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Syllabus: Mastering Mathematics for Engineers: Calculus I:
from functions to differential equations
Index
1. Course overview
2. Learning objectives
3. What we expect from you
4. What you can expect from the course team
5. Course structure
6. Resources, Tools & Browsers
7. Assessment & Certificate
8. A note about fraud
9. License
1. Course overview
This course is part of our Mastering Mathematics for Engineers program: a series of
MOOCs to refresh and review your bachelor level mathematics. This is the first of two
Calculus MOOCs - Calculus I.
In this course we focus on functions of one variable. In the first five weeks of the
course, you will learn all the basic integration, differentiation and approximation
techniques required in a first calculus course of an engineering bachelor education.
In the final week these topics will all come together as you solve and analyze several
ordinary differential equations.
We use examples that are based on real-life applications and allow you to practice
your mathematical skills in an engineering context.
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2. Learning objectives
So, what will you actually learn in this course? At the end of this course,
you will be able to:
Apply differentiation techniques such as the chain rule and implicit
differentiation.
1.
Apply integration techniques such as integration-by-parts and
substitution.
2.
Solve ordinary differential equations that are important in engineering
like a damped, forced harmonic oscillator.
3.
4.
Compute horizontal asymptotes to find equilibria and growth rates.
5.
Analyze challenging engineering problems using these techniques.
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3. What we expect from you
Each week, the concepts are explained in videos and text, usually with
examples. You can check your understanding by doing the exercises. In all
of these exercises you will get feedback on your answers. If something is
still unclear, whether it is about the video content or about an exercise,
you can ask your question in the discussion forum that is attached to each
unit.
Resources and exercises (Grasple)
Before you start with the course activities and materials, it's very
important to get acquainted with the environment. In the Getting Started
section you will find some introductory activities to get yourself prepared
for this course; particularly pay attention to the section on how to enter
answer in the exercises.
You are expected to follow forum and collaboration guidelines. Respect
the course policies, academic integrity and most importantly, the
instructors and other learners.
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4. What you can expect from the course team
The moderator will be available to assist with questions on a regular basis
in the Discussion Forums. For any content-related or certification issues,
please use the Discussion forums.
For technical or financial questions, please email
onlinelearningsupport@tudelft.nl
Response Time: We will respond to all your questions and posts within 2448 hours at least.
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5. Course structure
Week 1: Functions, graphs, inverse functions, inverse trigonometric functions,
compositions of functions
Week 2: Differentiation, tangent lines, implicit differentiation, differentiation of
inverses
Week 3: Approximation errors, Linear approximation, Differentials, Taylor
polynomials, Taylor’s inequality
Week 4: Horizontal asymptotes, Growth rates, computing horizontal asymptotes
Week 5: Integration, Integration by parts, Substitution method, integration by Taylor
polynomial, integrals over unbounded domains
Week 6: Differential equations, direction fields, first order separable and linear
equations, forced and damped harmonics oscillators, approximating solutions to
differential equations using Taylor polynomials.
Resources and exercises (Grasple)
Before you start with the course activities and materials, it is very important
to get acquainted with the environment and in the Getting Started section
you'll find some introductory activities to get yourself prepared for this
course; particularly pay attention to the section on how to use Grasple.
4. Title (date when the content opens)
Your text
[Give a brief explanation of what will be covered in this unit, the tasks to perform,
the resources, the deliverables and what elements are graded. The idea is to give a
general overview, since more detailed information will be found in the course.]
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6. Resources, Tools & Browsers
All educational resources will be available in the course. They consist of
short videos and exercises to support you in the completion of the weekly
learning activities. You will, however, have to regsister on Grasple if you
are a verified/paid learner.
In order to truly understand mathematics it is necessary to grapple with
exercises and problem. In this course we will use exercises from the online
learning platform Grasple. Grasple is made particularly for mathematics
exercises and importantly provides specific feedback to correct and
wrong answers immediately. You will find a short tutorial to set you up with
the correct syntax to use Grasple. After each lesson you will find a
dedicated unit with exercises to get the necessary practice to master
mathematics.
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7. Assessment & Certificate
Only verified participants have access to the final exam on Grasple. In
order to successfully complete the course, you need to pass the final
exam with a score of 50%.
Upgrade to a Verified Certificate gives you:
a certificate if you successfully completed the course and obtained a
passing grade;
access to graded assignments;
access to the archived course after the end date.
These certificates will indicate you have successfully completed the
course, but will not include a specific grade. Certificates will be issued by
edX under the name of DelftX, designating the institution from which the
course originated.
Do you need financial assistance? edX offers a discount on our verified
certificates to learners who cannot afford to pay full price. Check the edX
support page for financial assistance.
Generating an ID verified certificate
Certificates for verified learners will be issued at the beginning of each
month for participants who successfully completed the final exam the
previous month.
Certificates can be downloaded from your Student Dashboard (look for
the Download button next to the name of our course). An ID verified
Certificate of Achievement is available for the amount specified on the
course home page. You can Upgrade on your edX Dashboard to Verified
during the course. Once produced, a certificate cannot be reissued, hence
it is very important that you verify the way in which your name appears.
Check that, in your edx.org account, your name is correctly spelled, since
it will appear on the final certificate.
Do you need financial assistance? edX offers a discount on our verified
certificates to learners who cannot afford to pay full price. Check the edX
support page for financial assistance.
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8. A note about fraud
Plagiarism is a violation of copyright as it involves reproducing (parts of) another
person’s work without stating the source, and thereby failing to comply with an
essential aspect of copyright. This includes images, calculations, mathematical
answers and the use of AI-generated content, unless clearly acknowledged and
referenced. Intentional plagiarism constitutes a transgression within the academic
world. In many cases plagiarism is unintentional, negligence or simply poor source
acknowledgement, but do take care to give all authors credit or ask for assistance if
required.
Whenever you reference content from a source, you need to cite it correctly. For
further details on how and when to cite sources, see the TU Delft Library's website.
Please note that you are expected to follow the Learning and Assessment
Regulations of the TU Delft Extension School for Continuing Education.
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9. License
Delft University of Technology holds the copyright to all DelftX courses,
including Mastering Mathematics for Engineers: Calculus I: from
functions to differential equations. Unless otherwise stated, the course
materials of this MOOC are licensed under a Creative Commons
Attribution-NonCommercial-ShareAlike 4.0 License. For licensing
purposes, "course materials" are defined as the syllabus, learning
objectives, unit descriptions and explanations, videos and the framing text
that accompanies resources curated from third parties. That excludes the
third party resources themselves, forum discussions, quizzes,
exercises and all forms of assessment.