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MTH303Sciences3 Unitsintermediate

Vector And Tensor Analysis

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.

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150h
Study Time
13
Weeks
12h
Per Week
advanced
Math Level
Course Keywords
VectorsTensorsVector AlgebraDifferentiationIntegration

Course Overview

Everything you need to know about this course

Course Difficulty

Intermediate Level
Builds on foundational knowledge
65%
intermediate
∑
Math Level
Advanced Math
📖
Learning Type
Theoretical Focus

Course Topics

Key areas covered in this course

1

Vector Algebra

2

Vector Differentiation

3

Line Integrals

4

Green's Theorem

5

Stokes's Theorem

6

Tensor Analysis

Total Topics6 topics

Requirements

Knowledge and skills recommended for success

MTH142-Vector and Geometry

MTH281-Mathematical Methods 1

💡 Don't have all requirements? Don't worry! Many students successfully complete this course with basic preparation and dedication.

Assessment Methods

How your progress will be evaluated (3 methods)

assignments

Comprehensive evaluation of course material understanding

Written Assessment

tutor-marked assessments

Comprehensive evaluation of course material understanding

Written Assessment

final examination

Comprehensive evaluation of course material understanding

Written Assessment

Career Opportunities

Explore the career paths this course opens up for you

Aerospace Engineer

Apply your skills in this growing field

Mechanical Engineer

Apply your skills in this growing field

Data Scientist

Apply your skills in this growing field

Applied Physicist

Apply your skills in this growing field

Research Mathematician

Apply your skills in this growing field

Industry Applications

Real-world sectors where you can apply your knowledge

AerospaceFluid DynamicsGeneral RelativityComputer GraphicsMachine Learning

Study Schedule Beta

A structured 13-week journey through the course content

Week
1

Module 1: Elementary Vector Algebra

4h

Unit 1: Elementary Vector Algebra

4 study hours
  • •Review scalar and vector quantities, angle between two vectors.
  • •Practice problems involving scalar products of two vectors.
Week
2

Module 1: Elementary Vector Algebra

4h

Unit 2: Vector Differentiation (Gradient, Divergence and Curl)

4 study hours
  • •Practice differentiation of vector quantities.
  • •Solve problems to find the gradient of scalar and vector fields.
Week
3

Module 1: Elementary Vector Algebra

4h

Unit 3: The Line Integral

4 study hours
  • •Evaluate line integrals of vector functions.
  • •Solve problems related to line integrals.
Week
4

Module 2: Green's Theorem, Divergence Theorem and Stokes's Theorem

4h

Unit 1: Green's Theorem, Divergence Theorem and Stoke's Theorem

4 study hours
  • •Understand and apply Green's Theorem.
  • •Solve problems using Green's Theorem.
Week
5

Module 2: Green's Theorem, Divergence Theorem and Stokes's Theorem

4h

Unit 1: Green's Theorem, Divergence Theorem and Stoke's Theorem

4 study hours
  • •Understand and apply Divergence Theorem.
  • •Solve problems using Divergence Theorem.
Week
6

Module 2: Green's Theorem, Divergence Theorem and Stokes's Theorem

4h

Unit 1: Green's Theorem, Divergence Theorem and Stoke's Theorem

4 study hours
  • •Understand and apply Stoke's Theorem.
  • •Solve problems using Stoke's Theorem.
Week
7

Module 2: Green's Theorem, Divergence Theorem and Stokes's Theorem

4h

Unit 2: Tensor Analysis

4 study hours
  • •Define tensors and perform basic operations.
  • •Practice problems on tensor analysis.
Week
8

Module 2: Green's Theorem, Divergence Theorem and Stokes's Theorem

4h

Unit 2: Tensor Analysis

4 study hours
  • •Understand transformation of co-ordinates.
  • •Solve problems on transformation of co-ordinates.
Week
9

Module 2: Green's Theorem, Divergence Theorem and Stokes's Theorem

4h

Unit 2: Tensor Analysis

4 study hours
  • •Understand Cartesian Tensor.
  • •Solve problems on Cartesian Tensor.
Week
10

Module 2: Green's Theorem, Divergence Theorem and Stokes's Theorem

4h

Unit 2: Tensor Analysis

4 study hours
  • •Understand Contravariant and Covariant Vector.
  • •Solve problems on Contravariant and Covariant Vector.
Week
11

Module 2: Green's Theorem, Divergence Theorem and Stokes's Theorem

4h

Unit 2: Tensor Analysis

4 study hours
  • •Understand Contravariant, Covariant and Mixed Tensor.
  • •Solve problems on Contravariant, Covariant and Mixed Tensor.
Week
12

Module 2: Green's Theorem, Divergence Theorem and Stokes's Theorem

4h

Unit 2: Tensor Analysis

4 study hours
  • •Understand Fundamental Operations with Tensor.
  • •Solve problems on Fundamental Operations with Tensor.
Week
13

Module 2: Green's Theorem, Divergence Theorem and Stokes's Theorem

4h

Unit 2: Tensor Analysis

4 study hours
  • •Understand Outer Multiplication.
  • •Solve problems on Outer Multiplication.

This study schedule is in beta and may not be accurate. Please use it as a guide and consult the course outline for the most accurate information.

Course PDF Material

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Study Tips & Exam Preparation

Expert tips to help you succeed in this course

1

Review all unit summaries and key definitions.

2

Practice solving problems from each unit, focusing on tutor-marked assignments.

3

Create concept maps linking vector algebra, differentiation, and integration.

4

Focus on understanding the applications of Green's, Stokes's, and Divergence Theorems.

5

Practice tensor manipulations and transformations.

6

Allocate time to review past examination papers and solutions.

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