Calculus I: From Functions to Differential Equations
Source: https://learningforlife.tudelft.nl/calculus-i-from-functions-to-differential-equations/ Parent: https://learningforlife.tudelft.nl/our-courses/core-stem-skills/
Share webpage
- Apply differentiation techniques such as the chain rule and implicit differentiation.
- Apply integration techniques such as integration-by-parts and substitution.
- Solve ordinary differential equations that are important in engineering like a damped, forced harmonic oscillator.
- Compute horizontal asymptotes to find equilibria and growth rates.
- Analyze challenging engineering problems using these techniques.
Free
- Type Course
- Location Online
- Pacing Starts anytime / Self-paced
- Length
For instructor paced courses this is the length of the course.
For self-paced courses this is the length of the course if you spend the amount of time per week as specified. You're free to go faster or slower as you see fit.
6 Weeks - Effort 4 - 6 Hours per week
Loading...
Subscribe to back in stock notification
Subscribe
Refresh and review your bachelor-level calculus. This course covers all the various differentiation and integration techniques and guides you through several important methods for solving differential equations.
A strong foundation in mathematics is critical for success in all science and engineering disciplines. Whether you want to make a strong start to a master’s degree, prepare for more advanced courses, solidify your knowledge in a professional context or simply brush up on fundamentals, this course will get you up to speed.
This course allows you to get a solid basis by refreshing and reviewing your bachelor-level calculus. \ \ The course focuses on functions of one variable. In the first 5 weeks 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 so you can practice your mathematical skills in an engineering context. Our courses in calculus offer enough depth to cover what you need to succeed in your engineering master’s or profession in areas such as modeling, physics, fluid dynamics, dynamical systems and more.
This is a review course\ This self-contained course is modular, so you do not need to follow the entire course if you wish to focus on a particular aspect. As a review course you are expected to have previously studied or be familiar with most of the material. Hence the pace will be higher than in an introductory course.
This format is ideal for refreshing your bachelor level mathematics and letting you practice as much as you want. Through the Grasple platform, you will have access to plenty of exercises and receive intelligent, personal and immediate feedback. - Details
##### Course Syllabus
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
- Qualifications
##### Chartered Engineering Competences
All our online courses and programs have been matched to the competences determined by KIVI’s Competence Structure, a common frame of reference for everyone, across all disciplines, levels and roles.
These competences apply to this course:
- A1: Extend your theoretical knowledge of new and advancing technologies.
- Admission
This is a Massive Open Online Course (MOOC) that runs on edX.
##### Prerequisites
Prior knowledge of all the material covered.
In this course we develop the calculus up to a level required for solving and analyzing several important ordinary differential equations. As such the course requires you to have a grasp of or be familiar with pre-university level mathematics including basic elementary functions, trigonometry, algebra and differentiation.
- Course format: MOOC
This course is a Massive Open Online Course (MOOC). Our MOOCs are delivered on edX.org and are open to all. They include video lectures, readings, assignments, and community discussions. Content is free, with optional certificates and additional exercises available for a fee.
Related Products
Press to go to carousel navigation
Calculus II: Multivariable Functions
4 - 6 Hours per week
Free
Linear Algebra I: Vectors and Linear Equations
4 - 6 Hours per week
Free
Linear Algebra II: Matrices and Linear Transformations
4 - 6 Hours per week
Free