Fundamentals and Techniques of Differentiation - Calculus (Undergraduate Foundation)

Calculus measures change. This course teaches you to calculate the exact rate at which variables move. You will start with the fundamental definition of the derivative through first principles to understand the underlying logic. You will then master the primary shortcuts for finding gradients, including the power, product, quotient, and chain rules. These techniques transform complex curves into manageable equations, enabling you to analyse movement and growth with mathematical precision. Structural engineering, physics, and electronics depend on these principles. Engineers use differentiation to determine the maximum strength of a beam or the minimum fuel required for a trip. In physics, it defines the relationship between position, speed, and acceleration. Software developers and economists use these tools to model real-world systems. This knowledge moves you beyond basic arithmetic into the logic used to improve efficiency and reduce waste in any technical field. By the end of this module, you will calculate derivatives for any standard algebraic function. You will know how to use first principles to prove results and apply specific rules for complex problems involving multiple variables. You will master the chain rule for functions within functions and gain the ability to find turning points on any graph. These skills are the first step in solving optimisation problems across all branches of science and industry. The course is for first-year university students in engineering, science, and mathematics. It is also suitable for secondary school leavers preparing for university work or technical entrance exams. Programmers and data analysts will find the logic helpful for understanding how algorithms handle shifting data. The lessons provide the essential mathematical grounding needed for any career in technology or the physical sciences.

Enrolment valid for 12 months
This course is also part of the following learning tracks. You may join a track to gain comprehensive knowledge across related courses.
AMS 102: Basic Mathematics
AMS 102: Basic Mathematics
Management and administration require precise numerical logic for decision-making. This track follows the official NUC CCMAS syllabus for AMS 102, covering real numbers, set theory, and complex systems. You will master algebraic operations, permutations, and combinations alongside the foundations of trigonometry and calculus. It provides the mathematical tools to model financial trends, handle business data, and solve optimisation problems in corporate settings. This programme is built for first-year university students in Accounting, Business Administration, Banking, Finance, and Public Administration. It also serves secondary school leavers preparing for management degrees and professionals needing a refresher on business mathematics. It is suitable for anyone moving into roles that demand accurate quantitative analysis and logical deduction. You will gain the ability to simplify complex business formulas, calculate probabilities for risk assessment, and find the exact points where profits are highest. You will be able to handle sequences for interest calculations and use differentiation to manage production costs. Completing this track ensures success in university examinations and builds the analytical strength required for careers in financial analysis, auditing, and strategic management.

Management and administration require precise numerical logic for decision-making. This track follows the official NUC CCMAS syllabus for AMS 102, covering real numbers, set theory, and complex systems. You will master algebraic operations, permutations, and combinations alongside the foundations of trigonometry and calculus. It provides the mathematical tools to model financial trends, handle business data, and solve optimisation problems in corporate settings. This programme is built for first-year university students in Accounting, Business Administration, Banking, Finance, and Public Administration. It also serves secondary school leavers preparing for management degrees and professionals needing a refresher on business mathematics. It is suitable for anyone moving into roles that demand accurate quantitative analysis and logical deduction. You will gain the ability to simplify complex business formulas, calculate probabilities for risk assessment, and find the exact points where profits are highest. You will be able to handle sequences for interest calculations and use differentiation to manage production costs. Completing this track ensures success in university examinations and builds the analytical strength required for careers in financial analysis, auditing, and strategic management.

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MTH 102: Elementary Mathematics II - Calculus
MTH 102: Elementary Mathematics II - Calculus
Calculus is the mathematical tool for measuring change and finding the best results in any system. This track follows the official NUC CCMAS MTH 102 curriculum to teach you how functions behave, how to calculate exact rates of change, and how to sum up tiny movements to find total areas or volumes. You will move from basic limits to complex integration techniques used to solve practical problems in the physical world. This track is for first-year university students in engineering, science, and economics departments across Nigeria. It also serves secondary school leavers preparing for technical degrees or university entrance exams. Anyone needing to build a strong foundation in mathematical logic for data analysis or professional licensing will find these lessons essential. After finishing this programme, you will calculate derivatives using first principles and shortcuts, find turning points for optimisation, and solve definite integrals for land measurement or tank design. You will use the trapezium and Simpson's rules to handle experimental data accurately. These skills ensure you pass your university exams and excel in technical careers like civil engineering, physics research, or financial forecasting.

