MATH102-16S1 (C) Semester One 2016

Mathematics 1A

15 points

Details:
Start Date: Monday, 22 February 2016
End Date: Sunday, 26 June 2016
Withdrawal Dates
Last Day to withdraw from this course:
  • Without financial penalty (full fee refund): Sunday, 6 March 2016
  • Without academic penalty (including no fee refund): Sunday, 22 May 2016

Description

An introductory course in calculus and linear algebra that is designed primarily for students who have done well in NCEA Mathematics with Calculus. This course deals with basic ideas in calculus and linear algebra which have applications in many areas of science and commerce.

The work in MATH102 is based around the fundamental ideas in linear algebra and calculus which students started studying at school. It is designed for science and commerce students taking a quantitatively based degree programme and can be taken as a standalone course or as the first part of a three part core in mathematics, MATH102-MATH103-MATH201.

Topics:
Linear equations and matrices; functions, limits and continuity; determinants; differentiation; functions of more than one variable; integration, including an introduction to first order differential equations.

Recommended preparation:
Suitable backgrounds for MATH102 include good NCEA level 3 calculus results (see entry recommendations for recent school leavers) or a pass in MATH101.

Learning Outcomes

  • Students who have succeeded in this course will be able to:

    Define the key concepts in:
  • solving systems of linear equations
  • matrix algebra
  • functions and their inverses
  • the conceptual foundations of calculus (i.e. limits)
  • derivatives of one-variable  and two-variable functions
  • integrals of one-variable calculus.

    Describe and interpret:
  • the connection between matrices and linear systems
  • solutions of linear systems geometrically, and in the context of commerce and science problems
  • the key theorems of calculus
  • the connection between differential and integral calculus
  • the properties of determinants from a geometrical viewpoint
  • a two-variable function from its level curves
  • solutions of first order differential equations in context.

    Use techniques from the course (including the use of MAPLE where appropriate) to:
  • solve systems of linear equations by elimination, matrix algebra and Cramer's rule
  • evaluate limits of functions and solve continuity problems
  • find derivatives and use them in commerce and science applications
  • find determinants by row operations and cofactor expansions
  • find partial derivatives and interpret these geometrically and physically
  • find critical values of functions of two variables and determine their nature
  • find integrals and use them in science and commerce applications
  • solve separable first order differential equations.

Restrictions

MATH108, MATH199, EMTH118

Course Coordinator / Lecturer

Liz Ackerley

Lecturer

Hannes Diener

Assessment

Assessment Due Date Percentage 
Tutorial Assessment 10%
Quizzes 12%
Online Test 3%
Tests 30%
Final Examination 45%

Textbooks / Resources

There is no required text for this course.

Recommended reading:
Calculus: Early Transcendentals, Anton, Bivens, Davis; 10th edition; Wiley (8th and 9th edition also suitable).
Note: If you are carrying on with MATH103, this text is a worthwhile investment.

Indicative Fees

Domestic fee $720.00

International fee $3,450.00

* All fees are inclusive of NZ GST or any equivalent overseas tax, and do not include any programme level discount or additional course-related expenses.

For further information see Mathematics and Statistics .

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