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Introduction to Calculus

The focus and themes of the Introduction to Calculus course address the most important foundations for applications of mathematics in science, engineering and commerce. The course emphasises the key ideas and historical motivation for calculus, while at the same time striking a balance between theory and application, leading to a mastery of key threshold concepts in foundational mathematics.

Students taking Introduction to Calculus will:

• gain familiarity with key ideas of precalculus, including the manipulation of equations and elementary functions (first two weeks),

Students taking Introduction to Calculus will:

• gain familiarity with key ideas of precalculus, including the manipulation of equations and elementary functions (first two weeks),

• develop fluency with the preliminary methodology of tangents and limits, and the definition of a derivative (third week),

• develop and practice methods of differential calculus with applications (fourth week),

• develop and practice methods of the integral calculus (fifth week).

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What's inside

Syllabus

Precalculus (Setting the scene)

This module begins by looking at the different kinds of numbers that fall on the real number line, decimal expansions and approximations, then continues with an exploration of manipulation of equations and inequalities, of sign diagrams and the use of the Cartesian plane.

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Develops key ideas of precalculus and strengthens preliminary methodology for intermediate learners

Taught by David Easdown, who is recognized for their work in mathematics

Introduces techniques of differential and integral calculus, strengthening an existing foundation

Examines applications of calculus, which are highly relevant in engineering, science, and commerce

Covers foundational calculus concepts similar to an accredited institute, building a strong foundation for beginners

Uses Leibniz notation, which is standard in the field of engineering

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Reviews summary

Solid foundation in calculus basics

According to learners, this course provides a strong foundation in calculus, essential for science, engineering, and commerce. Many found the lectures and explanations clear and easy to follow, helping them grasp core concepts like limits, derivatives, and integrals. While some noted the pace might be challenging for absolute beginners without solid precalculus skills, the overall sentiment is largely positive. Students appreciated the balance between theory and application and found the content highly relevant for further study.

Assumes comfort with precalculus basics.

"Make sure your precalculus is solid before starting this course. The first couple of weeks move quickly."

"The initial modules cover precalculus topics like functions and algebra, but assume a certain level of comfort."

"It is helpful if you brush up on fundamental functions and algebraic manipulation beforehand to keep up."

Pace is good for some, fast for others.

"The pace is just right if you have a bit of math background, moving efficiently through topics."

"I found the pace a bit too fast initially, especially when tackling some of the later modules like integration."

"It might be challenging if you haven't touched math in a while. Requires dedication and practice outside the videos."

Good mix of conceptual and practical.

"The course strikes a good balance between theoretical understanding and showing how calculus is applied in real-world contexts."

"Liked that it wasn't just formulas and proofs, but also explained *why* things work and how they're used."

"Provides both the 'how' to solve problems and the 'why' behind the concepts, which is crucial for mastery."

Lectures make complex topics understandable.

"The instructor's explanations were incredibly clear, even for difficult concepts like limits and the definition of a derivative."

"The lectures simplify complex ideas effectively, breaking them down into manageable parts."

"I appreciated how the material was presented in a very logical and easy-to-digest manner throughout the modules."

Provides a solid base for calculus concepts.

"This course gave me a really solid foundation in calculus. Everything is built step-by-step and clearly explained."

"I feel much more confident about calculus after completing this program. It's a great introduction to the core ideas."

"Highly recommend this course for anyone needing to grasp the essential concepts before pursuing more advanced math or science courses."

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 Introduction to Calculus with these activities:

Review precalculus concepts

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Ensure a strong foundation by reviewing fundamental precalculus concepts.

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Review basic algebra concepts, such as solving equations and inequalities.
Review basic trigonometry concepts, such as the definitions of the trigonometric functions and the unit circle.
Practice applying these concepts to solve problems.

Explore online tutorials on the chain rule

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The chain rule is a fundamental technique in calculus. Explore online tutorials to enhance your understanding.

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Start by searching for online tutorials on the chain rule.
Watch the tutorials and follow along with the examples.
Pause the tutorials when necessary to take notes.
Practice applying the chain rule to your own problems.

Join a study group to discuss key concepts

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Engage with peers to clarify understanding, challenge perspectives, and reinforce learning.

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Join a study group for the course.
Attend study group meetings regularly.
Participate actively in discussions.
Help other students with concepts they may be struggling with.

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Practice integration techniques

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Practice additional integration problems to improve your skills and build confidence.

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Start by reviewing the basic integration techniques.
Choose the appropriate integration technique for each problem.
Carry out the integration.
Check your answer by differentiating the result.

Practice solving related-rate problems

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Related-rate problems can be challenging to solve, but they are an important application of derivatives. Practice additional problems to build your skills.

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Start by reading the problem carefully to understand what is being asked.
Identify the variables that are changing and the relationship between them.
Write an equation that relates the variables.
Differentiate the equation with respect to time.
Solve the resulting equation for the unknown rate.

Create a study guide for the derivative

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To reinforce learning about derivatives, create a study guide that summarizes the key concepts.

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Start by reviewing your notes and the textbook.
Identify the key concepts that you need to include in the study guide.
Write out clear and concise explanations of each key concept.
Include examples to illustrate the key concepts.
Review your study guide regularly to help you remember the material.

Develop a presentation on applications of calculus in real life

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To further explore the practical relevance of calculus, create a presentation that showcases its applications in various fields.

Browse courses on Applications of Calculus

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Start by brainstorming different fields where calculus is applied.
Research specific examples of how calculus is used in each field.
Create a presentation that explains these applications in a clear and engaging way.
Include visuals and examples to illustrate the concepts.
Practice presenting your presentation to get feedback.

