Die doel van hierdie verhandeling is om 'n algoritme vir kleinstekwadrate-benaderings te vind en om met behulp van die algoritme 'n rekenaarprogram te ontwikkel vir die minimering van die kleinstekwadrate- benadering en die passings van krommes deur gegewe eksperimentele data. Eerstens word die norm en die pseudo-inverse van matrikse sowel as Householder-transformasies bespreek, aangesien ons daarvan gebruik maak in die oplossing van ons probleem. In die lineere kleinstekwadrate-probleem word die koeffisiente matriks A ontbind in 'n produk van 'n ortogonale en 'n bo-driehoeksmatriks. Hierdie produk word dan gebruik om die pseudo-inverse van A te verkry. Die algoritme wat ontwikkel is vir die nie-lineere kleinstekwadrate- probleem is gebaseer op die Gauss-Newton-Marquardt-metode, waar met elke stap 'n lineere kleinstekwadrate-probleem opgelos word. Resultate wat met behulp van die algoritme verkry is, word ook vergelyk met die resultate van ander algoritmes. / Dissertation (MSc)--University of Pretoria, 1977. / gm2014 / Mathematics and Applied Mathematics / Unrestricted

It appears from the literature that the mastery of motor skills is essential for the optimal development of young school beginners' cognitive, perceptual, sport-specific and emotional skills. Researchers agree that the optimal development and mastering of motor skills occurs during specific sensitive periods in each child's life, and this is why it is important that children are provided with appropriate opportunities to develop these skills. The conditions in which a child grows up appear to be a significant factor influencing motor development during childhood. Environmental factors such as socio-economic conditions seem to play a role in the development of young children 's motor skills . Literature suggests that poor motor development generally occurs among children with insufficient areas for playing, and results from low socio-economic conditions in which the parents have a low income and limited resources. A large percentage of South African children are exposed to low socio-economic conditions that may consequently affect their development. The objectives of this study therefore were to determine the effect of socio-economic conditions on the motor- and object-control skills of Grade 1-learners. Eight hundred and sixteen (N=816) (+0.39 sd) Grade 1-learners with an average age of 6.8 years from 20 different schools in the North West Province, representing five different school types (quintile 1 (low) to quintile 5 (high), participated in the study. The short form (SF) of the "Bruininks-Oseretsky Test of Motor Proficiency" 2nd edition (BOT-2) (Bruininks & Bruininks, 2005), as well as several subscales (strength and agility and balance) of the longer form (LF) were used to evaluate gross and fine motor development and divide learners into various categories of mastering. The “Test of Gross Motor Development” 2nd edition (TGMD-2), was used to evaluate object control skills and divide subjects into various mastered categories. The data was analyzed by means of analysis of variance correlation coefficients using the "Statistica for Windows" (Statsoft, 2012) program. The results were adjusted for height and age. Two-way frequency tables and cross-tabulations were also used to analyze the data. With regards to objective 1 , the resluts showed that learners from quintile 4 and 5 schools, representing schools from higher socio-economic conditions, scored significantly better than quintile 1 to 3 schools in six sub-items (fine motor precision, fine motor integration, manual dexterity, bilateral coordination, strength and upper limb coordination) of the BOT-2 (SF) (p<0.05) while no differences were found in the LF subscales. Quintile 4 and 5 schools also received significantly better (p<0.05) scores in the SF standard score and percentiles of the BOT-2. The results indicate d> that the motor proficiency of learners from higher socio-economic conditions were better than those of learners from lower socio-economic conditions. With regards to the second objective of the study, the analysis of the results indicated that quintile 5 schools performed significantly better (p<0.05) in throwing, hitting, dribbling, and catching than quintile 1 to 3 schools, while quintile 1 and 3 schools performed significantly better (p≤0.05) in the kicking skill. Quintile 4 and 5 schools also fared significantly better (p<0.05) in the object control standard score than quintile 1 to 3 schools. The group's age equivalent, according to the TGMD-2, was 5.5 years, and ranged from 5.1 years to 5.9 years, indicating a mean age difference of 1.3 years compared with the chronological age of the group. / MA (Kinderkinetics), North-West University, Potchefstroom Campus, 2014

