Single-Variable Functions and Their Graphs

This course introduces the basic concept of a function of a single real variable. It explores how such functions are represented algebraically and graphically, emphasizing interpretation and behavior on the real number line. You’ll learn to identify domain, range, and key features of graphs such as intercepts, symmetry, and asymptotic behavior. The goal is to build a solid understanding of how functions behave visually and analytically. This course sets the foundation for everything else in calculus. It is designed to be intuitive, but also precise in its treatment of core ideas.

7 hrs

$ 7.15

Payment required for enrolment
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.
[FUTA, Akure] MTS 102: Introductory Mathematics II
[FUTA, Akure] MTS 102: Introductory Mathematics II
This learning track is structured for first-year students at the Federal University of Technology, Akure (FUTA) and mirrors the standard second-semester coverage of elementary calculus. It begins with single-variable functions and their graphs, then walks learners through limits, continuity, differentiation techniques, and curve sketching—just as covered in the official MTS 102 outline. You’ll also explore anti-derivatives and integration, learning both the techniques and how to apply them to solve practical problems in science and engineering contexts. Everything is broken down into short, focused video lessons that keep things clear and manageable, especially for students who might be engaging this content for the first time. If you're not a FUTA student but need to build a solid foundation in these same topics, this track can serve you just as well. The structure and explanations are universal, ensuring that learners with similar academic goals can benefit fully.

This learning track is structured for first-year students at the Federal University of Technology, Akure (FUTA) and mirrors the standard second-semester coverage of elementary calculus. It begins with single-variable functions and their graphs, then walks learners through limits, continuity, differentiation techniques, and curve sketching—just as covered in the official MTS 102 outline. You’ll also explore anti-derivatives and integration, learning both the techniques and how to apply them to solve practical problems in science and engineering contexts. Everything is broken down into short, focused video lessons that keep things clear and manageable, especially for students who might be engaging this content for the first time. If you're not a FUTA student but need to build a solid foundation in these same topics, this track can serve you just as well. The structure and explanations are universal, ensuring that learners with similar academic goals can benefit fully.

[UNILAG, Akoka] MTH 102: Elementary Mathematics II
[UNILAG, Akoka] MTH 102: Elementary Mathematics II
This learning track is designed to guide first-year students at the University of Lagos through key concepts in calculus, beginning with the fundamentals of single-variable functions and their graphs. It builds gradually into the core topics of limits, continuity, and differentiability, with each course tailored to simplify these foundational ideas for early learners. The focus is not just on theory but also on building the skill to solve problems confidently, especially those typically encountered in university-level exams. You’ll move from understanding the concept of a limit to mastering how derivatives work and how to apply them to sketch curves and analyze function behavior. Although built for UNILAG students, this track is suitable for anyone looking to strengthen their understanding of introductory calculus at the university level. Whether you're preparing for school assessments or seeking a solid refresher, this track will help you follow a structured path.

This learning track is designed to guide first-year students at the University of Lagos through key concepts in calculus, beginning with the fundamentals of single-variable functions and their graphs. It builds gradually into the core topics of limits, continuity, and differentiability, with each course tailored to simplify these foundational ideas for early learners. The focus is not just on theory but also on building the skill to solve problems confidently, especially those typically encountered in university-level exams. You’ll move from understanding the concept of a limit to mastering how derivatives work and how to apply them to sketch curves and analyze function behavior. Although built for UNILAG students, this track is suitable for anyone looking to strengthen their understanding of introductory calculus at the university level. Whether you're preparing for school assessments or seeking a solid refresher, this track will help you follow a structured path.

[OAU, Ife] MTH 201: Mathematical Methods I
[OAU, Ife] MTH 201: Mathematical Methods I
Comprehensive treatise of advanced calculus covering limits, continuity and differentiability, infinite sequences and series, partial differentiation, numerical methods and ordinary differential equations. Curated for second-year students of engineering and physical sciences at Obafemi Awolowo University, Ile-Ife, Nigeria. Students and professionals with similar learning goal will also find this learning track useful.

Comprehensive treatise of advanced calculus covering limits, continuity and differentiability, infinite sequences and series, partial differentiation, numerical methods and ordinary differential equations. Curated for second-year students of engineering and physical sciences at Obafemi Awolowo University, Ile-Ife, Nigeria. Students and professionals with similar learning goal will also find this learning track useful.

Course Chapters

1
Introduction

What are real numbers, and how do they differ from natural numbers, integers, rational numbers, irrational numbers? Meaning of infinity; defining finite and infinite intervals.

Chapter lessons

1.Number systems18:36

An explanation of natural numbers, integers, rational numbers, irrational numbers, real numbers and complex numbers.

2.Rationals and irrationals26:08

A closer look at differences between rational and irrational numbers.

3.Intervals16:55

Meaning and examples of intervals on the real line.

4.Infinity14:44

Meaning and use of infinity.

2
Real-Valued Functions

Real-valued functions - meaning, domain, range and graphs.

Chapter lessons

1.Introduction24:36

Meaning of functions and real-valued functions.

2.Domain of functions31:32

Domain of functions and its calculation.

3.Range of functions6:17

Meaning of the range of functions.

4.Worked examples (1)24:55

More worked examples on the domain of real-valued functions.

3
Kinds of Real-Valued Functions

A look at different kinds of real-valued functions - composites, piecewise functions, polynomials, rational functions, algebraic functions, transcendental functions, odd and even functions.

Chapter lessons

1.Polynomials12:01

Meaning, domain and examples of polynomials.

2.Rational functions7:47

Meaning, domain and examples of rational functions.

3.Algebraic functions5:19

Meaning, domain and examples of algebraic functions.

4.Piecewise-defined functions16:00

Meaning, domain and examples of piecewise-defined functions.

5.Odd and even functions4:05

Meaning and examples of odd and even functions.

4
Transcendental Functions

Meaning, examples and properties of transcendental functions.

Chapter lessons

1.Meaning5:30

An introduction to transcendental functions.

2.Exponential and logarithmic functions17:17

Meaning, domain and examples of exponential and logarithmic functions.

3.Trigonometric functions21:24

Meaning, domain and examples of trigonometric functions.

4.Inverse trigonometric functions7:37

Meaning, domain and examples of inverse trigonometric functions.

5.Hyperbolic functions20:21

Meaning, domain and examples of hyperbolic functions.

6.Inverse hyperbolic functions19:37

Meaning, domain and examples of inverse hyperbolic functions.