MATH08014 2019 Vector Calculus and Geometry
Full Title
Vector Calculus and Geometry
Transcript Title
Vector Calculus and Geometry
Code
MATH08014
Attendance
N/A %
Subject Area
MATH - 0541 Mathematics
Department
MEMA - Mech and Manufact Eng
Level
08 - Level 8
Credit
05 - 05 Credits
Duration
Semester
Fee
€
Start Term
2019 - Full Academic Year 2019-20
End Term
9999 - The End of Time
Author(s)
Donny Hurley
Programme Membership
SG_EPREC_K08 201900 Bachelor of Engineering (Honours) in Precision Engineering and Design
Description
This mathematics module provides a geometric approach to vectors, matrices and vector fields and their application to forces and velocities in three dimensions.
Learning Outcomes
On completion of this module the learner will/should be able to;
1.
Calculate dot product of vectors and apply this to find the angle between vectors, project one vector onto another and derive the cosine rule
2.
Calculate cross products of vectors and apply this to find the area of a parallelogram, angular velocities and the volume of a parallelpiped
3.
Understand and determine the linear independence of vectors (with geometric interpretation) and find vector equations of lines and planes
4.
Understand and find linear transformations and isometries as matrix operations: rotation, reflection, translation, eigenvalues and eigenvectors
5.
Manipulate and understand vector fields and partial derivatives including their physical meaning
6.
Calculate the vector operators gradient, divergence and curl as well as some applications of them
7.
Calculate the radial and tangential components of rotating systems, derivatives of vector fields and applications
Teaching and Learning Strategies
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Module Assessment Strategies
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Repeat Assessments
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Indicative Syllabus
Vector addition, subtraction and scalar multiplication
Dot product of vectors and applications (angle between vectors, projection of one vector onto another, the cosine rule)
Cross product of vectors and applications (area of a parallelogram, angular velocity in three dimensions)
Scalar triple product and applications (volume of a parallelepiped)
Vector equations of lines and planes
Linear independence of vectors (with geometric interpretation)
Radial and tangential components of rotating systems
Derivatives of vector fields and applications (including Coriolis force)
Introduction to vector fields
Partial derivatives and introduction to the vector operators gradient, divergence and curl, and their physical meaning
Linear transformations and isometries as matrix operations: rotation, reflection, translation, eigenvalues and eigenvectors
Coursework & Assessment Breakdown
Coursework & Continuous Assessment
20 %
End of Semester / Year Formal Exam
80 %
Coursework Assessment
| Title | Type | Form | Percent | Week | Learning Outcomes Assessed | |
|---|---|---|---|---|---|---|
| 1 | Continuous Assessment | Coursework Assessment | Assessment | 20 % | OnGoing | 1,2,3,4,5,6,7 |
End of Semester / Year Assessment
| Title | Type | Form | Percent | Week | Learning Outcomes Assessed | |
|---|---|---|---|---|---|---|
| 1 | Final Exam | Final Exam | Closed Book Exam | 80 % | End of Semester | 1,2,3,4,5,6,7 |
Full Time Mode Workload
| Type | Location | Description | Hours | Frequency | Avg Workload |
|---|---|---|---|---|---|
| Independent Learning | Not Specified | Independent Learning | 4 | Weekly | 4.00 |
| Lecture | Flat Classroom | Lecture | 4 | Weekly | 4.00 |
Total Full Time Average Weekly Learner Contact Time 4.00 Hours
Part Time Mode Workload
| Type | Location | Description | Hours | Frequency | Avg Workload |
|---|---|---|---|---|---|
| Independent Learning | Not Specified | Independent Learning | 4 | Weekly | 4.00 |
| Lecture | Classroom Equipped for OLL. | Lecture | 4 | Weekly | 4.00 |
Total Part Time Average Weekly Learner Contact Time 4.00 Hours
Module Resources
Non ISBN Literary Resources
K.A. Stroud: "Engineering Mathematics", any edition
K.A. Stroud: "Further Engineering Mathematics", any edition
Other Resources
Khan Academy
Additional Information
None