- Code MATH1013
- Unit Value 6 units
- Offered by Mathematical Sciences Institute
- ANU College ANU Joint Colleges of Science
- Course subject Mathematics
- Areas of interest Mathematics
- Academic career UGRD
- Mode of delivery In Person
The course has been adjusted for remote participation in Sem1 2021. On-campus activities will be available. Email enquiries to firstname.lastname@example.org
This course covers single-variable calculus and introductory linear algebra. The emphasis will be on understanding the material so that it both can be applied across a range of fields including the physical and biological sciences, engineering and information technologies, economics and commerce, and can also serve as a base for future mathematics courses. Many applications and connections with other fields will be discussed although not developed in detail. The material will not be developed in a rigorous theorem-proof style. Students interested in a deeper understanding of mathematics or more mathematical/theoretical aspects of topics including engineering, science and economics, should enrol in MATH1115.
Topics to be covered include:
Calculus - Limits, including infinite limits and limits at infinity. Continuity and global properties of continuous functions. Differentiation, including mean value theorem, chain rule, implicit differentiation, inverse functions, antiderivatives and basic ideas about differential equations. Transcendental functions: exponential and logarithmic functions and their connection with integration, growth and decay, hyperbolic functions. Local and absolute extrema, concavity and inflection points. L'Hopital's rule. Riemann integration and the Fundamental Theorem of Calculus. Techniques of integration including the method of substitution and integration by parts. Volumes.
Linear Algebra - Solution of linear systems of equations. Matrix algebra including matrix inverses, partitioned matrices, linear transformations, matrix factorisation and subspaces. Determinants. Example applications including graphics, the Leontief Input-Output Model and various linear models in science and engineering. Complex numbers. Emphasis is on understanding and on using algorithms.
Upon successful completion, students will have the knowledge and skills to:
- Explain the fundamental concepts of calculus and linear algebra and their role in modern mathematics and applied contexts. These concepts include the solution of linear systems, matrix algebra, linear transformations and determinants in Linear Algebra; and limits, continuity, differentiation, local and absolute extrema, Riemann integration and the fundamental theorem of calculus in Calculus.
- Demonstrate accurate and efficient use of calculus and linear algebra techniques as they relate to the concepts listed above.
- Demonstrate capacity for mathematical reasoning through explaining concepts from calculus and linear algebra.
- Apply problem-solving using calculus and linear algebra techniques applied to diverse situations in physics, engineering and other mathematical contexts.
Secondary School Prerequisite: A satisfactory result in ACT Specialist Mathematics Major-Minor or NSW HSC Mathematics Extension 1 or equivalent. Students with a good pass in ACT Specialist Mathematics Major or NSW HSC Mathematics or equivalent will be considered. Students with a level of mathematics equivalent to ACT Mathematical Methods should enrol in the bridging course MATH1003.
- Workshop assessment (completed during workshops) (10) [LO 1,2,3,4]
- Online quizzes (10) [LO 1,2,3,4]
- Assignments (10) [LO 1,2,3,4]
- Midsemester examination (20) [LO 1,2,4]
- Final examination (50) [LO 1,2,4]
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The expected workload will consist of approximately 130 hours throughout the semester including:
• Face-to face component which may consist of 4 x 1 hour lectures per week (48 hours) as well as a total of 15 hours of workshop time.
• Approximately 67 hours of self-study per semester which will include preparation for lectures, quizzes and other assessment tasks.
There are no course-specific inherent requirements.
Requisite and Incompatibility
• Linear Algebra (3rd edition or later) by David Lay.
• Essential Calculus (2nd edition) by James Stewart.
Tuition fees are for the academic year indicated at the top of the page.
Commonwealth Support (CSP) Students
If you have been offered a Commonwealth supported place, your fees are set by the Australian Government for each course. At ANU 1 EFTSL is 48 units (normally 8 x 6-unit courses). More information about your student contribution amount for each course at Fees.
- Student Contribution Band:
- Unit value:
- 6 units
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