
Twente Introduction Mechanical Engineering (TIME)
TIME is developed to let students experience how engineering problems can be solved in a systematic way, and how mathematics plays a major role in this process.
We explain how the period of a pendulum is computed. The pendulum problem is an excellent showcase of how engineering problems can be solved in a systematic way. It also greatly exemplifies the role of mathematics in this process since it is related to several mathematical concepts and theorems such as differentiation, linear differential equations, Taylor series approximation, and so forth.
Besides content related learning objectives (see below), the overall aim of TIME is to awake the curiosity in students and motivate them for mechanical engineering problems and challenges. TIME consists of 5 lectures where students get familiar with the course content and 5 tutorials where students can individually practice the course content on a similar problem. Because TIME is a base for studying Mechanical Engineering in Twente we expect all students to be present.
After successfully finish TIME the student is able to solve a mechanical engineering problem in a systematic way. This is described in the following smaller learning objectives:
The student is able to:
 Analyse the problem by identifying the governing parameters and to perform a dimension analysis.
 Describe the position of the mass in various coordinate systems and calculate from that the velocities and accelerations in multiple directions.
 Draw a free body diagram, to identify the forces working on the body, and to derive the governing differential equation(s) by application of Newton’s second law.
 To solve the differential equation(s) and to verify the solution by checking its dimensions and behavior, by checking the boundary conditions, and by sketching the solution.
Calculus 1A
As a result of the course a student is able to:
 Work with vectors:
 apply elementary vector operations
 calculate dot product and cross product
 determine equations of line and planes
 Work with limits and functions of 1 variable:
 calculate limits, also applying l’Hospital’s rule to indeterminate forms of limits and work with limits involving infinity
 state and apply the definition of (left, right) continuity and of differentiability
 calculate and apply linear approximations and differentials
 calculate the absolute extreme values on a closed bounded interval
 Investigate functions of 2 variables:
 plot graphs and contour lines
 investigate continuity and differentiability
 calculate partial derivatives
 calculate the tangent plane and linearization



This is a part of module 1, ME 1 Design and Manufacturing of the Bachelor Mechanical Engineering.. See here for the compete description of the module.
External students who are interested in this elective: please contact j.g.dekiewit@utwente.nl



 Assumed previous knowledgeBachelor Mechanical Engineering 
  Required materialsBookMathematics  Thomas Calculus Early Transcendentals, ISBN 9781784498139 
 ReaderTIME  Lecture Notes  Twente's Introduction to Mechanical Engineering, Hagmeijer, August 2018 (will be supplied by the programme) 

 Recommended materialsInstructional modesCasePresence duty   Yes 
 LecturePresence duty   Yes 
 Self study
 Tutorial

 TestsExam TIME
 Exam Calculus 1A


 