It appears from the literature that the mastery of motor skills is essential for the optimal development of young school beginners' cognitive, perceptual, sport-specific and emotional skills. Researchers agree that the optimal development and mastering of motor skills occurs during specific sensitive periods in each child's life, and this is why it is important that children are provided with appropriate opportunities to develop these skills. The conditions in which a child grows up appear to be a significant factor influencing motor development during childhood. Environmental factors such as socio-economic conditions seem to play a role in the development of young children 's motor skills . Literature suggests that poor motor development generally occurs among children with insufficient areas for playing, and results from low socio-economic conditions in which the parents have a low income and limited resources. A large percentage of South African children are exposed to low socio-economic conditions that may consequently affect their development. The objectives of this study therefore were to determine the effect of socio-economic conditions on the motor- and object-control skills of Grade 1-learners. Eight hundred and sixteen (N=816) (+0.39 sd) Grade 1-learners with an average age of 6.8 years from 20 different schools in the North West Province, representing five different school types (quintile 1 (low) to quintile 5 (high), participated in the study. The short form (SF) of the "Bruininks-Oseretsky Test of Motor Proficiency" 2nd edition (BOT-2) (Bruininks & Bruininks, 2005), as well as several subscales (strength and agility and balance) of the longer form (LF) were used to evaluate gross and fine motor development and divide learners into various categories of mastering. The “Test of Gross Motor Development” 2nd edition (TGMD-2), was used to evaluate object control skills and divide subjects into various mastered categories. The data was analyzed by means of analysis of variance correlation coefficients using the "Statistica for Windows" (Statsoft, 2012) program. The results were adjusted for height and age. Two-way frequency tables and cross-tabulations were also used to analyze the data. With regards to objective 1 , the resluts showed that learners from quintile 4 and 5 schools, representing schools from higher socio-economic conditions, scored significantly better than quintile 1 to 3 schools in six sub-items (fine motor precision, fine motor integration, manual dexterity, bilateral coordination, strength and upper limb coordination) of the BOT-2 (SF) (p<0.05) while no differences were found in the LF subscales. Quintile 4 and 5 schools also received significantly better (p<0.05) scores in the SF standard score and percentiles of the BOT-2. The results indicate d> that the motor proficiency of learners from higher socio-economic conditions were better than those of learners from lower socio-economic conditions. With regards to the second objective of the study, the analysis of the results indicated that quintile 5 schools performed significantly better (p<0.05) in throwing, hitting, dribbling, and catching than quintile 1 to 3 schools, while quintile 1 and 3 schools performed significantly better (p≤0.05) in the kicking skill. Quintile 4 and 5 schools also fared significantly better (p<0.05) in the object control standard score than quintile 1 to 3 schools. The group's age equivalent, according to the TGMD-2, was 5.5 years, and ranged from 5.1 years to 5.9 years, indicating a mean age difference of 1.3 years compared with the chronological age of the group. / MA (Kinderkinetics), North-West University, Potchefstroom Campus, 2014

Die historiese wortels van apartheid is vasgele in die tydperk tussen 1652 en 1948. Die Ned. Geref. Kerk het vanaf die dertigerjare van die twintigste eeu die regering versoek om apartheid statuter uit te bou. Met die bewindsverandering in 1948 het 'n nuwe fase van meer as veertig jaar in Suid-Afrika aangebreek. Gedurende hierdie tydperk vind ons 'n hegte band tussen die owerheid en die Ned. Geref. Kerk. Die Ned. Geref. Kerk het in 1948 apartheid vanu it die Skri f geregverd i g en het sy profetiese getuienis daarmee sterk onder verdenking gebring. Die statutere implementering van apartheid het hierna gevolg. Die Ned. Geref. Kerk en die owerheid het hulle standpunte gegrond op die beginsel van voogdyskap. Hiervolgens was blankes die voogde van nie-blankes wat hulle tot mondigheid moet begelei. Na republiekwording is die tuislandbeleid ontwikkel sodat swartmense onafhanklikheid kon verkry. In die praktyk het swartes afhanklik en ondergeskik aan blankes gebly. In 1974 verskyn Ras, Volk en Nasie as amptelike beleidsdokument van die Ned. Geref. Kerk. Die Skriftuurlike begronding verdwyn en apartheid word om praktiese redes onderskryf. Die onluste van 1976 het 'n fase van kritiese evaluering van apartheid ingelei. Die regering het begin om toegewings oor apartheid te maak. As gevolg van die diep kloof tussen politieke oortuigings van Ned Geref. Kerklidmate was die vroee tagtigerjare 'n fase vol huiwering vir die Ned. Geref. Kerk oor apartheid. Die besluit tydens die Algemene Sinode van 1986 dat die Ned. Geref. Kerk "oop" is, was in beginsel 'n sprong weg van apartheid soos gereflekteer in die nuwe beleidsdokument, Kerk en Samelewing. In die fase tussen 1986 en 1991 vind die besliste ontstrengeling van apartheid plaas. Die Ned. Geref. Kerk en die owerheid het dus saam apartheid geimplementeer en saam daarvan weg beweeg. Die Ned. Geref. Kerk het met sy ondersteuning van apartheid en hegte band met die owerheid meegewerk om sy baie "bevoorregte" posisie ten opsigte van die owerheid ongedaan te maak. 'n Era is afgesluit en in die nuwe Suid-Afrika is daar nou 'n nuwe owerheid met nuwe vennote. Indien die Ned. Geref. Kerk nuwe geleenthede aangryp, kan sy Skriftuurlike opdrag, met 'n duidelike profetiese stem, 66k teenoor die owerheid, gehoor word. Die alternatief is 'n eensame pad ... / Thesis (DD)--University of Pretoria, 1994. / gm2014 / Practical Theology / Unrestricted