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Unit of study_

Vector Calculus and Differential Equations - MATH2021

Year - 2019

This unit opens with topics from vector calculus, including vector-valued functions (parametrised curves and surfaces; vector fields; div, grad and curl; gradient fields and potential functions), line integrals (arc length; work; path-independent integrals and conservative fields; flux across a curve), iterated integrals (double and triple integrals, polar, cylindrical and spherical coordinates; areas, volumes and mass; Green's Theorem), flux integrals (flow through a surface; flux integrals through a surface defined by a function of two variables, through cylinders, spheres and other parametrised surfaces), Gauss' and Stokes' theorems. The unit then moves to topics in solution techniques for ordinary and partial differential equations (ODEs and PDEs) with applications. It provides a basic grounding in these techniques to enable students to build on the concepts in their subsequent courses. The main topics are: second order ODEs (including inhomogeneous equations), higher order ODEs and systems of first order equations, solution methods (variation of parameters, undetermined coefficients) the Laplace and Fourier Transform, an introduction to PDEs, and first methods of solutions (including separation of variables, and Fourier Series).

Classes
3x1-hr lectures; 1x1-hr tutorial; and 1x1-hr practice class/wk

Assessment
2 x quizzes (24%); 2 x assignments (16%); final exam (60%)

Textbooks
As set out in the Intermediate Mathematics Handbook

Pre-requisites

(MATH1X21 or MATH1931 or MATH1X01 or MATH1906) and (MATH1XX2) and (MATH1X23 or MATH1933 or MATH1X03 or MATH1907)

Prohibitions

MATH2921 or MATH2065 or MATH2965 or (MATH2061 and MATH2022) or (MATH2061 and MATH2922) or (MATH2961 and MATH2022) or (MATH2961 and MATH2922) or MATH2067

Details

Faculty: Science

Semester 1

25 Feb 2019

Department/School: Mathematics and Statistics Academic Operations
Study Mode: Normal (lecture/lab/tutorial) day
Census Date: 31 Mar 2019
Unit of study level: Intermediate
Credit points: 6.0
EFTSL: 0.125
Available for study abroad and exchange: Yes
Faculty/department permission required? No
Location
Camperdown
More details
Unit of Study coordinator: Dr Daniel Hauer
HECS Band: 2
Courses that offer this unit

Non-award/non-degree study If you wish to undertake one or more units of study (subjects) for your own interest but not towards a degree, you may enrol in single units as a non-award student. Cross-institutional study If you are from another Australian tertiary institution you may be permitted to undertake cross-institutional study in one or more units of study at the University of Sydney.

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