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Nicholas Crouch,
Dr. Melissa Humphries,
Dr. Danny Stevenson,
Dr. David Butler,
and
Dr. Brendan Harding
This course is part three of the MathTrackX XSeries Program which has been designed to provide you with a solid foundation in mathematical fundamentals and how they can be applied in the real world.
This course will cover basic concepts and techniques relating to differentiation; a fundamental tool of calculus. Derivatives are key to the understanding of rates of change, that is the extent to which a function responds to changes in a dependent variable.
Read more
This course is part three of the MathTrackX XSeries Program which has been designed to provide you with a solid foundation in mathematical fundamentals and how they can be applied in the real world.
This course will cover basic concepts and techniques relating to differentiation; a fundamental tool of calculus. Derivatives are key to the understanding of rates of change, that is the extent to which a function responds to changes in a dependent variable.
Read more
This course is part three of the MathTrackX XSeries Program which has been designed to provide you with a solid foundation in mathematical fundamentals and how they can be applied in the real world.
This course will cover basic concepts and techniques relating to differentiation; a fundamental tool of calculus. Derivatives are key to the understanding of rates of change, that is the extent to which a function responds to changes in a dependent variable.
Guided by experts from the School of Mathematics and the Maths Learning Centre at the University of Adelaide, this course will cover concepts and techniques to provide a foundation for the applications of differentiation in STEM related careers and/or further study at the undergraduate level.
Join us as we provide opportunities to develop your skills and confidence in applying mathematics to solve real world problems.
Register for this course and see more details by visiting:
OpenCourser.com/course/8dysaq/mathtrackx
What's inside
Learning objectives
- How derivatives relate to the slope of a function
- How to calculate the derivative of polynomials and special functions
- Differentiation rules for evaluating the derivative of non-trivial functions
- The concept and application of ‘the second derivative’
- How to use differentiation to solve problems in basic motion, mechanics and optimisation.
- How derivatives relate to the slope of a function
- How to calculate the derivative of polynomials and special functions
- Differentiation rules for evaluating the derivative of non-trivial functions
- The concept and application of ‘the second derivative’
- How to use differentiation to solve problems in basic motion, mechanics and optimisation.
Traffic lights
Traffic lights
Read about what's good
what should give you pause and
possible dealbreakers
Develops understanding in special function derivatives, which are important across STEM industries
Provides essential knowledge for careers in STEM-related fields
Foundation for advanced mathematical topics
Taught by university experts in math
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Reviews summary
Differential calculus: strong stem foundation
According to learners, MathTrackX: Differential Calculus is a largely positive experience, praised for providing a solid foundational understanding of calculus. Students highlight the clear and understandable explanations by instructors and the effectiveness of practice problems and quizzes in reinforcing concepts. Many appreciate the inclusion of real-world applications, making abstract concepts tangible for STEM careers and further academic study. While generally well-received, some found the pace inconsistent depending on their prior knowledge, occasionally requiring external supplementation for deeper understanding.
Useful real-world examples and applications are included.
"I particularly appreciated the real-world examples which made the abstract concepts much more tangible."
"The explanations of how derivatives relate to real-world problems (motion, optimization) were particularly useful to me."
"I found the application sections very practical and relevant to STEM fields."
Provides a strong base for STEM careers and university-level study.
"I highly recommend this for anyone looking to solidify their calculus foundation for STEM."
"This course truly prepares you for further study in STEM. I'd recommend it for pre-university or first-year students."
"As someone who needed a strong review of calculus for engineering, this was perfect."
"I gained a good grasp of the fundamentals needed for higher-level courses in my field."
Quizzes and problems are highly effective for concept reinforcement.
"The practice problems and quizzes were highly effective in reinforcing the concepts."
"The exercises really helped me grasp the concepts. It built my confidence for university-level math."
"The quizzes are fair, though sometimes they have minor technical issues with formatting."
"I found the practice questions ample and well-designed, truly helpful for learning."
Instructors deliver topics in a very clear and understandable way.
"The instructors explained complex topics in a very clear and understandable way."
"The explanations were spot on, and the exercises really helped me grasp the concepts."
"The lectures are clear, and the examples are pertinent. I especially liked the step-by-step approach to problem-solving."
"I found the instructors to be very knowledgeable, and the curriculum was logically structured."
Engagement in the course discussion forums is limited.
"The forum activity was low, making it hard to get questions answered quickly."
"I found the community aspect of the course less active than I'd hoped."
Learners may need to use external resources for deeper understanding.
"I had to supplement with external resources to fully understand certain derivations."
"I don't expect it to be all-encompassing; additional study may be required for depth."
