture180:309:00Recorded introductory lectures sem one
Scheduled Learning And Teaching ActivitiesLecture101:0010:00Recorded introductory lectures sem two
Structured Guided LearningLecture materials182:0036:00Lecture notes sem one
Structured Guided LearningLecture materials101:0010:00Reviewing lecture notes (Statistics, Semester 2)
Structured Guided LearningLecture materials45:0020:00case study support material
Guided Independent StudyAssessment preparation and completion28:0016:00CBA exam
Guided Independent StudyAssessment preparation and completion51:005:00case study report
Guided Independent StudyAssessment preparation and completion151:0015:00Statistics exam
Scheduled Learning And Teaching ActivitiesLecture101:0010:00In person lectures (Statistics, Semester 2)
Guided Independent StudySkills practice201:0020:00Problem sheet exercises sem one
Guided Independent StudySkills practice101:0010:00Computer based exercises sem one
Guided Independent StudySkills practice101:0010:00Problem sheet exercises sem two
Scheduled Learning And Teaching ActivitiesDrop-in/surgery61:006:00In-person drop-in tutorials (Statistics, Semester 2)
Guided Independent StudyIndependent study101:0010:00Case study research
Scheduled Learning And Teaching ActivitiesScheduled on-line contact time131:0013:00Synchronous tutorials
Total200:00
##### Jointly Taught With
Code Title
ENG2011Engineering Mathematics II
##### Teaching Rationale And Relationship

Pre-recorded videos will be used in conjunction with ‘printed’ material to introduce each topic and worked examples, in place of normal lectures. In-person classroom time will not be possible for this large group this year. Live (synchronous) on-line tutorials will be used to address student queries, with on-screen mathematical work. Computer-based exercises and tests will help students to check and improve their skills. Bookable ‘office hour’ personal tutorials will support students on demand. Exercise sheets are for practice of methods and reinforcement of understanding and applications.

Statistics, Semester 2: In-person lectures convey the statistical concepts and theory and their application in engineering. Tutorial questions will be supplied for students' self-study. Drop-in tutorials will be used to address student queries and aid understanding.

Student’s should consult their individual timetable for up-to-date delivery information.

#### Assessment Methods

The format of resits will be determined by the Board of Examiners

##### Exams
Description Length Semester When Set Percentage Comment
Written Examination602A25Statistics exam
##### Exam Pairings
Module Code Module Title Semester Comment
ENG2011Engineering Mathematics II1N/A
CME1027Data Analysis in Process Industries2N/A
##### Other Assessment
Description Semester When Set Percentage Comment
Case study2A25modelling report
Computer assessment1M25NUMBAS CBA 24 hours
Computer assessment1M25NUMBAS CBA 25%
##### Assessment Rationale And Relationship

The two CBA assessments in Semester 1 provide a suitable means of testing mathematical knowledge and technical competence. The modelling case study report in Semester 2 permits a more open-ended assessment appropriate for developing and communicating ideas. The written statistics assessment in Semester 2 is appropriate for presenting data-intensive questions and testing the application of statistical techniques on these.