This research aims to solve the basic knowledge problems of undergraduate students who study Calculus 1 for Engineers in the Faculty of Engineering Rajamangala University of Technology Phra Nakhon. Basic Mathematics tutorials are conducted in order to improve their knowledge which leads to increase the efficiency of learning the Calculus 1 for Engineers. The basic mathematics lessons are designed and their efficiency is assessed in the tutored group using the 60/60 criteria. The pretest and posttest are assigned to both tutored and tutorless groups as well as the tutored student satisfactions with thedesigned lessons and the Calculus 1 for Engineers are conducted. The result shows that the efficiency of the designed lessons is 76.60/64.67 which is higher than the criteria; hence they are proper to be used. For the treatment group the posttest grades are higher than the pretest grades significantly (.05) with the effectiveness of 34.67. The comparison of the learning achievement for the Calculus 1 for Engineers shows that the grades of the tutored group are higher than the grades in the tutorless group significantly (.05) as well. The student satisfactions for both the designed lessons and the Calculus 1 for Engineers are at the levels of good and very good.

The objectives of this research are: to study the characteristics of students in the Faculty of Engineering at Rajamangala University of Technology Pra Nakorn North Bangkok Campus that influence to the risk of withdrawal from Calculus 2 for Engineers; to predict the risk of withdrawal from Calculus 2 for Engineers; and to use the results of the study for planning and solving the problems of withdrawal from Calculus 2 for Engineers. The sample is 226 students in the Faculty of Engineering at Rajamangala University of Technology who enrolled the Calculus 2 for engineers in the second semester of the academic year 2009. The data are from the questionnaire. The factors considered are grad point average the number of enrollments for the Calculus 1 for engineers Calculus 1 for Engineers grade the number of courses that emphasize on calculation that were enrolled in the second semester of the academic year 2009 the sacrifices of students for the Calculus 2 for Engineers course and the need to withdraw from Calculus 2 for Engineers course before other courses. The logistic regression model in which the parameters are estimated by using Bayesian methods is used for analyzing the data. The study shows that the factors that influence to the risk of withdrawal from the Calculus 2 for Engineers are grade point average Calculus 1 for Engineers grade the number of courses that emphasize on calculation that were enrolled in the second semester of the academic year 2009 and the sacrifices of students for the Calculus 2 for Engineers and the need to withdraw from Calculus 2 for Engineers before other courses. The factor that does not influence to the risk of withdrawal from the Calculus 2 for Engineers is the number of enrollments for the Calculus 1 for Engineers.