Career center

Learners who complete Introduction to Calculus will develop knowledge and skills that may be useful to these careers:

Mathematician

Mathematicians use mathematical principles to solve problems and develop new theories. They work in a variety of fields, including academia, research, and industry. This course's emphasis on the key ideas and historical motivation for calculus, as well as its focus on applications of mathematics in science, can help build a foundation for understanding the complex mathematical concepts used in this field.

See salaries and explore the career path for Mathematician

Statistician

Statisticians use mathematical and statistical techniques to collect, analyze, and interpret data. They work in a variety of fields, including academia, research, and industry. This course's emphasis on the key ideas and historical motivation for calculus, as well as its focus on applications of mathematics in science, can help build a foundation for understanding the complex statistical models used in this field.

See salaries and explore the career path for Statistician

Quantitative Analyst

Quantitative Analysts use mathematics and statistics to analyze financial data and make investment decisions. This course's emphasis on the key ideas and historical motivation for calculus, as well as its focus on applications of mathematics in commerce, can help build a foundation for understanding the complex financial models used in this field.

See salaries and explore the career path for Quantitative Analyst

Data Scientist

Data Scientists use mathematics, statistics, and computer science to extract insights from data. They work in a variety of fields, including finance, healthcare, and marketing. This course's emphasis on the key ideas and historical motivation for calculus, as well as its focus on applications of mathematics in science, can help build a foundation for understanding the complex data analysis techniques used in this field.

See salaries and explore the career path for Data Scientist

Financial Analyst

Financial Analysts utilize mathematics, statistics, and computer models to make sound investment decisions. This course's emphasis on key ideas and historical motivation for calculus can help build a foundation for understanding the complex financial models used in this field. Additionally, its focus on applications of mathematics in commerce may be particularly relevant to this role.

See salaries and explore the career path for Financial Analyst

Actuary

Actuaries use mathematical and statistical skills to assess risk and uncertainty. They work in a variety of fields, including insurance, finance, and healthcare. This course's emphasis on key ideas and historical motivation for calculus, as well as its focus on applications of mathematics in commerce, can help build a foundation for understanding the complex statistical models used in this field.

See salaries and explore the career path for Actuary

Economist

Economists use mathematical and statistical techniques to analyze economic data and make predictions about the economy. They work in a variety of fields, including academia, research, and government. This course's emphasis on the key ideas and historical motivation for calculus, as well as its focus on applications of mathematics in commerce, can help build a foundation for understanding the complex economic models used in this field.

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Market Researcher

Market Researchers use mathematical and statistical techniques to collect and analyze data about consumer behavior. They work in a variety of fields, including marketing, advertising, and product development. This course's emphasis on the key ideas and historical motivation for calculus, as well as its focus on applications of mathematics in commerce, can help build a foundation for understanding the complex data analysis techniques used in this field.

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Business Analyst

Business Analysts use mathematical and statistical techniques to analyze business data and make recommendations for improvement. They work in a variety of industries, including consulting, finance, and healthcare. This course's emphasis on the key ideas and historical motivation for calculus, as well as its focus on applications of mathematics in commerce, can help build a foundation for understanding the complex data analysis techniques used in this field.

See salaries and explore the career path for Business Analyst

Financial Planner

Financial Planners use mathematical and statistical techniques to develop financial plans for individuals and families. They work in a variety of settings, including banks, investment firms, and insurance companies. This course's emphasis on the key ideas and historical motivation for calculus, as well as its focus on applications of mathematics in commerce, can help build a foundation for understanding the complex financial models used in this field.

See salaries and explore the career path for Financial Planner

Technical Writer

Technical Writers use mathematical and statistical techniques to write technical manuals, reports, and other documents. They work in a variety of industries, including software development, engineering, and manufacturing. This course's emphasis on the key ideas and historical motivation for calculus, as well as its focus on applications of mathematics in science, can help build a foundation for understanding the complex technical concepts used in this field.

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Software Engineer

Software Engineers design, develop, and test software systems. They work in a variety of industries, including technology, finance, and healthcare. This course's emphasis on the key ideas and historical motivation for calculus, as well as its focus on applications of mathematics in science, can help build a foundation for understanding the complex algorithms and data structures used in this field.

See salaries and explore the career path for Software Engineer

Operations Research Analyst

Operations Research Analysts apply analytical methods to solve complex business problems. They use techniques such as linear programming, queuing theory, and simulation to optimize processes and improve efficiency. This course's focus on the development of differential calculus with applications may be particularly relevant to this role.

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Teacher

Teachers use mathematical and statistical techniques to teach students about math and science. They work in a variety of settings, including elementary schools, high schools, and colleges. This course's emphasis on the key ideas and historical motivation for calculus, as well as its focus on applications of mathematics in science, can help build a foundation for understanding the complex mathematical concepts used in this field.

See salaries and explore the career path for Teacher

Operations Manager

Operations Managers plan and oversee the production of goods and services. They work in a variety of industries, including manufacturing, healthcare, and retail. This course's emphasis on the key ideas and historical motivation for calculus, as well as its focus on applications of mathematics in commerce, can help build a foundation for understanding the complex operations management techniques used in this field.

See salaries and explore the career path for Operations Manager

Reading list

We've selected 12 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 Introduction to Calculus.

Calculus

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This comprehensive textbook covers all the topics typically covered in a first-year calculus course, as well as some more advanced topics. It good choice for students who want a deep understanding of calculus.

Introduction to Calculus

What's inside

Syllabus

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Save this course

Reviews summary

Solid foundation in calculus basics

Activities

Career center

Reading list

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