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The Hong Kong University of Science and Technology

Calculus for Engineers

The Hong Kong University of Science and Technology via Coursera

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Overview

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This course offers a streamlined approach to university-level calculus, tailored for engineers and scientists. We begin with a review of precalculus in the first module, followed by derivatives and integrals in the second and third modules. The fourth module introduces Taylor series, while the fifth and sixth modules cover important applications of calculus. The course features 59 concise lecture videos, each accompanied by practice problems. After each major topic, you will find a short practice quiz to reinforce your understanding. Solutions to problems and practice quizzes are included in the instructor-provided lecture notes. At the end of each module, there is an assessed quiz to evaluate your progress. Score over 80% on these quizzes to earn a course certificate. Download the lecture notes: https://www.math.hkust.edu.hk/~machas/calculus-for-engineers.pdf Watch the promotional video: https://youtu.be/mDuHJos21wo

Syllabus

  • Foundations
    • Functions lie at the foundations of calculus. First, we revisit the set of real numbers and then introduce complex numbers. We define functions and their inverses, as well as discuss the concepts of limits and continuity. Finally, we introduce the essential functions studied in calculus, including polynomial and rational functions, exponential functions, logarithmic functions, trigonometric functions, and inverse trigonometric functions.
  • Differentiation
    • In this module, we define the derivative and explore methods to differentiate various functions. We begin by learning the power rule to differentiate power functions, followed by learning the sum, product, quotient, and chain rules. We then learn how to differentiate exponential functions, natural logarithms, trigonometric functions, and finally, inverse trigonometric functions.
  • Integration
    • In this module, we define the integral and explore methods to integrate various functions. We begin by learning how the definite integral is used to calculate areas. We then find a connection between integration and differentiation by proving the first and second fundamental theorems of calculus. These theorems motivate us to define an indefinite integral as an anti-derivative. Throughout the module, we will examine various integration techniques, including integration by substitution, integration by parts, integration of trigonometric functions, trigonometric substitution, and integration by partial fractions.
  • Infinite Series
    • In this module, we explore sequences and series. We learn how an infinite power series can converge to a function. These convergent series are known as Taylor series, and we will determine the Taylor series for the most important functions of calculus, including the exponential function, sine and cosine functions, the natural logarithm, and the arctangent. We also learn L’Hospital’s rule, a very useful tool for finding indeterminate limits.
  • Applications I
    • In this module, we begin to apply the calculus. Using Taylor series, we define the complex exponential function and use it to prove key trigonometric identities. We employ calculus to derive the circumference and area of a circle, as well as the surface area and volume of a sphere. Finally, we show how calculus can be used in numerical methods to find the roots of equations and to integrate and differentiate functions.
  • Applications II
    • In this module, we continue exploring applications of calculus. We learn how to use derivatives to find local extrema of functions. We prove that among rectangles with a given perimeter, the one that maximizes the area is a square. We find the shortest path between two villages after collecting water from a river. We determine the optimal position on a beach for a lifeguard to enter the sea to rescue a swimmer in distress. We discuss how calculus is used in physics to define velocity and acceleration, and how to determine the position and velocity of an object falling under gravity. Lastly, we explore differential equations related to growth, decay, and oscillation, including equations for compound interest and the oscillating pendulum.

Taught by

Jeffrey R. Chasnov

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Reviews

4.7 rating, based on 7 Class Central reviews

4.9 rating at Coursera based on 27 ratings

Start your review of Calculus for Engineers

  • Anonymous
    very good course, teach me many useful knowledge, I appreciate this teacher, hope publish more course in the future
  • Anonymous
    Professor Chasnov is outstanding. This class was a great review of Calc I and Calc II. I wish I had Professor Chasnov when I was in school.
  • Anonymous
    I've taken all of Jeffrey Chesnov's courses on Coursera and a large part of my foundational Math skills are because of him. Excellent lectures and I really enjoy listening to his thick New York accent. His books are a great reference too. Despite being listed as beginner difficulty, another provider would probably rate it as intermediate or even advanced. Good companion course for Khan Academy BC I'd say.
  • Anonymous
    Through the 6 weeks that I have been doing this course, I learned everything I wanted to. The course format with readings assignments and quizes definitely helped a lot, to move by the different sections of the course. I was really satisfied by it and by the way the professor explain each topic.
  • Anonymous
    This course was an excellent review of college calculus. The professor explains the topic thoroughly and efficiently for an engineer. The practice problems and test aid in testing the knowledge gained from each lesson/section.
  • Anonymous
    The Coursera Calculus course offers clear explanations, practical examples, and well-structured lessons—great for mastering the fundamentals and beyond.

  • Anonymous
    Great course, learned a lot about calculus, this course was very intuitive and the tasks were real fun to do.
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