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MTH282Sciences3 Unitsintermediate

Mathematical Methods Ii

This course, Mathematical Methods II, reviews vector theory, including vector algebra, scalar and vector products, and triple products. It explores differential operators such as gradient, divergence, and curl, applying them in orthogonal curvilinear coordinates. The course also covers Jacobians, transformation of coordinates, and complex variables, including complex numbers, polar operations, Demoivre's theorem and roots of unity. It aims to equip students with essential mathematical tools for advanced studies in science and technology.

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156h
Study Time
13
Weeks
12h
Per Week
intermediate
Math Level
Course Keywords
VectorsDifferential OperatorsCurvilinear CoordinatesComplex VariablesJacobians

Course Overview

Everything you need to know about this course

Course Difficulty

Intermediate Level
Builds on foundational knowledge
65%
intermediate
📊
Math Level
Moderate Math
📖
Learning Type
Theoretical Focus

Course Topics

Key areas covered in this course

1

Vector Algebra

2

Scalar and Vector Products

3

Differential Operators (Gradient, Divergence, Curl)

4

Orthogonal Curvilinear Coordinates

5

Jacobians

6

Complex Numbers

7

Demoivre's Theorem

8

Roots of Unity

Total Topics8 topics

Requirements

Knowledge and skills recommended for success

MTH111

MTH121

💡 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 Assignments

Comprehensive evaluation of course material understanding

Written Assessment

Final Examination

Comprehensive evaluation of course material understanding

Computer Based Test

Career Opportunities

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Data Analyst

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Applied Mathematician

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Software Engineer

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Aerospace Engineer

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Electrical Engineer

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Industry Applications

Real-world sectors where you can apply your knowledge

EngineeringPhysicsComputer ScienceData ScienceTelecommunications

Study Schedule Beta

A structured 13-week journey through the course content

Week
1

Module 1: Review of Vector Theory

4h

Unit 1: Vector Algebra

4 study hours
  • •Review vector definitions, including magnitude and direction.
  • •Practice vector addition, subtraction, and scalar multiplication.
  • •Solve problems involving unit vectors and rectangular components.
Week
2

Module 1: Review of Vector Theory

4h

Unit 2: Vector Algebra-Product of Vectors

4 study hours
  • •Differentiate between scalar and vector products.
  • •Calculate scalar products to find work done.
  • •Calculate vector products to find area of parallelogram.
  • •Solve problems involving scalar and vector products.
Week
3

Module 1: Review of Vector Theory

4h

Unit 3: Vector Functions

4 study hours
  • •Define limit and continuity of vector functions.
  • •Find derivatives of vector functions.
  • •Interpret vector derivatives geometrically to determine velocity.
  • •Solve problems related to vector functions.
Week
4

Module Two: Differential Operators

4h

Unit 1: The Operator Del (∇)

4 study hours
  • •Define the Del operator.
  • •Apply the Del operator to find the gradient of scalar functions.
  • •Interpret the gradient physically.
  • •Solve exercises involving gradients.
Week
5

Module Two: Differential Operators

4h

Unit 2: Divergence of a Vector Field

4 study hours
  • •Understand divergence as a measure of vector field spread or convergence.
  • •Calculate the divergence of vector fields.
  • •Apply the Laplacian operator.
  • •Solve exercises related to divergence and the Laplacian.
Week
6

Module Two: Differential Operators

4h

Unit 3: The Curl of a Vector Field

4 study hours
  • •Define the curl of a vector field.
  • •Interpret the physical implications of the curl.
  • •Solve mathematical problems involving the curl of vector fields.
  • •Relate curl to fluid dynamics and electromagnetic fields.
Week
7

Module Three: Orthogonal Curvilinear Co-ordinates

4h

Unit 1: Jacobians

4 study hours
  • •Define the Jacobian and use it in transformations.
  • •Solve exercises involving the Jacobian.
  • •Relate Jacobians to curvilinear coordinates.
  • •Apply Jacobians to change variables in integrals.
Week
8

Module Three: Orthogonal Curvilinear Co-ordinates

4h

Unit 2: Orthogonal Curvilinear Coordinates

4 study hours
  • •Define orthogonal curvilinear coordinates.
  • •Determine scale factors for transformations.
  • •Calculate elemental volume.
  • •Solve problems in cylindrical and spherical coordinates.
Week
9

Module 4: Complex Variables

4h

Unit 1: Complex Numbers

4 study hours
  • •Define complex numbers and their components.
  • •Perform mathematical operations with complex numbers.
  • •Find the modulus and argument of complex numbers.
  • •Solve exercises on complex numbers.
Week
10

Module 4: Complex Variables

4h

Unit 2: Polar Operations with Complex Numbers

4 study hours
  • •Express complex numbers in polar form.
  • •Carry out multiplication and division of complex numbers in polar form.
  • •Apply Demoivre's Theorem.
  • •Find roots and work with fractional powers of complex numbers.
Week
11

Module 4: Complex Variables

4h

Unit 3: The nth root of Unity

4 study hours
  • •Understand the concept of nth roots of unity.
  • •Solve problems related to nth roots of unity.
  • •Apply complex numbers to solve algebraic equations.
  • •Relate complex roots to geometric representations.
Week
12

Module 1: Review of Vector Theory

6h

Final Revision

6 study hours
  • •Review all modules.
  • •Work on assignments.
  • •Prepare for tutor-marked assignments.
Week
13

Module 2: Differential Operators

6h

Final Revision

6 study hours
  • •Review all modules.
  • •Work on assignments.
  • •Prepare for tutor-marked assignments.

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 vector algebra, focusing on addition, subtraction, and products (dot and cross).

2

Practice calculating gradients, divergences, and curls in Cartesian coordinates.

3

Master coordinate transformations, especially cylindrical and spherical.

4

Work through complex number manipulations: addition, multiplication, division, and polar forms.

5

Apply Demoivre's Theorem to find complex roots and powers.

6

Solve past exam papers to familiarize yourself with question types and difficulty levels.

7

Create concept maps linking vector operations to their geometric interpretations.

8

Dedicate specific study sessions to orthogonal curvilinear coordinates.

9

Practice problems involving Jacobians and variable transformations.

10

Review all TMAs and address any areas of weakness identified.

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