# Mathematics

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## MATHEMATICS FOR STATISTICS 214

Calculus and Linear Algebra

This module serves as a basic introduction to Calculus and Linear Algebra.  In the first part of the module (Calculus) exponential and logarithmic functions, limits, continuity, derivatives and – as an application – optimization problems are discussed, as well as indefinite and definite integrals, the Fundamental Theorem of Calculus, the techniques of substitution and integration by parts and – as an application – areas between curves.  In the second part (Linear Algebra) the following topics are discussed:  Gauss elimination, matrix algebra, the inverse and determinant of a matrix, as well as the following aspects of vectors in the 3-dimensional vector space over the real numbers:  rules of computation, unit vectors, linear combinations of vectors, linear independence and bases, and dot product.  Finally the binomial theorem is discussed.

Module Information

• 58378 214 (16) Mathematics for Statistics 214
• Second year, first semester, of the following programmes:  BComm, BComm (Management Sciences), BComm (Economic Sciences)
• Teaching load: 3 lectures and one tutorial of 2 hours per week
• Corequisite module:  Statistics 214
• Language specification : A/E

Lecturer

• Me L Wessels; Office 1009B, Industrial Psychology/Mathematics Building; Email lwessels@sun.ac.za

Learning Material

• Prescribed Textbook:  Hoffmann, Bradley;  Applied Calculus for Business, Economics and the Social and Life Sciences, 10th Edition, McGraw-Hill, 2010.

Learning Opportunities

• The learning material is completely covered during the lecture periods.
• During the tutorial periods problems are solved under supervision.
• Attendance of all lectures and tutorials is compulsory.

Assessment

• Method:  Obtain class mark (KP = 40) and pass exam (final mark PP = 50).
• The class mark is determined by short (compulsory) tests which are written during the tutorial periods (30%), together with the class test (70%).
• Formula for final mark:  PP = 0,4 KP + 0,6 EP, where EP = exam mark.
• The dates and times of the class test and exam are published in the University’s EXAM AND TEST TIMETABLES book.  For more information on exam regulations, see the Yearbook of the University, Parts 1 and 10.
• The class test is graded and returned as soon as possible.  Final marks are made known on the date as determined in the Year Program of the University.

Rationale

This module is presented within the following programmes:  BComm, BComm (Management Sciences), BComm (Economic Sciences).  It provides a basic training in Mathematics which is essential for the successful completion of certain other modules (including Statistics 214) in these programmes.

Outcomes

A student who has passed this module should be equipped with the knowledge and comprehension of the basic concepts and procedures in Calculus and Linear Algebra.  Specifically such a student should have the following knowledge and skills:

• Understand the basic concepts in connection with functions (including exponential and logarithmic functions), limits, continuity, derivatives and integrals.
• Can determine first and higher order derivatives using rules of differentiation.
• Can evaluate indefinite and definite integrals using rules of integration, the Fundamental Theorem of Calculus and the techniques of substitution and integration by parts.
• Can apply the definite integral to find areas between curves.
• Know the technique of Gauss elimination.
• Can do algebra with matrices, determine the inverse and determinant of  matrix and use their properties.
• Can work with vectors in the 3-dimensional vector space over the real numbers, understand the concepts of unit vectors, linear combinations of vectors, linear independence and bases, and can determine the dot product.
• Can apply the binomial theorem.