A course introducing calculus and matrix theory and their use in mathematical modelling. Emphasis will be placed on developing facility, technique and use in applications. Modelling of processes and phenomena which occur in economics and the physical, environmental and life sciences will be used as a vehicle throughout. This course also provides a pathway to higher level mathematics courses.

Topics to be covered include: Linear models, linear systems; Matrices, eigenvalues and eigenvectors, predator-prey models; Functions and graphs, the transcendental functions and limits; Techniques and applications of differentiations and integrations; Unlimited, limited and logistic growth models; Introduction to differential equations: predator-prey systems, equilibrium states.

On satisfying the requirements of this course, students will have the knowledge and skills to:

(1) Develop critical thinking and problem solving skills, in the context of calculus and matrix models.
(2) Describe the algebraic and graphical properties of elementary functions (linear, polynomial, exponential, logarithmic, trigonometric  and their inverses) and their applications to economics and sciences.
(3) Explain the significance of the derivative and the integration and be able to apply techniques for the derivative and the integration to diverse situations in economics and sciences.
(4) Demonstrate accurate and efficient use of ordinary differential equations and develop basic methods for solving them.
(5) Develop an appreciation of matrix models in economics and the physical, environmental and life sciences.

Assessment will be based on:

• Tutorials/quizzes (20%; LO 1-5)
• Mid-semester test (30%; LO 1-5)
• Final Examination (50%; LO 1-5)

48 one hour lectures and 10 2-hour laboratory sessions, plus additional individual work

ACT Mathematical Methods or NSW HSC Mathematics or equivalent.

MATH1001. This course cannot be taken concurrently with or after the successful completion of MATH1013/MATH1115.