Unit of study_

# MATH2021: Vector Calculus and Differential Equations

### 2025 unit information

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).

## Unit details and rules

#### Science

 Prerequisites: ? [(MATH1061 or MATH1961 or MATH1971) and (MATH1062 or MATH1962 or MATH1972)] or [(MATH1X21 or MATH1931 or MATH1X01 or MATH1906) and (MATH1XX2 or a mark of 65 or above in MATH1014) and (MATH1X23 or MATH1933 or MATH1X03 or MATH1907)] None MATH2921 or MATH2065 or MATH2965 or (MATH2061 and MATH2022) or (MATH2061 and MATH2922) or (MATH2961 and MATH2022) or (MATH2961 and MATH2922) or MATH2067 None

At the completion of this unit, you should be able to:

• LO1. demonstrate a conceptual understanding of vector-valued functions, partial derivatives, curves, and integration over a region, volume, and surface as well as solving basic differential equations thorough background in a variety of techniques and applications of mathematical analysis.
• LO2. understanding the definitions, main theorems, and corollaries for path integrals, conservative fields, multiple integrals Green's theorem, Gauss' theorem, and Stokes' theorem, but also to understand the structure of the solutions of linear differential equations, the method of series solutions, the Laplace transform, solving boundary-value problems involving Sturm-Liouville operators on either a bounded interval or a rectangle, and to understand what is an eigenvalue.
• LO3. be fluent with substitutions in integrals and changing coordinate systems from cartesian into polar, cylindrical, or spherical ones.
• LO4. develop appreciation and strong working knowledge of the theory and applications of elementary Vector Analysis and Differential Equations.
• LO5. be fluent with important examples, theorems, and applications of the theory.

## Unit availability

This section lists the session, attendance modes and locations the unit is available in. There is a unit outline for each of the unit availabilities, which gives you information about the unit including assessment details and a schedule of weekly activities.

The outline is published 2 weeks before the first day of teaching. You can look at previous outlines for a guide to the details of a unit.

Session MoA   Location Outline
Semester 1 2024
Normal day Camperdown/Darlington, Sydney
Session MoA   Location Outline
Semester 1 2025
Normal day Camperdown/Darlington, Sydney
Outline unavailable
Session MoA   Location Outline
Semester 1 2020
Normal day Camperdown/Darlington, Sydney
Semester 1 2021
Normal day Camperdown/Darlington, Sydney
Semester 1 2021
Normal day Remote
Semester 1 2022
Normal day Camperdown/Darlington, Sydney
Semester 1 2022
Normal day Remote
Semester 1 2023
Normal day Camperdown/Darlington, Sydney
Semester 1 2023
Normal day Remote

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### Modes of attendance (MoA)

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