- Code MATH2305
- Unit Value 6 units
- Offered by Mathematical Sciences Institute
- ANU College ANU Joint Colleges of Science
- Course subject Mathematics
- Areas of interest Mathematics
This course shows the modelling process in the context of differential equations and case studies from a number of areas such as population dynamics, economics, electric circuits, mechanical systems, fluid flow, physics and astrophysics. Analytic methods from the elementary theory of differential equations and calculus will be provided to allow for the analysis of the various models being investigated. The numerical package MATLAB will be used to study model behaviour and to obtain deeper understanding of the consequences of analytical studies.
Topics to be covered include:
First order differential equations; second order linear equations; systems of first order equations; nonlinear differential equations; power series solutions; Bessel and Legendre equations; the gamma function.
Advanced Vector Calculus - Curves and surfaces in three dimensions; parametric representations; curvilinear coordinate systems; Surface and volume integrals; use of Jacobians; gradient, divergence and curl; identities involving vector differential operators; the Laplacian; Green's and Stokes' theorems.
Upon successful completion, students will have the knowledge and skills to:
On successful completion of this course, students will be able to:
1. Explain the fundamental concepts of differential equations and vector calculus and their role in modern applied mathematics and real-world contexts.
2. Demonstrate accurate and efficient use of techniques involved in solving differential equations and applying vector differential operators.
3. Demonstrate capacity for mathematical reasoning through analyzing, proving and explaining concepts from the theory of differential equations.
4. Apply problem-solving using techniques in differential equations and vector calculus in diverse situations in physics, engineering and other mathematical contexts.
Assessment will be based on:
- Exams (65%; LO 1-5)
- Workshop participation and presentation (10%; LO 1-5)
- Assignments (15%; LO 1-5)
- Quizzes (10%; LO 1-5)
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WorkloadThree lectures per week and regular workshops.
Requisite and Incompatibility
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- Student Contribution Band:
- Unit value:
- 6 units
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