"Sometimes I wished for more in-depth coverage and had to look up additional explanations."
The pace is perceived differently by learners based on their background.
"The pace was a bit slow at times for someone with some prior exposure to calculus..."
"I found this course quite difficult to follow. The explanations often assumed a level of prior mathematical intuition that I didn't possess."
"Some parts felt rushed, and I felt too fast-paced for me. I had to pause and re-watch videos frequently."
"It's good for a quick overview if you already have some background."
Activities
Be better prepared
before
your course. Deepen your understanding
during
and
after
it. Supplement your coursework and achieve mastery of the topics covered
in MathTrackX: Differential Calculus with these
activities:
Organize Course Materials
Show steps
Organize your notes, assignments, and resources for easy access and review.
Browse courses on
Differentiation
Show steps
-
Create a system for organizing your materials, such as folders or digital notebooks.
-
Categorize materials based on topic or relevance.
-
Highlight important concepts and formulas for quick reference.
Review Pre-Calculus Concepts
Show steps
Refresh your understanding of pre-calculus concepts, providing a solid foundation for differentiation.
Browse courses on
Pre-Calculus
Show steps
-
Review notes or textbooks on pre-calculus topics.
-
Solve practice problems to test your understanding.
-
Identify areas where you need additional support or clarification.
Read 'Understanding Calculus' by Thomas
Show steps
Gain a comprehensive overview of calculus, including differentiation, through a well-regarded textbook.
View
University Calculus: Early Transcendentals,...
on Amazon
Show steps
-
Obtain a copy of 'Understanding Calculus' by Thomas.
-
Allocate dedicated time for reading and studying the relevant chapters.
-
Take notes and summarize key concepts, highlighting their application to differentiation.
-
Complete practice problems and exercises included in the text.
Five other activities
Expand to see all activities and additional details
Show all eight activities
Explore Online Differentiation Video Tutorials
Show steps
Supplement your learning by seeking out engaging and informative video tutorials that provide alternative perspectives and explanations.
Browse courses on
Differentiation
Show steps
-
Search for reputable online platforms or channels offering differentiation tutorials.
-
Select videos that align with your learning style and specific areas of interest.
-
Take notes or summarize the key points covered in the tutorials.
-
Apply the concepts covered in the tutorials to practice problems or real-world examples.
Create a Differentiation Concept Map
Show steps
Visualize and organize differentiation concepts, improving your comprehension and retention.
Browse courses on
Differentiation
Show steps
-
Identify key concepts, definitions, and formulas related to differentiation.
-
Connect the concepts using arrows or branches, creating a visual representation.
-
Add examples and explanations to illustrate the relationships between concepts.
-
Review and refine your concept map regularly to enhance understanding.
Participate in Differentiation Study Group
Show steps
Contribute to and engage with discussions on differentiation concepts, reinforcing your understanding and identifying areas for improvement.
Browse courses on
Differentiation
Show steps
-
Join a study group focused on differentiation.
-
Actively participate in discussions, posing questions and sharing insights.
-
Regularly review group notes and contributions to solidify your understanding.
Solve Differentiation Practice Problems
Show steps
Enhance your problem-solving skills and deepen your understanding of differentiation techniques through regular practice.
Browse courses on
Differentiation
Show steps
-
Find online or textbook resources with differentiation practice problems.
-
Allocate dedicated time for practice, aiming for consistency rather than quantity.
-
Review your solutions thoroughly, identifying areas where you need improvement.
-
Seek guidance from your instructor or classmates if necessary.
Develop a Differentiation Tool
Show steps
Deepen your understanding by creating a tool that automates differentiation calculations or visualizes concepts.
Browse courses on
Differentiation
Show steps
-
Identify a need or problem related to differentiation.
-
Design and develop a tool that addresses the identified need.
-
Test and refine your tool to ensure accuracy and functionality.
-
Share your tool with others for feedback and potential use.
Organize Course Materials
Show steps
Organize your notes, assignments, and resources for easy access and review.
Browse courses on
Differentiation
Show steps
Show steps
Show steps
- Create a system for organizing your materials, such as folders or digital notebooks.
- Categorize materials based on topic or relevance.
- Highlight important concepts and formulas for quick reference.
Review Pre-Calculus Concepts
Show steps
Refresh your understanding of pre-calculus concepts, providing a solid foundation for differentiation.
Browse courses on
Pre-Calculus
Show steps
Show steps
Show steps
- Review notes or textbooks on pre-calculus topics.
- Solve practice problems to test your understanding.
- Identify areas where you need additional support or clarification.
