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Many students find themselves facing the daunting requirement of calculus as they pursue their academic goals. Fortunately, a variety of exceptional calculus courses offered by prestigious institutions such as MIT, Harvard, and the University of Sydney are available to help. After examining over 1,400 courses in the Class Central Calculus subject, I’ve compiled a list of the ten highest-rated options for those seeking a comprehensive educational experience.
Below are some of the standout selections:
Top Picks
Use the links provided to navigate directly to detailed course information.
What is Calculus?
Calculus is fundamentally the mathematical analysis of continuous change. Emerging in the 17th century through the work of Isaac Newton and Gottfried Wilhelm Leibniz, the discipline is divided into two primary segments: differential calculus, which examines instantaneous rates of change and curve slopes, and integral calculus, which looks at the accumulation of quantities and areas beneath curves.
This branch of mathematics relies on the convergence of infinite sequences and series to establish defined limits, offering vital tools for various fields, including statistics, science, machine learning, engineering, economics, and more. It provides mathematical frameworks for formulating and solving complex real-world problems.
Khan Academy emphasizes the necessity of a solid grasp of algebra, geometry, and trigonometry as foundational knowledge before tackling calculus.
Statistics
- 9 courses available for free or for auditing
- 1 course comes with a fee
- 6 courses offer completion certificates
- 93,000 learners have shown interest in the Calculus subject on Class Central
- Coursera features the most courses, with a total of 5 offerings
Introduction to Calculus
Designed for students gearing up for careers in science, engineering, or commerce or those wishing to rejuvenate their calculus knowledge, the Introduction to Calculus course requires no specific prerequisites. It offers a balanced approach to both theory and practical application, starting from precalculus fundamentals and advancing to integral calculus.
Topics covered include:
- Precalculus fundamentals, such as equation manipulation and understanding of elementary functions
- Tangents, limits, and the definition of derivatives
- Methods of differential calculus with real-world applications
- Fundamental Theorem of Calculus and techniques for calculating areas under curves
Instructor David Easdown praises the effectiveness of this course, which has achieved a 4.8/5.0 rating on Class Central.
Pre-University Calculus
Awarded the 2016 Open Education Award for Excellence, this course by Bart van den Dries is aimed at students ensuring a strong mathematical base before stepping into university-level calculus. It includes critical content that illustrates the practical applications of mathematical principles across various fields of study.
Key focus areas include:
- Functions, equations, differentiation, integration, and analytic geometry
- Practical application of mathematics in engineering and science
This course has attracted over 153,000 enrollments and maintains a rating of 4.4/5.0.
Single Variable Calculus
This course from the University of Pennsylvania, taught by Robert Ghrist, offers an introduction to single-variable calculus. It emphasizes a conceptual understanding suitable for students interested in fields like engineering and the sciences. A total commitment of 62 hours is expected to complete this extensive sequence.
The curriculum aims to equip students with:
- A comprehensive understanding of single-variable calculus concepts
- Knowledge of Taylor series, limits, and their applications
Multivariable Calculus
Offered by MIT, this course delves into functions of multiple independent variables, introducing advanced concepts necessary for studying higher-level mathematics. It focuses on practical applications in STEM disciplines and requires prior knowledge of single-variable calculus.
Topics include:
- Gradients and directional derivatives
- Complex multivariable functions
Vector Calculus for Engineers
This course provides an in-depth exploration of vectors, focusing on their applications in engineering. Jeffrey R. Chasnov offers practical and theoretical insight that prepares students for real-world challenges in areas such as Electromagnetism and Fluid Mechanics.
Mathematics for Machine Learning: Multivariate Calculus
Aimed at those pursuing machine learning, this course presents multivariate calculus through engaging exercises and coding practices, ensuring that students gain both theoretical knowledge and applicable skills in Python.
Precalculus: Relations and Functions
This introductory course is perfect for students in disciplines like natural science or computer science and covers essential mathematical concepts. By focusing on functions and their applications, it prepares learners for future studies in calculus and data analysis.
Ultimate Integral Starter
A targeted approach to integral calculus, this course emphasizes essential techniques for tackling integrals, enhancing students’ confidence and skills through practical examples.
Calculus Applied!
This course highlights the practical applications of calculus across various professions. By using real-world case studies, students will see how calculus informs decision-making in fields from healthcare to environmental sciences.
AP Calculus AB & BC: Help and Review
Designed for high school students preparing for AP exams, this course covers essential concepts effectively, providing a robust review aimed at enhancing students’ confidence before they take the exam.
Additional Resources
For those looking to strengthen their understanding of specific mathematical concepts necessary for mastering calculus, several supplementary resources and YouTube channels are available to augment learning.
Why Trust This Information
Class Central aggregates a vast collection of online courses and reviews, with over 100 million learners benefiting from its resources. The platform’s team brings firsthand experience, having completed a significant number of online courses across various disciplines.
Methodology for Selecting Courses
The picks for this guide were made using a systematic approach, focusing on course credibility, instructor expertise, student popularity, and comprehensive content review. This multifaceted strategy ensures a balanced selection that meets diverse educational needs in the field of calculus.
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