BDIC1043J Maths 4

Academic Year 2021/2022

This module is the forth module of calculus, about multi-variable integration calculus, ordinary differential equations (ODEs), and Fourier series and Fourier transform.
By learning multi-variable calculus, students will know how to extend the techniques of single-variable case to the multi-variable case, where new methods and ideas apply.
By learning ODEs, students will receive the training of mathematical modelling; that is, for a concrete problem in finance and other areas, one needs to find a differential equation to describe the system, and then to solve it. Students should be aware of the fact that not every equation is solvable; only some particular types of equations have had an analytical solution, where the solving procedure strongly depends on the equation’s type.
By learning Fourier series and Fourier transform, students are expected to obtain a first idea for integration transforms, and get prepared for future study on market dynamics, free pricing and other topics in mathematical finance.

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Curricular information is subject to change

Learning Outcomes:

Students are expected to achieve the following competence:
• Computing double integrals in right coordinates, especially iterated integrals;
• Computing double integrals in polar coordinates;
• Computing triple integrals in right coordinates;
• Computing triple integrals in cylindrical and spherical coordinates;
• Being able to recognize some particular types of first and second order ODEs, and to find their solutions. Emphasis is placed on the geometric meaning of the equations and solutions.
• Achieving the basic knowledge of orthogonal functions, being able to compute the Fourier series of a period function in terms of sinusoidal functions.
• To acquire basic knowledge about integration transforms, and be able to perform the Fourier transform.

Indicative Module Content:

Teaching Plan

Week 9 Double integrals in Rt coordinates.
Week10 Double integrals in polar coordinates, and triple integrals in Rt coordinates.
Week11 Triple integrals in Rt, cylindrical and spherical coordinates.
Week12 First order ODEs: different types, and geometric and practical meaning of the solutions.
Week13 Second order ODEs: different types, and geometric and practical meaning of the solutions.
Week14 Orthogonal functions; Fourier series for period functions.
Week15 Integration transforms; Fourier transforms for aperiodic functions.
Week16 Revision.

* Tutorials will be held every week.

Student Effort Hours: 
Student Effort Type Hours
Lectures

48
Practical

17
Total

65
Approaches to Teaching and Learning:
Lecturing (face-to-face teaching) + tutorials + close-book examinations. 
Requirements, Exclusions and Recommendations

Not applicable to this module.


Module Requisites and Incompatibles
Not applicable to this module.
 
Assessment Strategy  
Description Timing Open Book Exam Component Scale Must Pass Component % of Final Grade
Continuous Assessment: Attendence recording and tutorial participation. Throughout the Trimester n/a Pass/Fail Grade Scale No

20
Examination: Final Exam.
90 minutes of examination, at the end of the module.		 Unspecified No Alternative linear conversion grade scale 40% No

65
Assignment: Research proposal based on group work. Unspecified n/a Alternative linear conversion grade scale 40% No

15

Carry forward of passed components
No
 
Resit In Terminal Exam
Summer Yes - 2 Hour
Please see Student Jargon Buster for more information about remediation types and timing. 
Feedback Strategy/Strategies

• Group/class feedback, post-assessment

How will my Feedback be Delivered?

Not yet recorded.