MAT 1102 Algebra and Calculus I

STAFFING:

RATIONALE:

In fields ranging from engineering to economics, the techniques of differential and integral calculus provide powerful investigative tools because rates of change and summation are key elements in the description and analysis of the relationships between measurable quantities. Linear systems also arise commonly in fields of application in business, economics, engineering and science, and matrix, vector and complex number techniques are often used to model the associated problems. This course provides the opportunity to master the fundamental concepts and operations of calculus, matrix algebra, vectors and complex numbers.

SYNOPSIS:

This course investigates the elementary functions of mathematics: polynomials, logarithms, trigonometric functions, their inverses, arithmetic combinations and compositions of these functions and functions implicitly defined through relationships between them. Properties of these functions and the rules for finding their derivatives and anti-derivatives are developed and used in applications and the solution of problems. Systems of linear algebraic equations are formulated and solved in a variety of settings. Vectors, matrices and complex numbers are used to formulate and solve problems from various fields of application, and to describe the geometry of two and three dimensional space.

OBJECTIVES:

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

1. demonstrate competence in geometric, numeric, and algebraic approaches to concept development and problem solving using the fundamental techniques of algebra and calculus;
2. produce meaningful representations and solutions of practical applications of algebra and calculus;
3. use computer aided methods to develop concepts in algebra and calculus;
4. communicate mathematical ideas and conclusions in writing;
5. evaluate approximate rates of change;
6. evaluate limits to compare relative sizes of quantities in given neighbourhoods and to find instantaneous rates of change;
7. find the derivatives of polynomial, algebraic, exponential and trigonometric functions, and their inverses (where they exist), as well as combinations and compositions of these functions;
8. find derivatives of functions defined implicitly;
9. find areas under curves;
10. understand the concept of the definite integral and the fundamental theorem of calculus;
11. reconstruct a function from its derivative;
12. construct anti-derivatives using definite integrals;
13. find integrals using tables, substitution, and integration by parts;
14. apply techniques of calculus to solve problems of function behaviour, rates of change, optimisation, and summation;
15. use vectors and their decompositions to solve problems involving 2 and 3 dimensions;
16. find equations of lines and planes in three dimensions and use these to establish their relative positions and intersections;
17. formulate systems of simple linear equations, find solutions when they exist, and interpret the results meaningfully;
18. use matrices and matrix algebra to store and manipulate data;
19. simplify and evaluate expressions containing vectors, matrices and complex numbers, and demonstrate understanding of their geometric and algebraic properties;
20. solve simple polynomial equations for complex-valued solutions;
21. recognise and manipulate elementary functions of a complex variable.

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).

These books will also be used for course MAT2100.

REFERENCE MATERIALS:

STUDENT WORKLOAD REQUIREMENTS:

ASSESSMENT DETAILS:

NOTES:

1.

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

IMPORTANT ASSESSMENT INFORMATION

1. Attendance requirements:
   There are no attendance requirements for this course. However, it is the students' responsibility 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. Students should keep in contact with the course examiner and teaching team via Outreach, and use the course Webpage to keep themselves well informed.
2. Requirements for students to complete each assessment item satisfactorily:
   To complete the assignments satisfactorily, students must obtain at least 50% of the marks available for assignment. 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 20% 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 satisfactorily completing the examination and assignments. Students who do not qualify for a Passing grade may, at the discretion of the Examiner, be awarded a Supplementary Examination and/or assigned additional work to demonstrate to the Examiner that they have achieved the required standard. It is expected that such students will have gained at least 45 % of the total 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, calculator and battery-operated computer during the examination except the following: internet, 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