About this Course

“Engineering Calculus and Differential Equations” offers a deep dive into fundamental concepts of single-variable calculus and ordinary differential equations, exploring their application across various engineering fields. This introductory course, offered by HKUx and available in English, equips students with the necessary tools to model and solve real-world engineering problems using calculus and differential equations, focusing on applications such utility in electrical, civil, and space flight engineering.

Course Description

This course introduces the language of calculus and differential equations used by engineers to determine currents, materials for constructions, and other engineering necessities. With a blend of theoretical concepts and practical applications, the course covers techniques such as Laplace transform and incorporates animations and interactive visualizations to help understand complex topics.

What Students Will Learn

• Core concepts of limits, continuity, and differentiation in calculus.
• How to apply derivatives and integrations in engineering contexts.
• Understanding and solving first and higher order differential equations.
• Utilization of Laplace transforms in solving engineering problems related to vibrations and signal processing.
• Modeling and solving real engineering problems using appropriate mathematical methodologies.

Pre-requisites or Skills Necessary

This is an introductory level course and does not require any prerequisites. However, a basic understanding of algebra and familiarity with mathematical concepts might be beneficial.

Course Coverage

• Introduction to single-variable calculus
• Ordinary differential equations
• Applications of calculus and differential equations in engineering
• Laplace transforms and their use in engineering scenarios
• Interactive visualizations to understand dynamic systems

Who this Course is For

This course is ideal for prospective engineers, current engineering students, or professionals in the field who seek to enhance their understanding and application of calculus and differential equations in their work.

Real-World Application

The skills acquired in this course can be directly applied in various domains of engineering such as designing electrical circuits, constructing infrastructure, and developing new technologies in aerospace. These skills help in not only understanding but also controlling the systems to achieve desired outcomes in practical engineering projects.

Course Syllabus

1. Limits, Continuity, and Differentiation in Engineering Calculus
2. Applications of Derivatives
3. Parametric Equations and Polar Coordinates
4. Techniques of Integration
5. Applications of Definite Integrals
6. Engineering Differential Equations and First Order Equations
7. Homogeneous, Inhomogeneous, and Exact Equations
8. Homogeneous Linear Equations with Constant Coefficients
9. Cauchy-Euler Equations and Laplace Transforms
10. Problem Solving in Engineering Contexts