The emphasis will be on understanding the material so that it can both 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. However, the material will not be developed in a rigorous theorem-proof style.
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, Newton's method, Taylor polynomials, L'Hopital's rules. Riemann integration and the Fundamental Theorem of Calculus. Techniques of integration including the method of substitution and integration by parts.
Linear Algebra - Complex numbers. Solution of linear system 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. Emphasis is on understanding and on using algorithms.
Upon successful completion, students will have the knowledge and skills to:
Upon successful completion of this course, 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.
Other InformationCourse Contact: Dr Rebecca Cross
T: 02 61250982
Indicative AssessmentAssessment will be based on:
- Tutorials (25%) (LO1-4)
- Mid-semester test (25%) (LO1-4)
- Final examination (50%) (LO1-4)
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Workload160 hours of total student learning time made up from:
- 75 hours of lectures and tutorial-based activities.
- 85 hours of supported and independent student work.
Requisite and Incompatibility
Preliminary ReadingD.C. Lay, Linear Algebra and its Applications, Addison-Wesley
J. Stewart, Essential Calculus, Cengage Learning, Inc
Tuition fees are for the academic year indicated at the top of the page.
If you are a domestic graduate coursework or international student you will be required to pay tuition fees. Tuition fees are indexed annually. Further information for domestic and international students about tuition and other fees can be found at Fees.
- Student Contribution Band:
- Unit value:
- 6 units
If you are an undergraduate student and 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). You can find your student contribution amount for each course at Fees. Where there is a unit range displayed for this course, not all unit options below may be available.
Offerings, Dates and Class Summary Links
Class summaries, if available, can be accessed by clicking on the View link for the relevant class number.
|Class number||Class start date||Last day to enrol||Census date||Class end date||Mode Of Delivery||Class Summary|
|3999||25 Feb 2019||04 Mar 2019||31 Mar 2019||14 Jun 2019||In Person||N/A|