Use the Tab and Up, Down arrow keys to select menu items.
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. Course Aims:• to apply mathematical concepts and techniques in understanding and solving problems • to introduce the concepts of linear algebra and its applications• to consolidate and extend the ideas and techniques of calculus and its applications • to increase understanding of the mathematical foundations of the topics studiedSuitable backgrounds for MATH102 include good NCEA level 3 calculus results (see entry recommendations for recent school leavers) or a pass in MATH101.
Students will be able to:describe the connection between matrices and linear systems set up, systematically solve and interpret linear systems of equations from problems in commerce and sciencedemonstrate understanding of matrices as an algebraic systemfind inverses of matrices and use these to solve linear systemsdescribe and interpret the properties of determinants from a geometrical viewpointuse row operations and cofactor expansions to calculate determinantsuse Cramer's rule to solve systems of equationsdemonstrate understanding of function operations explain the conceptual foundations of calculus (i.e. limits) intuitively, numerically and geometricallyfind limits and solve continuity problems algebraicallyknow the definition of the derivative and use it to differentiate simple functionsapply the rules of differentiation to find derivativesexplain and interpret key theorems of calculus geometricallyidentify and describe key properties of curves, and use these to sketch the graphs of functionsset up optimisation problems and solve these using calculus techniques visualise a function of two variables by its level curvesfind partial derivatives and interpret these geometrically and physicallyfind critical values of functions of two variables and determine their natureappreciate the connection between differential and integral calculusexplain and use the Fundamental Theorem of Calculuschoose and apply appropriate techniques to evaluate definite and indefinite integralssolve first order separable differential equations, and describe and interpret these solutions
MATH108, MATH199, EMTH118
Liz Ackerley
There is no required text for this course. Recommended reading: Calculus: Early Transcendentals, Anton, Howard., Bivens, Irl., Davis, Stephen -any recent (8th, 9th or 10th) edition is suitable.
MATH102 homepage Entry recommendations for recent school leavers
Domestic fee $647.00
International fee $3,325.00
* 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 .