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.
UTS: Science: Mathematical SciencesCredit points: 6 cp
Result type: Grade and marks
Anti-requisite(s): 33130 Mathematical Modelling 1 AND 35101 Introduction to Linear Dynamical Systems
Recommended studies: two units of HSC Mathematics
Handbook description
Mathematical modelling is essential in all branches of science. This subject develops the knowledge and skills necessary for problem-solving and mathematical modelling at an introductory level. Topics covered include: vectors and geometry; complex numbers; calculus and its relationship to science; differentiation and integration of functions; inverse, trigonometric and hyperbolic functions; the solution of differential equations with applications to exponential growth and decay and oscillating systems; Taylor series; and an introduction to linear algebra. The computer algebra system Mathematica is used for symbolic, graphical and numerical computations.
Subject objectives
Upon successful completion of this subject students should be able to:
| 1. | Understand the relevance of mathematics to science. |
|---|---|
| 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. |
| 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. |
This subject also contributes specifically to the development of following course intended learning outcomes:
- An understanding of the nature, practice and application of the chosen science discipline. (1.0)
Contribution to the development of 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.
Assessment
Assessment task 1: Final examination
| Objective(s): | This assessment task contributes to the development of course intended learning outcome(s): 1.0 |
|---|---|
| Weight: | 60 |
| Criteria: | Correct use of terminology |
Assessment task 2: Class tests
| Objective(s): | This assessment task contributes to the development of course intended learning outcome(s): 1.0 |
|---|---|
| Weight: | 26 |
| Length: | Two 30 minute tests. |
| Criteria: | Correct use of terminology |
Assessment task 3: Weekly tutorial preparation tasks
| Objective(s): | This assessment task contributes to the development of course intended learning outcome(s): 1.0 |
|---|---|
| Weight: | 11 |
| Criteria: | Correct choice and use of problem solving strategies and procedures |
Assessment task 4: Computer Labs
| Weight: | 3 |
|---|---|
| Criteria: | Correct use of terminology Correct choice and use of problem solving strategies and procedures Careful mathematical reasoning |
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, Metric International 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
