33190 Mathematical Modelling for Science

Warning: The information on this page is indicative. The subject outline for a particular semester, location and mode of offering is the authoritative source of all information about the subject for that offering. Required texts, recommended texts and references in particular are likely to change. Students will be provided with a subject outline once they enrol in the subject.

Recommended studies: two units of HSC Mathematics

Handbook description

Topics covered in this subject include functions and their relationship to scientific experiments; differentiability; differential equations arising from scientific problems; solution by series; radioactive decay and exponential functions; oscillatory motion and trigonometric functions; integration; the logarithm function; inverse functions; inverse trigonometric functions; and solution of differential equations by integration and inverse functions. The computer algebra system Mathematica is used for symbolic, graphical and numerical computations.

Subject objectives/outcomes

By the end of this subject students should be able to:

1. Understand the relevance of mathematics to science.
2. Understand the way in which mathematics can supply useful tools and resources to model real world problems.
3. Use mathematical terminology and concepts.
4. Use formal and informal language to demonstrate understanding of these concepts.
5. Demonstrate a high level of skill in the computational techniques of the subject.
6. Demonstrate understanding of the theoretical results that justify the use of these techniques.
7. Communicate the above knowledge clearly, logically and critically.
8. Be able to work independently to further their knowledge of mathematical modelling
9. Be able to apply the subject matter covered in lectures, tutorials and assignments to previously unseen problems.
10. Be aware of the historical context of mathematical development.
11. Use the computer algebra system Mathematica to perform calculations and explore mathematical ideas relevant to the subject content.
    

Contribution to course aims and graduate attributes

By giving a broad introduction to the most important and widely used concepts in mathematics, this subject links directly to the graduate attribute “Disciplinary knowledge and its appropriate applications”. Throughout the course mathematics is presented as a tool, which students are invited to use in the solution to real-world problems. This subject thereby contributes to the graduate attributes “An enquiry-oriented approach” and “Professional skills and their appropriate application”.

Teaching and learning strategies

Lectures: three hours/week
Tutorials: one hour per week
Computer Labs: 3 sessions of one hour, at intervals throughout the semester
 

Content

Vectors and scalars, and their relation to geometry. Complex numbers. Functions and derivatives, and their relationship to measurement and the interpretation of physical results. Differentiability. Differential equations arising from physical problems. Solution by series. Oscillatory motion. Trigonometric functions and inverse trigonometric functions. Integrals and logarithms, inverse functions. Methods of integration. Introduction to matrices and linear algebra. The computer algebra system Mathematica will be used in the subject as an aid to computation, graph plotting and visualization.

Minimum requirements

A minimum of 40% is required in the final exam in order to pass the subject. If a mark of less than 40% is obtained in the exam, then the final mark will be either 47% or the mark according to the above weighting, whichever is the lower.

Required texts

J. Stewart: Calculus - concepts and contexts, 4th Edition, Cengage

References

• G. H. Smith and G. J. McLelland (2003). On the shoulders of giants: A course in single variable calculus. Sydney, UNSW Press.
• C. H. Edwards and D. E. Penney, Calculus with Analytic Geometry, 3rd or 4th Editions. Prentice Hall.
• S.L. Salas and E. Hille, Calculus: one and several variables, 7th edition, John Wiley and Sons, 1995
• J. Callahan and K. Hoffman, Calculus in context, W. H. Freeman and Company, 1995