Calculus for Engineers from Coursera

This course offers a streamlined approach to university-level calculus, tailored for engineers. 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

What's inside

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.

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Reviews precalculus, which ensures learners have a solid foundation before tackling more advanced calculus concepts, which is essential for engineering applications

Includes applications of calculus, such as finding extrema of functions and modeling physical phenomena, which are directly relevant to engineering problem-solving

Covers Taylor series, which are used in various engineering fields for approximating functions and solving differential equations

Features concise lecture videos and practice problems, which allows learners to efficiently grasp the material and apply it to practical scenarios

Explores differential equations related to growth, decay, and oscillation, which are fundamental concepts in many engineering disciplines

Published by The Hong Kong University of Science and Technology, which is recognized for its strong engineering programs and research

Reviews summary

Calculus fundamentals for engineers

According to learners, the Calculus for Engineers course offers a solid foundation in calculus, particularly valued by those in engineering fields. Many found the lecture videos clear and concise, praising the accompanying lecture notes as particularly useful resources. The inclusion of practice problems and quizzes after key topics was seen as effective for reinforcing learning. While generally well-received, some students mentioned that the pace can feel quick if calculus concepts are entirely new to them. Specific areas like Taylor series or certain integration methods were noted as challenging by a portion of reviewers. Although the applications modules are relevant, some wished for greater depth or broader coverage.

Useful applications are covered.

"The applications modules showed me how calculus is actually used in physics and engineering problems, which was very motivating."

"While the applications were relevant, I hoped for more detailed examples from different engineering fields than just the physics/optimization ones."

"The examples were good for illustrating how calculus is applied, but felt a bit brief and surface-level."

"Applying calculus to optimization problems and physical scenarios was interesting and useful."

Practice problems aid understanding.

"Having practice problems right after the lectures helped solidify the concepts immediately."

"The practice quizzes are great for checking if I really understood the material before moving on."

"The solutions provided in the notes were key to learning from my mistakes on the practice problems."

"I found the end-of-module quizzes a fair test of the topics covered and good for self-assessment."

Explanations are clear and concise.

"The lecture videos were exceptionally clear and easy to follow, making complex topics understandable."

"The PDF lecture notes provided by the instructor are incredibly helpful; they summarize everything perfectly and are a great reference."

"I struggled with calculus before, but the way the concepts were explained here just clicked for me."

"The explanations for derivatives and integrals were very straightforward and well-presented."

Some specific topics are challenging.

"I had a lot of trouble with the infinite series module, especially Taylor series approximation and convergence."

"Integration techniques, particularly partial fractions and trigonometric substitution, required extra study outside the course material."

"Limits and continuity were harder than expected given the pace, needing careful review of the definitions."

"Understanding L'Hopital's rule and its applications took some effort."

Course moves quickly through topics.

"The course covers a lot of ground very quickly; definitely not for the faint of heart if you're a complete beginner with no prior math."

"Unless you have some prior math background, the speed might be challenging and require significant extra study time."

"It felt like we zipped through some topics I wish we had spent more time on for better mastery."

"Be prepared to pause lectures and review notes frequently because of the pace of the material presentation."

Activities

Be better prepared before your course. Deepen your understanding during and after it. Supplement your coursework and achieve mastery of the topics covered in Calculus for Engineers with these activities:

Review Precalculus Concepts

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Strengthen your understanding of precalculus topics like functions, trigonometry, and limits to build a solid foundation for calculus.

Browse courses on Precalculus

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Review function definitions and properties.
Practice solving trigonometric equations.
Work through limit problems.

Review: Single Variable Calculus

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Use this book to reinforce your understanding of single-variable calculus concepts.

View Single Variable Calculus: Early Transcendentals on Amazon

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Read chapters on limits, derivatives, and integrals.
Solve practice problems from the book.
Compare the book's explanations with the course lectures.

Review: Calculus: Early Transcendentals

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Supplement your learning with a comprehensive calculus textbook that provides detailed explanations and examples.

View Calculus on Amazon

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Read relevant chapters corresponding to the course modules.
Work through examples and exercises in the book.
Compare the book's approach to the course materials.

Four other activities

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Practice Differentiation Techniques

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Reinforce your understanding of differentiation rules by working through a variety of practice problems.

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Solve problems using the power rule, product rule, and quotient rule.
Differentiate trigonometric and exponential functions.
Apply the chain rule to complex functions.

Master Integration Techniques

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Improve your integration skills by practicing various integration techniques.

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Practice integration by substitution.
Solve problems using integration by parts.
Apply trigonometric substitution.
Integrate rational functions using partial fractions.

Create a Cheat Sheet for Integration Techniques

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Summarize key integration techniques and formulas in a concise cheat sheet for quick reference.

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Review integration techniques covered in the course.
Organize formulas and techniques logically.
Design a visually appealing and easy-to-use cheat sheet.

Project: Applying Calculus to Physics Problems

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Apply calculus concepts to solve real-world physics problems, such as projectile motion or optimization problems.

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Select a physics problem that can be solved using calculus.
Formulate the problem mathematically using calculus concepts.
Solve the problem and interpret the results.
Present your solution and findings in a report.

Career center

Learners who complete Calculus for Engineers will develop knowledge and skills that may be useful to these careers:

Mechanical Engineer

Mechanical engineers design, develop, build, and test mechanical and thermal devices. This Calculus for Engineers course helps you understand the mathematical principles crucial for designing and analyzing mechanical systems. The lectures on differentiation and integration provide the foundation for understanding dynamics, stress analysis, and fluid mechanics, all essential for the work of a mechanical engineer. The course's coverage of applications of calculus, including optimization problems and differential equations, provides a mechanical engineer with tools to solve real-world engineering challenges.

