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Semester 1

Several Variable Calculus and Differential Equations (MATH08063)

Subject

Mathematics

College

SCE

Credits

20

Normal Year Taken

2

Delivery Session Year

2022/2023

Pre-requisites

Visiting students are advised to check that they have studied the material covered in the syllabus of each pre-requisite course before enrolling.

Course Summary

A first several variable calculus course and a first methods course for differential equations. After a review of vector algebra, vector calculus is introduced, including gradient, divergence and curl functions. Double, triple, line, surface and volume integrals are discussed and practised. Green's Theorem, Stokes' theorem and divergence, (Gauss') theorem are distinct highlight. First order linear ordinary diff. eq. are solved by separation, using an integrating factor and numerically. Various solution methods for second order linear homogeneous equations are presented.The course ends with a discussion of the series expansion solutions

Course Description

Week 1 : Vectors and vector functions. (Book 1, Chapter 10) Weeks 1-3 : Partial derivatives. (Book 1, Chapter 11)Weeks 4-5 : Multiple integrals. (Book 1, Chapter 12) Weeks 6-7 : Vector calculus. (Book 1, Chapter 13) Weeks 8-9 : 1st order differential equations. (Book 2, Chapters 1 and 2)Weeks 9-11 : 2nd order differential equations. (Book 2, Chapters 3 and 5)

Assessment Information

Written Exam 60%, Coursework 40%, Practical Exam 0%

Additional Assessment Information

Coursework 40%, Examination 60%

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