Linear Algebra and Differential Equations
Gold Coast, Australia
Area of Study
Taught In English
Prerequisites : 1201SCG Linear Algebra and 1202SCG Calculus 1 OR
1011SCG or 1201BPS Mathematics 1A and 1012SCG or 1202BPS Mathematics 1B
Course Level Recommendations
ISA offers course level recommendations in an effort to facilitate the determination of course levels by credential evaluators.We advice each institution to have their own credentials evaluator make the final decision regrading course levels.
Recommended U.S. Semester Credits3 - 4
Recommended U.S. Quarter Units4 - 6
Hours & Credits
This course covers fundamental aspects of linear algebra and differential equations with applications to physical problems. Topics include: matrices and determinants; vector spaces; linear independence; basis sets; orthogonality; innner product spaces; eigenvalues and eigenvectors; series/sequences analysis; vector analysis; special functions and Laplace transforms.
This course consists of two parts - linear algebra and differential equations.
It investigates further topics of linear algebra, analysis, vector analysis, differential equations, special functions and Laplace transforms, for application to physical problems.
The purpose of this course is to provide further mathematical techniques required for applied mathematicians and physical scientists. It is a defining course for the Applied Mathematics major, and is a supporting mathematical course (prior assumed) for some courses in the Physics major. The course is divided into two subsections : Differential Equations and Linear Algebra.
A good understanding of linear algebra is essential for many parts of mathematics, for developing mathematical models and in the numerical solution of linear and nonlinear problems. This topic should expand students’ knowledge of linear algebra and its importance in the scheme of mathematics learning.
This topic will cover matrix multiplication, row reduction, determinants, matrix inverse, dimension, subspaces, orthogonality and bases, including relevant computations in an easy to learn manner providing students with a lot of experience using a wide array of problem solving techniques in linear algebra. MATLAB software will be used routinely.
This course is concerned with teaching mathematical tools, ideas which themselves have mathematical interest, but more importantly can be applied to practical problems in the real world. As such, the course material will not deal with the applications directly, but instead will concentrate on the mathematical development, with some motivation given where possible. Students will fully appreciate the applications of these tools when taking higher level courses in applied mathematics, engineering, physics, and other physical sciences.
After successfully completing this course you should be able to:
1 Use Gaussian elimination to determine the solution (or solubility) of systems of linear equations.
2 Use matrices and their properties to determine the solution (or solubility) of systems of linear equations.
3 Understand the definition, key properties, and broader mathematical significance of vector spaces.
4 Understand the notions of linear dependence and independence, basis sets and dimension.
5 Represent linear transformations in terms of matrices.
6 Define and use the concepts of inner products and vector norm in common vector spaces.
7 Understand the process of orthogonalisation and its uses.
8 Define eigenvalues and eigenvectors and understand some important applications.
9 Understand the concepts of convergence for infinite sequences and infinite series.
10 Apply standard tests to determine whether or not infinite series converge.
11 Determine the radius of convergence for infinite power series.
12 Manipulate Gamma and Beta functions, and use these special functions to evaluate certain definite integrals.
13 Understand fundamental properties of Laplace transforms.
14 Solve initial value problems using Laplace transforms.
15 Be familiar with standard curvilinear coordinate systems.
16 Compute scale factors for and determine properties of curvilinear coordinate systems.
17 Compute and interpret Wronskians.
18 Evaluate, manipulate and apply Jacobians.
19 Solve second order ordinary differential equations using variation of parameters.
Courses and course hours of instruction are subject to change.
Eligibility for courses may be subject to a placement exam and/or pre-requisites.
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.