Fundamentals of Calculus explores limits, derivatives, and integrals, explaining how quantities change and accumulate. It builds essential mathematical reasoning, enabling problem-solving across science, engineering, economics, and real-world analytical applications.
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Fundamentals of Calculus is a comprehensive online course designed to introduce learners to essential calculus basics and build a strong foundation in mathematical analysis. This course explores functions and graphs, limits and continuity, and key derivative concepts, helping students understand the principles that form the basis of advanced mathematics and effective calculus problem solving.
Through structured lessons on differentiation and integral calculus, learners will develop practical skills in analysing mathematical relationships and solving real-world problems. The course covers important topics including derivatives, applications of derivatives, and the connection between mathematical concepts, enabling students to confidently approach complex calculations and improve their analytical thinking abilities.
This Fundamentals of Calculus course is ideal for anyone looking to strengthen their understanding of core calculus principles. By studying limits, continuity, functions, derivatives, and their applications, learners will gain valuable knowledge required for further studies in science, engineering, economics, and other fields that rely on advanced mathematics and quantitative reasoning.
Learners complete an assignment designed to evaluate their understanding of the course content. The assignment is reviewed by qualified tutors who provide personalised feedback, allowing learners to demonstrate their applied knowledge and skills.
After completing the Fundamentals of Calculus course assessment, you will be eligible to receive a CPD-accredited certificate worth £9 from One Education to demonstrate your achievement.
The certificate is also available as a printed hard copy delivered by post for £15.
Quality Licence Scheme Endorsed Certificate
Learners also have the option to order a Quality Licence Scheme (QLS) Endorsed Certificate as additional proof of achievement. The QLS Endorsed Certificate can be delivered by post for £129, with an additional £10 postage charge for international students.
This course has been endorsed by the Quality Licence Scheme for its high-quality, non-regulated provision and training programmes. This course is not regulated by Ofqual and is not an accredited qualification. Your training provider will be able to advise you on any further recognition, for example progression routes into further and/or higher education. For further information please visit the Learner FAQs on the Quality Licence Scheme website.
Fundamentals of Calculus introduces learners to the core principles of mathematical analysis, including functions, limits, differentiation, and integration. This course explores essential calculus concepts, helping learners understand change, rates, graphs, and mathematical techniques used in science, engineering, and real-world applications.
Studying Fundamentals of Calculus develops logical reasoning, problem-solving, and analytical skills essential for advanced mathematics. The course provides a strong foundation in calculus problem-solving and supports further learning in mathematics, technology, engineering, economics, and other quantitative fields.
The Fundamentals of Calculus course has a total study time of 3 weeks, 4 days. This comprehensive programme is designed for flexible learning, allowing learners to progress at their own pace while exploring calculus fundamentals, including functions and graphs, limits and continuity, differentiation, integration, derivative concepts, integral calculus, mathematical analysis, and problem-solving techniques for advanced mathematics.
The Fundamentals of Calculus course requirements are simple and suitable for beginners. Learners should have a basic understanding of mathematics, an interest in problem-solving and mathematical analysis, and a willingness to explore functions, limits, differentiation, and integration. Access to an internet-enabled device and commitment to regular study and practice are recommended for effective learning and successful course completion.
This course introduces the essential concepts of calculus, including functions and graphs, limits and continuity, differentiation, derivatives, integration, integral calculus, mathematical analysis, and problem-solving techniques used in advanced mathematics and real-world applications.
No. It is suitable for beginners, students, and anyone interested in developing a strong foundation in calculus. A basic understanding of algebra and mathematics is recommended but not essential.
The course is delivered online, allowing you to learn at your own pace and develop your mathematical skills conveniently.
Yes. Calculus exercises, differentiation and integration problems, mathematical analysis tasks, practice activities, and quizzes may be included to reinforce learning.
You will receive a certificate of completion after successfully finishing the course.
This course supports career development in mathematics, engineering, physics, data science, economics, computer science, finance, research, education, and other fields that require analytical and advanced problem-solving skills.
