Calculus & Linear Algebra I
University of Queensland
Area of Study
Taught In English
Course Level Recommendations
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Host University Units2
Recommended U.S. Semester Credits4
Recommended U.S. Quarter Units6
Hours & Credits
OverviewCourse DescriptionVectors, linear independence, scalar product. Matrices, simultaneous equations, determinants, vector product, eigenvalues, eigenvectors, applications. Equation of straight line & plane. Extreme value theorem, maxima & minima. Sequences, series, Taylor series, L'Hopital's rules. Techniques of integration, numerical methods, volumes of revolution.Course IntroductionMATH1051 provides an important foundation in calculus and linear algebra that will prove useful for further studies in pure and applied sciences, engineering, finance or further mathematics pursuits.The calculus component extends high school concepts. We investigate optimisation techniques, limits and L'Hopital's rule, as well as standard techniques of integration and volumes of revolution. Another important topic is the study of sequences and series (infinite sums). This extends to Taylor series which are an important tool used throughout the sciences. Numerical integration techniques will be developed and you will implement them in MATLAB in the computer labs.Linear algebra is the study of vectors and matrices and is extensively used to model systems of interacting elements. For example, matrix methods are common in structural engineering and matrix algebra is necessary for computer graphics. This course covers vectors, linear independence and scalar product which are tools to manipulate vectors. The course continues with matrices, simultaneous equations and determinants. An important component of the study concerns eigenvalues and eigenvectors which model resonant frequencies in dynamical systems.A further component of MATH1051 comprises an introduction to the computational mathematics package MATLAB, which is useful for many real-life applications and is compulsory for further studies in engineering and scientific computation.Learning ObjectivesAfter successfully completing this course you should be able to:
Class Contact3 Lecture hours, 1 Tutorial hour, 1 Practical or Laboratory hourAssessment SummaryIn class quiz: 10%Computer Exercise: 10%Problem sets (4 assignments): 10%Mid-Semester Exam: 15%Final Exam: 55%
- Evaluate limits, derivatives, and integrals, explain the underlying mathematical basis, interpret the results geometrically, and perform calculations associated with a number of applications;
- Calculate the limits of sequences and series, and use them to approximate functions;
- Understand linear transformations using matrices;
- Work with matrices and vectors including a complete understanding of the behaviour of an m * n linear system;
- Understand the concept of invertibility for matrices, know many criteria for invertibility and be able to find inverses;
- Understand abstract concepts in linear algebra such as vector space, dimension and basis, and be able to construct simple proofs involving these concepts;
- Compute confidently with basic Matlab commands and interpret the results.
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Credits earned vary according to the policies of the students' home institutions. According to ISA policy and possible visa requirements, students must maintain full-time enrollment status, as determined by their home institutions, for the duration of the program.