Calculus & Linear Algebra II
University of Queensland
Area of Study
Taught In English
(MATH1051) + (MATH1052)
Course Level Recommendations
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Host University Units2
Recommended U.S. Semester Credits4
Recommended U.S. Quarter Units6
Hours & Credits
OverviewCourse DescriptionPlease note that the contact hours for summer semester is 5L2T. Matrices, solution to linear systems, vector & matrix norms. Numerical algorithms for eigensystems, optimisation. First & linear second order differential equations, variation of parameters, applications, numerical methods. Surface & volume integrals, Stoke's & Green's Theorems, applications (flux, heat equations).Course IntroductionMATH2000 covers four major topics: ordinary differential equations, integral calculus, vector calculus and linear algebra. The student will acquire a strong knowledge base of the fundamentals of each topic and be able to apply these concepts to solving a wide variety of problems. As a consequence of this course covering such a broad range of topics, the student can expect to end the semester with an essential mathematical toolkit at their disposal.Learning ObjectivesAfter successfully completing this course you should be able to:1. RECOGNISE AND UNDERSTAND THE MEANING OF
- 1.1 a vector field and the operators gradient, divergence and curl
- 1.2 parametrising curves and surfaces
- 1.3 a vector space, linear independence, basis and dimension
- 1.4 LU and PLU decomposition, the column space, row space and null space of a matrix
- 1.5 similar, orthogonal, symmetric, unitary, normal and Hermitian properties of matrices
- 2.1 certain families of first order and linear second order ordinary differential equations
- 2.2 hyperbolic functions in various mathematical contexts
- 2.3 multiple integrals using rectangular, polar, cylindrical and spherical coordinate systems
- 2.4 line integral and surface integral
- 2.5 a system of linear equations using Gaussian elimination, LU or PLU decomposition and matrix diagonalisation
- 2.6 the eigenvalues and eigenvectors of a matrix, the quadratic form and power method
Class Contact3hours Lecture, 1 hour TutorialAssessment SummaryAssignments (6): 30%Final Exam: 70%
- 3.1 physical problems using ordinary differential equations
- 3.2 multiple integrals to solve problems of flux, volume, area, centre of mass and moments of inertia
- 3.3 physical problems using gradient, divergence, and curl and apply the Theorems of Green, Gauss and Stokes
- 3.4 symmetric, unitary and Hermitian matrices to physical problems
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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.