Calculus is the mathematical tool for measuring change and finding the best results in any system. This track follows the official NUC CCMAS MTH 102 curriculum to teach you how functions behave, how to calculate exact rates of change, and how to sum up tiny movements to find total areas or volumes. You will move from basic limits to complex integration techniques used to solve practical problems in the physical world. This track is for first-year university students in engineering, science, and economics departments across Nigeria. It also serves secondary school leavers preparing for technical degrees or university entrance exams. Anyone needing to build a strong foundation in mathematical logic for data analysis or professional licensing will find these lessons essential. After finishing this programme, you will calculate derivatives using first principles and shortcuts, find turning points for optimisation, and solve definite integrals for land measurement or tank design. You will use the trapezium and Simpson's rules to handle experimental data accurately. These skills ensure you pass your university exams and excel in technical careers like civil engineering, physics research, or financial forecasting.

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Course Chapters

1. Introduction
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3
Differentiation measures how fast things change. This chapter introduces the gradient concept using first principles, proving the rules used in engineering and science. Mastering these proofs ensures you understand the limit logic behind every shortcut. You will understand average versus instantaneous rates; use the limit definition to find gradients; and prove the basic power rule formula.
Concept Overviews
4 Lessons
Problem Walkthroughs
3 Lessons
2. Fundamental Rules
3
3
Fundamental rules simplify differentiation for algebraic expressions. This chapter teaches you to handle powers, constants, and sums without repeating the long first principles method. These rules are the foundation for every derivative calculation. Master the general power rule; apply the constant multiple rule; and differentiate polynomials by treating each term separately.
Concept Overviews
3 Lessons
Problem Walkthroughs
3 Lessons
3. Product and Quotient
2
3
Many functions involve variables multiplied or divided together. This chapter provides specific rules for differentiating products and rational functions, which are vital for modelling physical systems. Apply the product rule correctly; use the quotient rule for fractions; and simplify resulting expressions for further use.
Concept Overviews
2 Lessons
Problem Walkthroughs
3 Lessons
4. Chain Rule
4
3
The chain rule allows you to differentiate functions nested inside other functions. You will apply this to composite expressions, including exponential and logarithmic functions found in natural growth models. Master the function of function technique; differentiate powers of complex expressions; and solve derivatives for base-e logarithms and exponentials.
Concept Overviews
4 Lessons
Problem Walkthroughs
3 Lessons
5. Trigonometric Functions
3
3
Trigonometric functions describe cycles and waves in electronics and mechanics. This chapter provides the derivatives for sine, cosine, and tangent, including their inverse forms used in angular measurements. Calculate derivatives for all primary trigonometric functions; handle composite trigonometric expressions; and differentiate inverse trigonometric functions correctly.
Concept Overviews
3 Lessons
Problem Walkthroughs
3 Lessons
6. Advanced Techniques
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5
Some relationships cannot be easily solved for one variable or use changing parameters. This chapter covers advanced techniques like implicit, parametric, and logarithmic differentiation for complex engineering curves. Differentiate equations where variables are mixed; find gradients for parametric equations; and solve variable-power functions using logs.
Concept Overviews
3 Lessons
Problem Walkthroughs
5 Lessons
7. Higher Order Derivatives
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3
Higher order derivatives measure the rate of change of the gradient itself. This successive differentiation is required to study acceleration in physics and find peaks or troughs on a graph. Find second and third derivatives; perform successive differentiation on standard functions; and master the notation for higher order results.
Concept Overviews
2 Lessons
Problem Walkthroughs
3 Lessons
8. Conclusion
1
The summary consolidates your knowledge of differentiation techniques. It ensures you have the technical foundation needed for the upcoming applications course. Review the hierarchy of differentiation rules; identify the best technique for any given function; and confirm mastery of successive differentiation.
Concept Overviews
1 Lesson