# Calculus & Linear Algebra II

University of Queensland

## Course Description

• ### Course Name

Calculus & Linear Algebra II

• ### Host University

University of Queensland

• ### Location

Brisbane, Australia

Calculus

• ### Language Level

Taught In English

• ### Prerequisites

(MATH1051) + (MATH1052)

• ### Course Level Recommendations

Lower

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.

### Hours & Credits

• Host University Units

2
• Recommended U.S. Semester Credits
4
• Recommended U.S. Quarter Units
6
• ### Overview

Course Description
Please 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 Introduction
MATH2000 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 Objectives
After 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. CALCULATE/SOLVE
• 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
3. APPLY/MODEL
• 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

Class Contact
3hours Lecture, 1 hour Tutorial

Assessment Summary
Assignments (6): 30%
Final Exam: 70%

### Course Disclaimer

Courses and course hours of instruction are subject to change.

Eligibility for courses may be subject to a placement exam and/or pre-requisites.

Some courses may require additional fees.

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.