MAT 2100 Algebra and Calculus II

STAFFING:

REQUISITES:

RATIONALE:

This course follows on directly from MAT1102 Algebra and Calculus I in developing the concepts and techniques of calculus and linear algebra for application to problems in engineering and science, or as a basis for higher study in mathematics.

SYNOPSIS:

Module 1 covers multivariable calculus including representation of functions of several variables, surfaces and curves in space, partial differentiation, optimisation, directional derivatives, gradient, divergence and curl, line integrals, iterated integrals, Green's theorem. Module 2 is an introduction to differential equations including direction fields, Euler's method, first order separable, first order linear and second order linear with constant coefficients. Module 3 extends the linear algebra of MAT1102 Algebra and Calculus I to cover vector space, bases, dimensions, rank, nullspace, systems of linear equations, projections, transformations, eigenvalues and eigenvectors, diagonalisation with applications.

OBJECTIVES:

On successful completion of this course students will be able to:

1. demonstrate an understanding of differential equations and their solutions;
2. distinguish between linear and non-linear differential equations and describe the properties of the solutions of linear differential equations;
3. apply qualitative and quantitative methods to obtain solutions of differential equations to an appropriate level of accuracy;
4. interpret differential equations and their solutions in terms of models for various physical systems;
5. represent functions of two variables as surfaces in space, or contour diagrams;
6. find partial derivatives of vector and scalar functions of several variables and demonstrate an understanding of their meaning;
7. find directional derivatives and gradients of scalar fields and demonstrate an understanding of their meaning;
8. find and classify the critical points of a scalar function of two variables;
9. represent curves and surfaces in space by parametric equations, or as a vector function of one or two variables;
10. evaluate line integrals through vector or scalar fields;
11. find the curl and divergence of a vector field;
12. evaluate iterated integrals, demonstrate an understanding of their meaning and apply them appropriately;
13. apply Green's theorem;
14. describe the properties of the solutions of linear algebraic equations;
15. compute appropriate bases for the solution of linear algebra problems including orthogonal projections, linear transformations and eigenvalues and eigenvectors;
16. communicate explanations and mathematical expositions in a clear and logical fashion.

TOPICS:

TEXT and MATERIALS required to be PURCHASED or accessed:

ALL textbooks and materials are available for purchase from USQ BOOKSHOP (unless otherwise stated). Orders may be placed via secure internet, free fax 1800642453, phone 07 46312742 (within Australia), or mail. Overseas students should fax +61 7 46311743, or phone +61 7 46312742. For costs, further details, and internet ordering, use the 'Textbook Search' facility at http://bookshop.usq.edu.au click 'Semester', then enter your 'Course Code' (no spaces).

REFERENCE MATERIALS:

STUDENT WORKLOAD REQUIREMENTS:

ASSESSMENT DETAILS:

NOTES:

1.

The weekly homework will be required only for the oncampus students.

2.

Examination dates will be available during the Semester. Please refer to Examination timetable when published.

IMPORTANT ASSESSMENT INFORMATION

1. Attendance requirements:
   It is the students' responsibility to attend and participate appropriately in all activities (such as lectures, tutorials, laboratories and practical work) scheduled for them, and to study all material provided to them or required to be accessed by them to maximise their chance of meeting the objectives of the course and to be informed of course-related activities and administration.
2. Requirements for students to complete each assessment item satisfactorily:
   To complete the assignments satisfactorily, students must obtain at least a total of 50% of the marks available for the assignments.To complete the examination satisfactorily, students must obtain at least 50% of the marks available for the examination.
3. Penalties for late submission of required work:
   If students submit assignments after the due date without prior approval then a penalty of 10% of the total marks gained by the student for the assignment will apply for each working day late.
4. Requirements for student to be awarded a passing grade in the course:
   To be assured of a passing grade, students must demonstrate, via the summative assessment items, that they have achieved the required minimum standards in relation to the objectives of the course by: (i) satisfactorily completing the examination and assignments; and (ii) obtaining at least 50% of the total weighted marks available for all summative assessment items.
5. Method used to combine assessment results to attain final grade:
   The final grades for students will be assigned on the basis of the aggregate of the weighted marks obtained for each of the summative assessment items in the course.
6. Examination information:
   In an Open Examination, candidates may have access to any material during the examination except the following: electronic communication devices, bulky materials, devices requiring mains power and material likely to disturb other students.
7. Examination period when Deferred/Supplementary examinations will be held:
   Any Deferred or Supplementary examinations for this course will be held during the examination period at the end of the semester of the next offering of this course.
8. University Regulations:
   Students should read USQ Regulations 5.1 Definitions, 5.6. Assessment, and 5.10 Academic Misconduct for further information and to avoid actions which might contravene University Regulations. These regulations can be found at the URL http://www.usq.edu.au/corporateservices/calendar/part5.htm or in the current USQ Handbook.

ASSESSMENT NOTES