Analisis Kesalahan Mahasiswa dalam Menyelesaikan Soal Kalkulus

Some students have difficulty solving math problems in the integral calculus course, one of the materials for the volume of rotating objects. The purpose of this research is to describe the types of errors made by students of class F Mathematics Education FKIP Ahmad Dahlan University and their causes in solving the volume of rotating objects in integral calculus courses in the Polya stage. This research is a quantitative quantitative research. The research subjects are one class with a total of 20 students. For interviews, 3 students were taken with the criteria of high, medium and low abilities. Collecting research data using test material, the volume of rotating objects and student interviews about the factors that cause mistakes made. The steps for solving the problem consist of four stages, namely: understanding the problem, planning for completion, implementing the plan, and examining the solutions obtained. From the results of the research on student errors based on Polya's stages: 1) understanding the problem 55.89%, planning for completion of 50.00%, errors in implementing planning 32.36%, and errors in re-checking the process and results 44.12%; 2) the causes of students making mistakes in solving integral calculus questions on the volume of rotating objects, namely students lacking mastery in drawing function graphs, students lacking in basic concepts and volume formulas for rotating objects, and students unable to analyze the questions given.

The Mathematical Model for the Tippe Top Inversion

The dynamics of rotating objects is an area of classical mechanics that has many unsolved problems. Among these problems are the gyroscopic effects manifested by the spinning objects of different forms. One of them is the Tippe top designed as the truncated sphere which is fitted with a short, cylindrical rod for rotation. The unexplainable gyroscopic effect of the Tippe top is manifested by its inversion towards the support surface. Researchers tried to describe this gyroscopic effect for two centuries, but all modelings were on the level of assumptions. It is natural because the Tippe top has a more complex design than the simple spinning disc, which gyroscopic effects did not have an analytical solution until recent time. The latest research, in the area of gyroscopic effects, reveals the action of the system of several interrelated inertial torques on any spinning object. The gyroscopic inertial torques are generated by their rotating mass. These inertial torques and the variable ratio of the angular velocities of the spinning object around axes of rotations constitute the fundamental principles of gyroscope theory. These physical principles of dynamics of rotating objects enable to description and compute of any gyroscopic effects and also the Tippe top inversion.

PEMANFAATAN MEDIA PEMBELAJARAN AUTOGRAPH MENGGUNAKAN PENDEKATAN PROBLEM SOLVING UNTUK MENINGKATKAN KEMAMPUAN METAKOGNISI SISWA SMA

Autograph Software is a special program used in learning mathematics. Autograph has the ability to make 2D and 3D graphics for material transformation, cone sections, vectors, slope, and derivatives. By using this software, users can observe how functions, graphs, equations, and calculations. Community service activities carried out at Al Fattah Private High School, especially for class XI, are expected students to understand the concept of integral applications, namely the volume of rotating objects and students' responses to mathematics learning through autograph learning media on the material of rotating objects. In this community service activity, it is hoped that class IX students can find an integral application problem solving for the volume of rotating objects. Autograph software is used to make it easier for students to understand the concept of the volume of a rotating object through two-dimensional and three-dimensional images with their metachogical abilities.

Non-static surfaces in MCNPX: The chopper extension1

Rotating objects, such as choppers, are common components of a neutron beamline, and the motion of these components is not described in the static geometry of an MCNPX model. The special case of non-static surfaces for rotation about a stationary point in space has been developed for MCNPX. In addition, velocity dependent kinematics due to the motion of the medium have been implemented. This implementation allows for the simulation of rotating objects at speeds comparable to the velocity of cold neutrons. Applications of the chopper extension will be discussed, including the direct simulation of a bandwidth chopper system, the thermalization of neutrons inside a spinning material, and the discussion of the implementation of a spinning single crystal.