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Fundamentals of Calculus

Overview The Fundamentals of Calculus course provides a comprehensive introduction to calculus, covering essential concepts and techniques. Starting with foundational …

Fundamentals of Calculus

Fundamentals of Calculus

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Fundamentals of Calculus Overview

The Fundamentals of Calculus course provides a comprehensive introduction to calculus, covering essential concepts and techniques. Starting with foundational mathematical tools and functions, the course progresses through limits, continuity, and derivatives, culminating in the application of derivatives to real-world problems. Students will gain a robust understanding of how calculus can be applied to analyse and solve complex problems in various fields.

Learning Outcomes

  • Understand and apply basic mathematical concepts and graphing tools.
  • Identify and evaluate different types of functions, including exponential, logarithmic, and trigonometric functions.
  • Grasp the concept of limits and use limit laws to solve problems.
  • Recognise and analyse continuity and types of discontinuity in functions.
  • Calculate derivatives and apply differentiation rules to various functions.
  • Understand and use the concept of instantaneous rate of change.
  • Apply derivatives to solve optimisation and related rates problems.
  • Analyse functions using the first and second derivative tests for extrema and concavity.
  • Use L’Hôpital’s Rule and the Mean Value Theorem to solve complex calculus problems.
  • Integrate knowledge of calculus concepts to model and solve real-world problems.

Who Is This Course For

This course is ideal for students and professionals seeking a foundational understanding of calculus. Whether you’re a university student needing a solid grasp of calculus for further studies or a professional looking to enhance your analytical skills, this course provides the necessary tools and knowledge. It’s particularly suitable for those pursuing careers in engineering, economics, physical sciences, and data analysis, where calculus plays a critical role in problem-solving and decision-making.

Eligibility Requirements

This course is suitable for individuals with a basic understanding of algebra and mathematics. Familiarity with foundational mathematical concepts will be beneficial. No prior calculus experience is required, making it accessible to beginners and those looking to refresh their skills.

Entry Requirements

  • Age Requirement: Applicants must be aged 16 or above, allowing both young learners and adults to engage in this educational pursuit.
  • Academic Background: There are no specific educational prerequisites, opening the door to individuals from diverse academic histories.
  • Language Proficiency: A good command of the English language is essential for comprehension and engagement with the course materials.
  • Numeracy Skills: Basic numeracy skills are required to effectively understand and work with course-related information. 

Why Choose Us

  • Affordable, engaging & high-quality e-learning study materials;
  • Tutorial videos/materials from the industry-leading experts;
  • Study in a user-friendly, advanced online learning platform;
  • Efficient exam systems for the assessment and instant result;
  • The UK & internationally recognised accredited
  • Access to course content on mobile, tablet or desktop from anywhere, anytime;
  • The benefit of career advancement opportunities;
  • 24/7 student support via email.

Career Path

Mastering calculus opens doors to a wide range of career opportunities. Professionals in engineering, physics, economics, and data analysis rely on calculus to tackle complex problems and develop innovative solutions. This course equips you with the skills necessary for roles such as data analyst, financial analyst, engineer, and research scientist, where a strong mathematical foundation is essential for success.

Course Curriculum

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 00:20:00
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

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