See salaries and explore the career path for Mechanical Engineer

Aerospace Engineer

Aerospace engineers design, test, and supervise the manufacturing of aircraft and spacecraft. This Calculus for Engineers course helps build the necessary mathematical expertise. The modules on differentiation, integration, and infinite series help tackle complex problems in aerodynamics and propulsion. The exploration of applications of calculus, such as determining optimal trajectories and analyzing the stability of flight, provides a solid foundation for aerospace engineers. This course is especially useful because it covers Taylor series and other advanced topics that are critical in aerospace engineering.

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Physicist

Physicists study the fundamental laws of nature and the behavior of matter and energy. This Calculus for Engineers course helps to develop skills vital for theoretical and applied physics. The modules on differentiation, integration, and differential equations provide the mathematical framework for understanding mechanics, electromagnetism, and quantum mechanics. The course's focus on Taylor series is invaluable. In particular, the course helps a physicist tackle problems related to growth, decay, and oscillation.

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Research Scientist

Research scientists design and conduct experiments, analyze data, and publish their findings to advance scientific knowledge. This Calculus for Engineers course can help enhance a scientist's mathematical skills. The course provides a solid foundation for understanding the mathematical principles behind various scientific models and simulations. The coverage of differentiation, integration, Taylor series, and applications of calculus provide valuable tools for a research scientist in fields such as physics, chemistry, and biology.

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Civil Engineer

Civil engineers design, construct, and maintain the built environment, including roads, bridges, canals, and buildings. This Calculus for Engineers course may be useful for structural analysis, fluid mechanics, and surveying. The course helps build a foundation for understanding the principles of structural mechanics and hydraulics. The applications of calculus covered in the course, such as optimization problems and the analysis of differential equations, provide valuable tools for a civil engineer in designs that maximize efficiency and safety.

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Electrical Engineer

Electrical engineers design, develop, test, and supervise the manufacturing of electrical equipment. The Calculus for Engineers course may be useful in understanding circuits, signal processing, and electromagnetism. The modules on differentiation, integration, and infinite series help build the necessary mathematical tools for analyzing complex electrical systems. The applications of calculus explored in the course, such as differential equations and Taylor series, provide electrical engineers with the methods needed to model and simulate electrical behavior.

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Operations Research Analyst

Operations research analysts use mathematical and analytical techniques to improve organizational efficiency and decision-making. This course may be useful for those in the field of operations research. The syllabus includes Taylor series and applications of calculus. Operations research analysts often use calculus to model and optimize complex systems, such as supply chains, logistics networks, and resource allocation problems. They can use calculus-based optimization to address real-world challenges.

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Actuary

Actuaries analyze risk and uncertainty, often in the context of insurance and finance. The Calculus for Engineers course may be beneficial due to its focus on mathematical modeling and problem solving. Actuaries use calculus to model and predict future events, assess financial risks, and develop pricing strategies for insurance products. The modules on integration and infinite series may be helpful for understanding statistical distributions and financial models. The treatment of compound interest could also prove invaluable for an actuary.

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Teacher

Teachers educate students in a variety of subjects. A calculus teacher imparts calculus concepts to their students. This Calculus for Engineers course may be helpful for understanding and reinforcing the fundamental concepts of calculus. The review of precalculus provides a solid base for teaching introductory calculus. The example problems and quizzes help the teacher anticipate where students will struggle. The lecturer's notes for the course may be helpful as well.

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Statistician

Statisticians collect, analyze, and interpret data. A statistician relies on calculus to understand underlying distributions. This Calculus for Engineers course reinforces the fundamental concepts of calculus needed for statistical analysis. The modules on integration and infinite series help build a foundation for understanding probability distributions and statistical inference. The knowledge gained can assist a statistician in modeling data and making informed decisions based on statistical evidence.

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Software Engineer

Software engineers design, develop, test, and maintain software applications and systems. This Calculus for Engineers course may be useful for understanding algorithms, optimization techniques, and numerical methods used in software development. The modules on differentiation, integration, and infinite series help build a foundation for understanding complex algorithms and data structures. The applications of calculus, such as finding roots of equations and solving differential equations, are relevant to various software engineering tasks. The coverage of limits and continuity is also valuable for a software engineer.

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Economist

Economists study the production, distribution, and consumption of goods and services. This Calculus for Engineers course may be useful in understanding economic models and optimization problems. The modules on differentiation, integration, and Taylor series help build a foundation for understanding concepts such as marginal analysis, consumer surplus, and economic growth. The applications of calculus, such as optimization problems and differential equations, are relevant to various economic analyses. The study of maxima and minima is valuable for an economist.

See salaries and explore the career path for Economist

Financial Analyst

Financial analysts evaluate investment opportunities, manage financial risk, and provide financial advice to businesses and individuals. This Calculus for Engineers course may provide a quantitative skill set that financial analysts can use to build financial models. This course may be helpful for understanding concepts such as optimization and differential equations, which are used in portfolio optimization and risk management. The module on applications of calculus may be particularly useful for a financial analyst, as it covers compound interest and other financial concepts.

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Data Scientist

Data scientists analyze large datasets to extract meaningful insights and help organizations make better decisions. This Calculus for Engineers course may be useful in understanding the mathematical concepts underlying machine learning algorithms and statistical models. The coverage of differentiation, integration, and Taylor series helps build a foundation for understanding optimization techniques and probability distributions. Those who wish to pursue data science may benefit from seeing how calculus is applied to numerical methods for finding roots of equations.

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Calculus for Engineers

What's inside

Syllabus

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Reviews summary

Calculus fundamentals for engineers

Activities

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