Applications of Differentiation - Calculus (Undergraduate Foundation)

Finding turning points is the core of this calculus course. You will locate stationary points where change stops and reverses. We cover identifying maxima and minima using direct mathematical tests. You will find points of inflection where a curve changes its bend. You will learn to sketch complex graphs by hand using these specific markers. Engineers and managers use these tools for optimisation and reducing waste. You can find the best size for a tank to use the least metal or the best speed to save petrol. In business, these methods help find the price that earns the most profit while keeping costs at the lowest level. Mastering these applications helps you solve real problems where you must find the best possible outcome for a physical system. By the end, you will find and name all stationary points on any graph. You will use derivative tests to prove if a point is a maximum, a minimum, or an inflection point. You will identify where a curve is concave or convex. You will sketch extreme curves showing all intercepts, turning points, and asymptotes clearly without needing a calculator. This course serves undergraduate foundation students and those entering engineering or management. It is for anyone needing to understand how different factors change together in science or business. Even those outside these fields gain the logic needed for technical problem-solving. These skills are essential for anyone who needs to study physical systems and find the most efficient ways to work.

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
3
2
This chapter focuses on the fundamental behaviour of functions and how they change over specific intervals. You will learn to identify where a curve is rising or falling and differentiate between local peaks and the overall highest points on a graph. These basics are the first step in describing the movement of physical and economic systems. You will learn to determine the intervals where a function is increasing or decreasing; understand the difference between global and local extrema; and use the sign of the first derivative to predict a function's direction.
Concept Overviews
3 Lessons
Problem Walkthroughs
2 Lessons
2. Tangents and Normals
3
3
This chapter applies the derivative to find the equations of lines that touch or cross curves at specific points. You will master the geometry of tangents and the perpendicular lines known as normals, which are essential for calculating paths and reflections in engineering. Understanding these linear approximations is a core requirement for advanced spatial modelling. You will learn to derive the equation of a tangent line at any given point; calculate the equation of a normal line using the negative reciprocal rule; and find the points where two different curves intersect.
Concept Overviews
3 Lessons
Problem Walkthroughs
3 Lessons
3. Stationary Points
3
4
Stationary points occur where the gradient of a curve is zero, marking peaks, troughs, or pauses. This chapter provides the mathematical tools to locate these points and determine their exact nature. These skills are mandatory for solving any optimisation problem. You will learn to locate coordinates where the derivative equals zero; use the second derivative test to identify maxima and minima; and find constants from given turning points.
Concept Overviews
3 Lessons
Problem Walkthroughs
4 Lessons
4. Curve Sketching
5
4
Accurate curve sketching involves identifying all critical features of a function without using a calculator. This chapter covers the location of inflection points and the determination of boundary lines called asymptotes. These markers define the global shape of any mathematical model. You will learn to locate inflection points and concavity changes; identify vertical, horizontal, and slant asymptotes; and combine these features into a single graph sketch.
Concept Overviews
5 Lessons
Problem Walkthroughs
4 Lessons
5. Optimisation
2
4
Optimisation is the practical art of finding the best possible solution within given constraints. This chapter applies differentiation to solve real-world problems involving maximum volume, minimum surface area, and lowest costs. These methods are critical for engineering design and economic efficiency. You will learn to construct mathematical models from word problems; find dimensions that maximise or minimise variables; and solve cost-based optimisation tasks.
Concept Overviews
2 Lessons
Problem Walkthroughs
4 Lessons
6. Rates of Change
3
5
Physical variables often change simultaneously in relation to time. This chapter uses the chain rule to link different rates and provides tools for estimating errors in measurement. These techniques are essential for modelling dynamic systems like flowing fluids or expanding structures. You will learn to apply the chain rule to related rates; calculate rates of change for linked variables; and estimate percentage errors using differentials.
Concept Overviews
3 Lessons
Problem Walkthroughs
5 Lessons
7. Conclusion
1
The conclusion provides a final review of differentiation as a tool for practical analysis. It ensures you can confidently apply optimisation and rates of change to any technical problem. This mastery is the final requirement for completing the foundation calculus sequence. You will review the strategy for identifying and classifying turning points; summarise the rules for curve sketching; and verify your understanding of related rates and error estimation.
Concept Overviews
1 Lesson