A novel concept of multiple deterministic analyses is proposed to design safer and more damage-tolerant structures, particularly when excited by dynamic including seismic loading in time domain. Since the presence of numerous sources of uncertainty cannot be avoided or overlooked, the underlying risk is estimated to compare design alternatives. To generate the implicit performance functions explicitly, the basic response surface method is significantly improved. Then, several surrogate models are proposed. The advanced factorial design and Kriging method are used as the major building blocks. Using these basic schemes, seven alternatives are proposed. Accuracies of these schemes are verified using basic Monte Carlo simulations. After verifying all seven alternatives, the capabilities of the three most desirable schemes are compared using a case study. They correctly identified and correlated damaged states of structural elements in terms of probability of failure using only few hundreds of deterministic analyses. The modified Kriging method appears to be the best technique considering both efficiency and accuracy. Estimating the probability of failure, the post-Northridge seismic design criteria are found to be appropriate. After verifying the proposed method, a Site-Specific seismic safety assessment method for nonlinear structural systems is proposed to generate a suite of ground excitation time histories. The information of risk is used to design a structure more damage-tolerant. The proposed procedure is verified and showcased by estimating risks associated with three buildings designed by professional experts in the Los Angeles area satisfying the post-Northridge design criteria for the overall lateral deflection and inter-story drift. The accuracy of the estimated risk is again verified using the Monte Carlo simulation technique. In all cases, the probabilities of collapse are found to be less than 10% when excited by the risk-targeted maximum considered earthquake ground motion satisfying the intent of the code. The spread in the reliability indexes for each building for both limit states cannot be overlooked, indicating the significance of the frequency contents. The inter story drift is found to be more critical than the overall lateral displacement. The reliability indexes for both limit states are similar only for few cases. The author believes that the proposed methodology is an alternative to the classical random vibration and simulation approaches. The proposed site-specific seismic safety assessment procedure can be used by practicing engineers for routine applications. The proposed reliability methodology is not problem-specific. It is capable of handling systems with different levels of complexity and scalability, and it is robust enough for multi-disciplinary routine applications. In order to show the multi-disciplinary application of the proposed methodology, the probability of failure of lead-free solders in Ball Grid Array 225 surface-mount packaging for a given loading cycle is estimated. The accuracy of the proposed methodology is verified with the help of Monte Carlo simulation. After the verification, probability of failure versus loading cycles profile is calculated. Such a comprehensive study of its lifetime behavior and the corresponding reliability analyses can be useful for sensitive applications.

Philosophiae Doctor - PhD / This study attempts to understand how distance education practices influence the learning of calculus. Understanding student learning in a distance education environment is an important factor to consider in improving the learning experiences of those students who for one reason or the other opt not to study in conventional institutions of higher education. On one hand, understanding student learning may illuminate the influences that the learning environment has on student learning and on the other hand, it may inform on how learning experiences can be improved. The aim of this study is to acquire a deeper understanding of the diverse manner in which distance students learn calculus. Specific focus is also placed on how the distance education context of the Zimbabwe Open University (ZOU) influences student learning. The study describes a group of students' experiences of learning calculus in the ZOU distance education environment. The study also describes the students' learning styles and relates these to their mathematical understanding of certain calculus concepts. The specific content topics of "limit of function" and "derivative of function" are used to view achievement and performance, thereby indicating the distance students' mathematical understanding. The information processing learning theory is used as the theoretical framework for this study. The constructs of learning styles and mathematical understanding are used to illuminate the student's learning processes. The study used the Felder-Silverman learning styles model and Hiebert and Carpenter's notion of mathematical understanding to expound these constructs. The distance education environment of the B.Sc. Mathematics and Statistics (BSMS) programme at the ZOU provided the context of the study and an interpretive case study approach was adopted. A group of students registered in a first year first semester calculus course were studied. Data were collected from students based in four ZOU regional centres; namely Harare, Mashonaland Central, Mashonaland West, and Masvingo. These regional centres were conveniently selected for the study on the basis of proximity and accessibility. A total sample of twenty six students was involved and data for the in-depth part of the study emanated from five students who were purposively selected to participate in interviews. The interviewees were selected on the basis of their performance in a written calculus test. Data for this study were collected through use of learning journals, learning styles preference questionnaires, calculus tests and interviews. The data on students' learning experiences were predominantly qualitative in nature though supported by some quantitative data. The data on learning styles and mathematical understanding were also qualitatively analysed and presented case by case for the five interviewees. The study established that in a distance education system, the type of learning environment has the potential to influence students' learning, both positively and negatively, of which the main contributing factor is the learning support system. The study found that the learning support system provided by the institution and distance educators can have an impact on student learning. With reference to the calculus course in the BSMS programme, the study identified specific aspects where the environment facilitated or deterred learning. The study also revealed that students have varied learning style preferences, and that the learning environment has the potential to impact on students' learning styles. Since learning styles occupy a central place when it comes to improving distance learning materials, the study further explored the relationship between the constructs of learning styles and mathematical understanding. The study revealed that students' learning styles can influence the students' mathematical understanding. Improving students' learning in a distance education environment rests mainly on improving the learning materials and the support systems. A carefully designed and well supported instructional distance learning package can facilitate learning. Implications of the findings point towards the improvement of the distance teaching processes through the improvement of learning materials and the learning support systems for the BSMS distance education programme.