MAT 1102 Algebra and Calculus I

SubjectCat-NbrClassTermModeDescriptionUnitsCampus
MAT1102281323, 2003EXTAlgebra and Calculus I1.00TWMBA
Academic Group:FOSCI
Academic Org:FOS003
HECS Band:2
ASCED Code:010101

Contents


STAFFING:

Examiner: Chris Harman
Moderator: Anita Frederiks



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 demonstrate:

  • competence in geometric, numeric, and algebraic approaches to concept development and problem solving using the fundamental techniques of algebra and calculus;

  • meaningful representation and solution of practical applications of algebra and calculus;

  • the ability to use computer aided methods to develop concepts in algebra and calculus;

  • competence in communicating mathematical ideas and conclusions in writing;

  • ability to evaluate approximate rates of change;

  • ability to evaluate limits to compare relative sizes of quantities in given neighbourhoods and to find instantaneous rates of change;

  • ability to 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;

  • ability to find derivatives of functions defined implicitly;

  • ability to find areas under curves;

  • understanding of the concept of the definite integral and the fundamental theorem of calculus;

  • ability to reconstruct a function from its derivative;

  • ability to construct anti-derivatives using definite integrals;

  • ability to find integrals using tables, substitution, and integration by parts;

  • ability to apply techniques of calculus to solve problems of function behaviour, rates of change, optimisation, and summation;

  • ability to apply vectors and their decompositions to physical problems in 2 and 3 dimensions;

  • ability to find equations of lines and planes in three dimensions and use these to establish their relative positions and intersections;

  • ability to formulate systems of linear equations, where appropriate, find solutions when they exist, and interpret the results meaningfully;

  • ability to use matrices and matrix algebra to store and manipulate data;

  • ability to simplify and evaluate expressions containing vectors, matrices and complex numbers, and demonstrate understanding of their geometric and algebraic properties;

  • ability to solve simple polynomial equations for complex-valued solutions;

  • ability to find elementary functions of a complex variable.



    • TOPICS:


    DescriptionWeighting (%)
    1. Calculus: Limits and Derivatives, including definitions of the derivative and basic differentiation rules. Applications of differentiation including the chain rule and maxima and minima problems. Transcendental Functions, including inverse Trigonometric Functions. Techniques of Integration including Mid-point and Trapezoidal approximations. Anti-derivative techniques using tables, algebraic and trigonometric substitutions, and integration by parts. Applications of Integration, including areas, arc lengths, volumes, and other physical problems.
    		 50.00
    2. Linear Algebra: Matrix operations; systems of linear equations, Gaussian elimination; the inverse matrix. Vectors, dot and cross products, projections, lines and planes. Determinants and adjoint matrices. Complex numbers, de Moivre's Theorem, Euler's form, elementary functions of a complex variable.
    		 50.00

    TEXT and MATERIALS required to be PURCHASED or accessed:

    Books can be ordered by fax or telephone. For costs and further details use the 'Book Search' facility at http://bookshop.usq.edu.au by entering the author or title of the text.

    Note that these books will also be used for the course MAT2100.

    Hughes-Hallett, D. et al 2002, Calculus. Single and Multivariable, 2nd edition, Wiley, New York.

    Larson, R. & Edwards, B 2003, Elementary Linear Algebra, 5th edition, Houghton Mifflin, Boston.

    (The 4th edition (2000) may still be used.)




    REFERENCE MATERIALS:

    Reference materials are materials that, if accessed by students, may improve their knowledge and understanding of the material in the course and enrich their learning experience.

    Hughes-Hallett, D. et al 2002, Student Solution Manual - Calculus. Single and Multivariable, 2nd edition, Wiley, New York.

    Larson, R. & Edwards, B 2000, Student Solutions Guide - Elementary Linear Algebra, 4th edition, Houghton Mifflin, Boston.

    Larson, R. & Edwards, B 1996, Technology Keystroke Guide: Elementary Linear Algebra, Heath, Lexington.

    Version 6 or earlier MATLAB, CEANET.

    (Version 6 or earlier)




    STUDENT WORKLOAD REQUIREMENTS:

    ACTIVITYHOURS
    Assessment16
    Directed Study84
    Examinations4
    Private Study65


    ASSESSMENT DETAILS:

    DescriptionMarks Out ofWtg(%)RequiredDue Date
    ASSIGNMENT 1100.0015.00Y12 Dec 2003
    ASSIGNMENT 2100.0015.00Y09 Jan 2004
    2 HR RESTRICTED EXAM (PART A)120.0035.00YEND S3(see note )
    2 HR OPEN EXAMINATION (PART B)120.0035.00YEND S3
    NOTES:
    .
    Examination dates will be available during the Semester. Please refer to 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 and Newsgroup to keep themselves well informed.
    2. Requirements for students to complete each assessment item satisfactorily:
      To complete each of the assignments satisfactorily, students must obtain at least 50% of the marks available for each 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: (i) satisfactorily completing the examination and assignments; and (ii) obtaining at least 50% of the total weighted marks available for all summative assessment items. 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 during the examination except the following: electronic communication devices, bulky materials, devices requiring mains power and material likely to disturb other students In a Restricted Examination, candidates are allowed access to specific materials during the examination. The only materials that candidates may use in the restricted examination for this course are: writing materials (non-electronic and free from material which could give the student an unfair advantage in the examination); graphic calculators which cannot hold textual information (students must indicate on their examination paper the make and model of any calculator(s) they use during the examination. Students who wish to use a translation dictionary MUST request and receive written approval from the Examiner at least one week before the examination date. Translation dictionaries will be subject to perusal and may be removed from the candidate's possession until appropriate disciplinary action is completed if found to contain material that could give the candidate an unfair advantage. The examination in this course is a combined examination. Part A is a Closed examination of 1 hour duration and 200 marks have been allocated for this part. Part B is an Open examination of 2 hours duration and 400 marks have been allocated for this part.
    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/SECARIAT/calendar/Part5/ or in the printed version of the current USQ Handbook.

    ASSESSMENT NOTES

    9.The due date for an assignment is the date by which a student must despatch the assignment to the USQ. The onus is on the student to provide proof of the despatch date, if requested by the Examiner. Students must retain a copy of each item submitted for assessment. If requested, students will be required to provide a copy of assignments submitted for assessment purposes. Such copies should be despatched to USQ within 24 hours of receipt of a request being made. The examiner may grant an extension of the due date of an assignment in extenuating circumstances. The Faculty will normally only accept assessments that have been written, typed or printed on paper-based media. The Faculty will NOT accept submission of assignments by facsimile. Students who do not have regular access to postal services or who are otherwise disadvantaged by these regulations may be given special consideration. They should contact the examiner of the course to negotiate such special arrangements. In the event that a due date for an assignment falls on a local public holiday in their area, such as a Show holiday, the due date for the assignment will be the next day. Students are to note on the assignment cover the date of the public holiday for the Examiner's convenience. Extensions of more than a week are not normally granted for assignments in this course, because solutions will be available at that stage. No marks at all will be granted for submission one week after the due date, because solutions need to be released as a valuable resource for students in this course. Students who, for medical, family/personal, or employment-related reasons, are unable to complete an assignment or to sit for an examination at the scheduled time may apply to defer an assessment in a course. Such a request must be accompanied by appropriate supporting documentation. One of the following temporary grades may be awarded IDS (Incomplete - Deferred Examination; IDM (Incomplete Deferred Make-up); IDB (Incomplete - Both Deferred Examination and Deferred Make-up).