Read 'Understanding Calculus' by Thomas
Show steps
Gain a comprehensive overview of calculus, including differentiation, through a well-regarded textbook.
View
University Calculus: Early Transcendentals,...
on Amazon
Show steps
Show steps
Show steps
- Obtain a copy of 'Understanding Calculus' by Thomas.
- Allocate dedicated time for reading and studying the relevant chapters.
- Take notes and summarize key concepts, highlighting their application to differentiation.
- Complete practice problems and exercises included in the text.
Five other activities
Expand to see all activities and additional details
Show all eight activities
Explore Online Differentiation Video Tutorials
Show steps
Supplement your learning by seeking out engaging and informative video tutorials that provide alternative perspectives and explanations.
Browse courses on
Differentiation
Show steps
Show steps
Show steps
- Search for reputable online platforms or channels offering differentiation tutorials.
- Select videos that align with your learning style and specific areas of interest.
- Take notes or summarize the key points covered in the tutorials.
- Apply the concepts covered in the tutorials to practice problems or real-world examples.
Create a Differentiation Concept Map
Show steps
Visualize and organize differentiation concepts, improving your comprehension and retention.
Browse courses on
Differentiation
Show steps
Show steps
Show steps
- Identify key concepts, definitions, and formulas related to differentiation.
- Connect the concepts using arrows or branches, creating a visual representation.
- Add examples and explanations to illustrate the relationships between concepts.
- Review and refine your concept map regularly to enhance understanding.
Participate in Differentiation Study Group
Show steps
Contribute to and engage with discussions on differentiation concepts, reinforcing your understanding and identifying areas for improvement.
Browse courses on
Differentiation
Show steps
Show steps
Show steps
- Join a study group focused on differentiation.
- Actively participate in discussions, posing questions and sharing insights.
- Regularly review group notes and contributions to solidify your understanding.
Solve Differentiation Practice Problems
Show steps
Enhance your problem-solving skills and deepen your understanding of differentiation techniques through regular practice.
Browse courses on
Differentiation
Show steps
Show steps
Show steps
- Find online or textbook resources with differentiation practice problems.
- Allocate dedicated time for practice, aiming for consistency rather than quantity.
- Review your solutions thoroughly, identifying areas where you need improvement.
- Seek guidance from your instructor or classmates if necessary.
Develop a Differentiation Tool
Show steps
Deepen your understanding by creating a tool that automates differentiation calculations or visualizes concepts.
Browse courses on
Differentiation
Show steps
Show steps
Show steps
- Identify a need or problem related to differentiation.
- Design and develop a tool that addresses the identified need.
- Test and refine your tool to ensure accuracy and functionality.
- Share your tool with others for feedback and potential use.
Career center
Learners who complete MathTrackX: Differential Calculus will develop knowledge and skills
that may be useful to these careers:
Data Analyst
Data Analyst
Data Analysts use their knowledge of mathematics, statistics, and programming to extract insights from data. Differential Calculus can help build a foundation for the mathematical concepts and techniques used in data analysis, such as derivatives and rates of change.
Financial Analyst
Financial Analyst
Financial Analysts use mathematical and statistical models to assess the risks and returns of investments. Differential Calculus can help build a foundation for the mathematical concepts and techniques used in financial analysis, such as derivatives and optimization.
Actuary
Actuary
Actuaries use mathematical and statistical models to assess the risks and costs of insurance policies. Differential Calculus can help build a foundation for the mathematical concepts and techniques used in actuarial science, such as derivatives and probability.
Operations Research Analyst
Operations Research Analyst
Operations Research Analysts use mathematical and statistical models to improve the efficiency of organizations. Differential Calculus can help build a foundation for the mathematical concepts and techniques used in operations research, such as derivatives and optimization.
Statistician
Statistician
Statisticians use mathematical and statistical models to collect, analyze, and interpret data. Differential Calculus can help build a foundation for the mathematical concepts and techniques used in statistics, such as derivatives and probability.
Economist
Economist
Economists use mathematical and statistical models to analyze economic data and make predictions about the economy. Differential Calculus can help build a foundation for the mathematical concepts and techniques used in economics, such as derivatives and optimization.
Quantitative Analyst
Quantitative Analyst
Quantitative Analysts use mathematical and statistical models to assess the risks and returns of investments. Differential Calculus can help build a foundation for the mathematical concepts and techniques used in quantitative analysis, such as derivatives and optimization.
Software Engineer
Software Engineer
Software Engineers use mathematical concepts and techniques to design, develop, and test software. Differential Calculus can help build a foundation for the mathematical concepts and techniques used in software engineering, such as derivatives and optimization.
