Vector And Tensor Analysis
- Sciences
- 300 level
- 3 credit units
- 53 pages
- 5 units
This course provides an understanding of Vectors and Tensors, building upon knowledge acquired in MTH142 and MTH281. It explores vector algebra, differentiation, and integration, including Green's Theorem, Stokes's Theorems, and Divergence Theorem. The course aims to equip students with the ability to solve problems in higher dimensional spaces and apply these concepts in engineering, physics, and other related fields, focusing on tensor analysis and its applications.
About this course
- Difficulty
- Intermediate
- Study hours
- 150 hours
- Maths
- Advanced
- Content
- Theoretical, problem solving
- Practical work
- No
- MTH142-Vector and Geometry
- MTH281-Mathematical Methods 1
- Assignments
- Tutor marked assessments
- Final examination
What you'll read
The real module and unit structure of MTH303, taken from the course material NOUN publishes.
One paragraph, so you can see how it reads
MTH303 · UNIT 2 VECTOR DIFFERENTIATION (GRADIENT, DIVERGENCE AND CURL)
In unit 1, we learnt about vector algebra and established some properties of vectors. In this unit, we shall consider vector differentiation and derive some important formula and properties of vector differentiation.
What you should be able to do
- Prove continuity and establish limit functions in Vectors and Tensors
- Define Divergence, Gradient of Scalar Functions, and Curl of Vectors
- Establish Green's Theorem, Stokes's Theorems and Divergence Theorem
- Work out answers to simple problems in Tensor Analysis
- Apply vector and tensor analysis to solve problems in physics and engineering
What it prepares you for
- Aerospace Engineer
- Mechanical Engineer
- Data Scientist
- Applied Physicist
- Research Mathematician
- Aerospace
- Fluid Dynamics
- General Relativity
- Computer Graphics
- Machine Learning
Where it gets hard
The units students slow down on, and what makes each one heavy.
- Module 2: Green's Theorem, Divergence Theorem and Stokes's Theorem
Unit 2: Tensor Analysis
Tensor analysis involves abstract mathematical concepts and requires a strong foundation in linear algebra and calculus.
- Module 2: Green's Theorem, Divergence Theorem and Stokes's Theorem
Unit 1: Green's Theorem, Divergence Theorem and Stoke's Theorem
The Divergence Theorem requires a strong understanding of vector calculus and multivariable integration.
A suggested way through it
13 weeks, about 52 hours in total. Yours will differ.
- Week 1Module 1: Elementary Vector Algebra
Unit 1: Elementary Vector Algebra · 4 hours
Review scalar and vector quantities, angle between two vectors.. Practice problems involving scalar products of two vectors..
- Week 2Module 1: Elementary Vector Algebra
Unit 2: Vector Differentiation (Gradient, Divergence and Curl) · 4 hours
Practice differentiation of vector quantities.. Solve problems to find the gradient of scalar and vector fields..
- Week 3Module 1: Elementary Vector Algebra
Unit 3: The Line Integral · 4 hours
Evaluate line integrals of vector functions.. Solve problems related to line integrals..
- Week 4Module 2: Green's Theorem, Divergence Theorem and Stokes's Theorem
Unit 1: Green's Theorem, Divergence Theorem and Stoke's Theorem · 4 hours
Understand and apply Green's Theorem.. Solve problems using Green's Theorem..
- Week 5Module 2: Green's Theorem, Divergence Theorem and Stokes's Theorem
Unit 1: Green's Theorem, Divergence Theorem and Stoke's Theorem · 4 hours
Understand and apply Divergence Theorem.. Solve problems using Divergence Theorem..
- Week 6Module 2: Green's Theorem, Divergence Theorem and Stokes's Theorem
Unit 1: Green's Theorem, Divergence Theorem and Stoke's Theorem · 4 hours
Understand and apply Stoke's Theorem.. Solve problems using Stoke's Theorem..
- Week 7Module 2: Green's Theorem, Divergence Theorem and Stokes's Theorem
Unit 2: Tensor Analysis · 4 hours
Define tensors and perform basic operations.. Practice problems on tensor analysis..
- Week 8Module 2: Green's Theorem, Divergence Theorem and Stokes's Theorem
Unit 2: Tensor Analysis · 4 hours
Understand transformation of co-ordinates.. Solve problems on transformation of co-ordinates..
- Week 9Module 2: Green's Theorem, Divergence Theorem and Stokes's Theorem
Unit 2: Tensor Analysis · 4 hours
Understand Cartesian Tensor.. Solve problems on Cartesian Tensor..
- Week 10Module 2: Green's Theorem, Divergence Theorem and Stokes's Theorem
Unit 2: Tensor Analysis · 4 hours
Understand Contravariant and Covariant Vector.. Solve problems on Contravariant and Covariant Vector..
- Week 11Module 2: Green's Theorem, Divergence Theorem and Stokes's Theorem
Unit 2: Tensor Analysis · 4 hours
Understand Contravariant, Covariant and Mixed Tensor.. Solve problems on Contravariant, Covariant and Mixed Tensor..
- Week 12Module 2: Green's Theorem, Divergence Theorem and Stokes's Theorem
Unit 2: Tensor Analysis · 4 hours
Understand Fundamental Operations with Tensor.. Solve problems on Fundamental Operations with Tensor..
- Week 13Module 2: Green's Theorem, Divergence Theorem and Stokes's Theorem
Unit 2: Tensor Analysis · 4 hours
Understand Outer Multiplication.. Solve problems on Outer Multiplication..
Preparing for the exam
- Review all unit summaries and key definitions.
- Practice solving problems from each unit, focusing on tutor-marked assignments.
- Create concept maps linking vector algebra, differentiation, and integration.
- Focus on understanding the applications of Green's, Stokes's, and Divergence Theorems.
- Practice tensor manipulations and transformations.
- Allocate time to review past examination papers and solutions.
Questions students ask about this course
What is MTH303 about?
This course provides an understanding of Vectors and Tensors, building upon knowledge acquired in MTH142 and MTH281. It explores vector algebra, differentiation, and integration, including Green's Theorem, Stokes's Theorems, and Divergence Theorem. The course aims to equip students with the ability to solve problems in higher dimensional spaces and apply these concepts in engineering, physics, and other related fields, focusing on tensor analysis and its applications.
How many units does MTH303 have?
MTH303, Vector And Tensor Analysis, has 5 units across 2 modules, over 53 pages of course material. You can read it one unit at a time.
How many credit units is MTH303?
MTH303 carries 3 credit units, at 300 level in Sciences.
Is MTH303 hard?
MTH303 is rated intermediate level, with advanced mathematical content. It is mostly theoretical and problem solving work.
How long does MTH303 take to study?
About 150 hours of study, spread across its 5 units.
How is MTH303 assessed?
MTH303 is assessed by assignments, tutor marked assessments and final examination.
What do I need before starting MTH303?
MTH142-Vector and Geometry MTH281-Mathematical Methods 1
What can I do with MTH303?
Aerospace Engineer, Mechanical Engineer, Data Scientist, Applied Physicist and Research Mathematician.