| Unit 01: Supplements | |||
| 1.1 Number Sets | 00:10:00 | ||
| 1.2 Graphing Tools | 00:06:00 | ||
| Unit 02: Functions | |||
| 2.1 Introduction | 00:01:00 | ||
| 2.2 Functions | 00:15:00 | ||
| 2.3 Evaluating a Function | 00:13:00 | ||
| 2.4 Domain | 00:16:00 | ||
| 2.5 Range | 00:05:00 | ||
| 2.6 One to One Function | 00:09:00 | ||
| 2.7 Inverse Functions | 00:10:00 | ||
| 2.8 Exponential Functions | 00:05:00 | ||
| 2.9 The Natural Exponential Function | 00:06:00 | ||
| 2.10 Logarithms | 00:13:00 | ||
| 2.11 Natural Logarithms | 00:07:00 | ||
| 2.12 Logarithm Laws | 00:06:00 | ||
| 2.13 Trigonometric Ratios | 00:15:00 | ||
| 2.14 Evaluating Trig Functions and Points | 00:18:00 | ||
| 2.15 Inverse Trigonometric Functions | 00:12:00 | ||
| Unit 03 Limits | |||
| 3.1 Introduction | 00:01:00 | ||
| 3.2 What is a Limit? | 00:17:00 | ||
| 3.3 Examples | 00:15:00 | ||
| 3.4 One-Sided Limits | 00:12:00 | ||
| 3.5 The Limit Laws | 00:08:00 | ||
| 3.6 Examples | 00:15:00 | ||
| 3.7 More Examples | 00:15:00 | ||
| 3.8 The Squeeze (Sandwich) Theorem | 00:09:00 | ||
| 3.9 Examples | 00:10:00 | ||
| 3.10 Precise Definition of Limits | 00:08:00 | ||
| 3.11 Examples | 00:15:00 | ||
| 3.12 limits at Infinity | 00:21:00 | ||
| 3.13 Examples | 00:15:00 | ||
| 3.14 Asymptotes and Limits at Infinity | 00:10:00 | ||
| 3.15 Infinite Limits | 00:12:00 | ||
| Unit 04: Continuity | |||
| 4.1 Introduction | 00:01:00 | ||
| 4.2 Continuity | 00:12:00 | ||
| 4.3 Types of Discontinuity | 00:12:00 | ||
| 4.4 Examples | 00:17:00 | ||
| 4.5 Properties of Continuous Functions | 00:11:00 | ||
| 4.6 Intermediate Value Theorem for Continuous Functions | 00:06:00 | ||
| Unit 05: Derivatives | |||
| 5.1 Introduction | 00:01:00 | ||
| 5.2 Average Rate of Change | 00:09:00 | ||
| 5.3 Instantaneous Rate of Change | 00:12:00 | ||
| 5.4 Derivative Definition | 00:14:00 | ||
| 5.5 Examples | 00:10:00 | ||
| 5.6 Non-Differentiability | 00:06:00 | ||
| 5.7 Constant and Power Rule | 00:09:00 | ||
| 5.8 Constant Multiple Rule | 00:07:00 | ||
| 5.9 Sum and Difference Rule | 00:07:00 | ||
| 5.10 Product Rule | 00:14:00 | ||
| 5.11 Quotient Rule | 00:08:00 | ||
| 5.12 Chain Rule | 00:14:00 | ||
| 5.13 Examples | 00:09:00 | ||
| 5.14 Derivative Symbols | 00:04:00 | ||
| 5.15 Graph of Derivatives | 00:10:00 | ||
| 5.16 Higher Order Derivatives | 00:08:00 | ||
| 5.17 Equation of the Tangent Line | 00:07:00 | ||
| 5.18 Derivative of Trig Functions | 00:07:00 | ||
| 5.19 Examples | 00:19:00 | ||
| 5.20 Derivative of Inverse Trig Functions | 00:08:00 | ||
| 5.21 Examples | 00:12:00 | ||
| 5.22 Implicit Differentiation | 00:17:00 | ||
| 5.23 Derivative of Inverse Functions | 00:13:00 | ||
| 5.24 Derivative of the Natural Exponential Function | 00:11:00 | ||
| 5.25 Derivative of the Natural Logarithm Function | 00:07:00 | ||
| 5.26 Derivative of Exponential Functions | 00:06:00 | ||
| 5.27 Derivative of Logarithmic Functions | 00:06:00 | ||
| 5.28 Logarithmic Differentiation | 00:15:00 | ||
| Unit 06: Application of Derivatives | |||
| 6.1 Introduction | 00:01:00 | ||
| 6.2 Related Rates | 00:08:00 | ||
| 6.3 Examples | 00:13:00 | ||
| 6.4 More Example | 00:09:00 | ||
| 6.5 More Example | 00:10:00 | ||
| 6.6 Optimisation | 00:16:00 | ||
| 6.7 Example | 00:11:00 | ||
| 6.8 More Example | 00:07:00 | ||
| 6.9 Extreme Values of Functions | 00:12:00 | ||
| 6.10 Critical Points | 00:08:00 | ||
| 6.11 Examples (First Derivative Test) | 00:16:00 | ||
| 6.12 More Examples | 00:18:00 | ||
| 6.13 Concavity | 00:15:00 | ||
| 6.14 Examples | 00:13:00 | ||
| 6.15 Second Derivative Test | 00:08:00 | ||
| 6.16 Graphing Functions | 00:08:00 | ||
| 6.17 Examples | 00:21:00 | ||
| 6.18 L’ Hôpital’s Rule | 00:12:00 | ||
| 6.19 Other Indeterminate Forms | 00:15:00 | ||
| 6.20 Rolle’s Theorem | 00:09:00 | ||
| 6.21 The Mean Value Theorem | 00:19:00 | ||
| 6.22Application of the Mean Value Theorem | 00:04:00 | ||
| Resources | |||
| Resource – Fundamentals of Calculus | 00:00:00 | ||
| Assignment | |||
| Assignment – Fundamentals of Calculus | 3 weeks, 3 days | ||
| Order Your Certificate | |||
| Order Your Certificate QLS | 00:00:00 | ||
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