Data Scientist
Data Scientist
Data Scientists use mathematical and statistical models to extract insights from data. Differential Calculus can help build a foundation for the mathematical concepts and techniques used in data science, such as derivatives and optimization.
Machine Learning Engineer
Machine Learning Engineer
Machine Learning Engineers use mathematical and statistical models to develop and deploy machine learning algorithms. Differential Calculus can help build a foundation for the mathematical concepts and techniques used in machine learning, such as derivatives and optimization.
Physicist
Physicist
Physicists use mathematical and statistical models to describe and predict the behavior of the physical world. Differential Calculus can help build a foundation for the mathematical concepts and techniques used in physics, such as derivatives and optimization.
Chemical Engineer
Chemical Engineer
Chemical Engineers use mathematical and statistical models to design and operate chemical plants. Differential Calculus can help build a foundation for the mathematical concepts and techniques used in chemical engineering, such as derivatives and optimization.
Civil Engineer
Civil Engineer
Civil Engineers use mathematical and statistical models to design and build infrastructure. Differential Calculus can help build a foundation for the mathematical concepts and techniques used in civil engineering, such as derivatives and optimization.
Mechanical Engineer
Mechanical Engineer
Mechanical Engineers use mathematical and statistical models to design and build machines. Differential Calculus can help build a foundation for the mathematical concepts and techniques used in mechanical engineering, such as derivatives and optimization.
Electrical Engineer
Electrical Engineer
Electrical Engineers use mathematical and statistical models to design and build electrical systems. Differential Calculus can help build a foundation for the mathematical concepts and techniques used in electrical engineering, such as derivatives and optimization.
For more career information including salaries, visit:
OpenCourser.com/course/8dysaq/mathtrackx
Reading list
We've selected 15 books
that we think will supplement your
learning. Use these to
develop background knowledge, enrich your coursework, and gain a
deeper understanding of the topics covered in
MathTrackX: Differential Calculus.
Great choice for students who want to learn more about chemistry and physics. It covers a wide range of topics, from basic concepts to more advanced applications.
Save
This classic textbook is known for its rigor and depth. It great choice for students who want to learn differential calculus in a mathematically rigorous way.
Great choice for students who want to learn more about mathematical methods for physics and engineering. It covers a wide range of topics, from basic concepts to more advanced applications.
Great choice for students who want to learn more about linear algebra. It covers a wide range of topics, from basic concepts to more advanced applications.
Great choice for students who want to learn more about numerical recipes. It covers a wide range of topics, from basic concepts to more advanced applications.
Great choice for students who want to learn more about physics. It covers a wide range of topics, from basic concepts to more advanced applications.
Great choice for students who want to learn more about physics formulas. It covers a wide range of topics, from basic concepts to more advanced applications.
Great choice for students who want to learn more about mathematical statistics. It covers a wide range of topics, from basic concepts to more advanced applications.
This textbook provides a comprehensive introduction to differential calculus, covering all the topics you would expect in a university-level course. It is written in a clear and engaging style, with plenty of examples and exercises to help you understand the concepts.
Great choice for students who want to learn more about probability and statistics. It covers a wide range of topics, from basic concepts to more advanced applications.
Save
This textbook comprehensive guide to differential calculus, covering all the topics you would expect in a university-level course. It is written in a clear and concise style, with plenty of examples and exercises to help you understand the concepts.
Great choice for students who want to learn more about differential equations. It covers a wide range of topics, from basic concepts to more advanced applications.
Great choice for students who want to learn more about partial differential equations. It covers a wide range of topics, from basic concepts to more advanced applications.
This textbook concise and accessible introduction to differential calculus. It great choice for students who want to learn the basics of differential calculus quickly and easily.
Great choice for students who are new to differential calculus and want to learn the basics in a fun and easy-to-understand way.
For more information about how these books relate to this course, visit:
OpenCourser.com/course/8dysaq/mathtrackx
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Rating
4.8
Effort
3 to 6 hours per week for 4 weeks
Level
Introductory
Via
edX
Institution
University of Adelaide
Instructors
Nicholas Crouch
Dr. Melissa Humphries
Dr. Danny Stevenson
Dr. David Butler
Dr. Brendan Harding
Language
English
Transcript
English
This course belongs to a
collection
called
MathTrackX. It's comprised of six courses:
- MathTrackX: Polynomials, Functions and Graphs
- MathTrackX: Differential Calculus (viewing)
- MathTrackX: Integral Calculus
- MathTrackX: Probability
- MathTrackX: Statistics
- MathTrackX: Special Functions
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