Differentiation and Integration of Vector-Valued Functions - Vectors (Undergraduate Foundation)

This course provides a foundational introduction to vector calculus, focusing on vector-valued functions of a single variable. You will master the rules for differentiating and integrating vectors, and learn how these operations relate to the geometry of parametric curves. The curriculum is built to give you a solid understanding of the mathematical tools that describe change in multiple dimensions. How do we precisely describe the motion of a satellite or a particle moving along a curved path? This course answers that question by bridging the gap between abstract calculus and the real-world physics of motion. You'll learn how the elegant tools of vector differentiation and integration allow us to model velocity, acceleration, and trajectories, providing the essential language for kinematics. This course is the essential next step for students who have a firm grasp of vector algebra and products. It is specifically designed for first-year university students in STEM fields who need to understand the calculus of vectors before tackling more advanced courses. This programme provides the critical foundation for future studies in vector mechanics, differential geometry, and the calculus of vector fields.

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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.
[OAU, Ife] MTH 104: Vectors
[OAU, Ife] MTH 104: Vectors
This comprehensive learning track guides you through the complete world of vector analysis. We begin with the fundamentals of vector algebra and its application to foundational geometry. You will then master scalar, vector, and triple products before using them to construct the vector equations of lines, planes, and conics. The journey culminates in advanced topics, including vector calculus, its applications in classical mechanics, and an introduction to differential geometry. Vectors are the essential language used to describe our physical world, making their mastery non-negotiable for any serious student of science or engineering. This track is designed to build your intuition for spatial reasoning and equip you with a powerful problem-solving toolkit. You will see direct applications in mechanics, analyzing forces and motion; in geometry, calculating angles and distances; and in calculus, modeling dynamic change over time. While this track is tailored to the first-year university curriculum for MTH 104 at Obafemi Awolowo University, Ile-Ife, Nigeria, it is an invaluable resource for a wide range of learners. It is ideal for any undergraduate student in mathematics, physics, engineering, or computer science seeking a comprehensive understanding of vector analysis. Furthermore, it serves as an excellent and thorough refresher for professionals who wish to solidify their foundational knowledge of this critical subject.

This comprehensive learning track guides you through the complete world of vector analysis. We begin with the fundamentals of vector algebra and its application to foundational geometry. You will then master scalar, vector, and triple products before using them to construct the vector equations of lines, planes, and conics. The journey culminates in advanced topics, including vector calculus, its applications in classical mechanics, and an introduction to differential geometry. Vectors are the essential language used to describe our physical world, making their mastery non-negotiable for any serious student of science or engineering. This track is designed to build your intuition for spatial reasoning and equip you with a powerful problem-solving toolkit. You will see direct applications in mechanics, analyzing forces and motion; in geometry, calculating angles and distances; and in calculus, modeling dynamic change over time. While this track is tailored to the first-year university curriculum for MTH 104 at Obafemi Awolowo University, Ile-Ife, Nigeria, it is an invaluable resource for a wide range of learners. It is ideal for any undergraduate student in mathematics, physics, engineering, or computer science seeking a comprehensive understanding of vector analysis. Furthermore, it serves as an excellent and thorough refresher for professionals who wish to solidify their foundational knowledge of this critical subject.

[FUTA, Akure] MTS 104: Introductory Applied Mathematics
[FUTA, Akure] MTS 104: Introductory Applied Mathematics
This learning track is designed for first-year students at the Federal University of technology, Akure (FUTA) and aligns with the second-semester coverage of introductory applied mathematics. It opens with vectors—what they are, how they work, and where they show up in real-world problems. From there, you’ll explore the geometry of circles and conic sections, gradually building up to the core ideas in basic dynamics. The lessons are short, clear, and practical—just the way we like it on UniDrills. Everything’s broken down to help you build strong intuition and problem-solving skills, especially if this is your first time engaging with applied math in this form. If you're not a FUTA student, no worries. The structure and explanations are broadly relevant, and the track works just as well for anyone looking to master these foundational topics in science and engineering.

This learning track is designed for first-year students at the Federal University of technology, Akure (FUTA) and aligns with the second-semester coverage of introductory applied mathematics. It opens with vectors—what they are, how they work, and where they show up in real-world problems. From there, you’ll explore the geometry of circles and conic sections, gradually building up to the core ideas in basic dynamics. The lessons are short, clear, and practical—just the way we like it on UniDrills. Everything’s broken down to help you build strong intuition and problem-solving skills, especially if this is your first time engaging with applied math in this form. If you're not a FUTA student, no worries. The structure and explanations are broadly relevant, and the track works just as well for anyone looking to master these foundational topics in science and engineering.

Course Chapters

1
Introduction

Welcome to the course and course outline.

Chapter lessons

1.Welcome

Welcome to the course and course outline.

2
Differentiation of Vectors

Differentiation of vector-valued functions; rules of vector differentiation; derivatives of vector products; some applications of vector differentiation.

Chapter lessons

1.The derivative

Formal definitions of differentiability and the derivative of a vector-valued function.

2.Rules

Rules of differentiation for vector-valued functions.

3.Triple products

Differentiating the scalar and vector triple products of vector-valued functions.

4.Worked examples (1)

Worked examples on the derivatives of vector-valued functions.

5.Worked examples (2)

More worked examples on the derivatives of vector-valued functions.

6.Worked examples (3)

More worked examples on the derivatives of vector-valued functions.

3
Integration of Vectors

Integration of vector-valued functions; definite, indefinite and line integrals of vector-valued functions; some applications of integration of vector-valued functions.

Chapter lessons

1.The anti-derivative

How to integrate a vector-valued function.

2.Line integral

Meaning of line integral and its relation to work done by a given force.

3.Position, velocity and acceleration

Linear and angular positions, velocity and acceleration of a body, and their calculus relations.

4.Worked examples (1)

Worked examples on the anti-derivatives of vector-valued functions and their mechanical applications.

5.Worked examples (2)

More worked examples on the anti-derivatives of vector-valued functions and their mechanical applications.

6.Worked examples (3)

More worked examples on the anti-derivatives of vector-valued functions and their mechanical applications.