Calculus is a fundamental branch of mathematics that explores concepts like change and motion.
It forms the bedrock for numerous fields, including engineering, physics, economics, and computer science.
By understanding calculus, you’ll gain the ability to model real-world phenomena, solve complex problems, and develop a deeper understanding of how things work.
Whether you’re aiming to pursue a STEM career or simply want to expand your mathematical knowledge, mastering calculus opens doors to a world of possibilities.
However, navigating the vast landscape of online learning platforms to find the perfect calculus course can be overwhelming.
You’re searching for a course that not only provides a solid theoretical foundation but also equips you with the practical skills to apply calculus in real-world scenarios.
You want a course that’s engaging, taught by experienced instructors, and tailored to your learning style.
For the best calculus course overall on Udemy, we recommend Become a Calculus 1 Master.
This comprehensive course covers all the essential concepts of Calculus 1, from limits and derivatives to integrals and applications, providing a strong foundation for further mathematical studies.
With clear explanations, engaging examples, and plenty of practice problems, this course is an excellent choice for anyone looking to master the fundamentals of calculus.
While Become a Calculus 1 Master is our top pick, Udemy offers a wealth of other excellent calculus courses catering to various needs and learning styles.
Whether you’re a beginner just starting out or an advanced learner seeking to delve deeper into specific topics, there’s a course out there for you.
Keep reading to explore our curated list of recommendations and find the perfect calculus course to embark on your mathematical journey.
Become a Calculus 1 Master
This Calculus 1 course covers everything you need to master the basics and tackle more challenging problems.
You start with limits and continuity, learning about different types of limits like one-sided limits and limits at infinity.
You even learn how to prove a limit doesn’t exist!
You’ll dive into the concept of continuity, exploring different types such as point discontinuities, jump discontinuities, and infinite discontinuities.
Next, you’ll learn about derivatives.
You will explore the definition of a derivative and learn important rules like the power rule, product rule, quotient rule, and chain rule.
You practice these rules on trigonometric functions, exponential functions, and even logarithmic functions.
The course goes deeper into inverse trigonometric derivatives, hyperbolic derivatives, and something called logarithmic differentiation.
You then discover how to apply derivatives to solve real-world problems.
You learn about tangent lines, normal lines, and how to find the value that makes two tangent lines parallel.
The course also covers implicit differentiation, where you find derivatives of equations that aren’t easily solved for one variable.
You’ll even learn about higher-order derivatives, which are derivatives of derivatives.
You also explore optimization and sketching graphs, using your knowledge of critical points, inflection points, and the first and second derivative tests.
You also explore linear approximation, which helps you estimate values of functions, and related rates, which involve finding how quantities change with respect to each other.
The course also covers derivative theorems like the Mean Value Theorem, Rolle’s Theorem, and L’Hospital’s Rule, which you’ll use to solve even more complex problems.
You finish the course by applying calculus to physics and economics, learning about concepts like position, velocity, and acceleration, and even how to model exponential growth and decay.
Become a Calculus 2 Master
In this course, you will embark on an exploration of integral calculus, starting with the fundamentals of antiderivatives and indefinite integrals.
You will learn about Riemann sums and other numerical methods like the Trapezoidal and Simpson’s rules to approximate definite integrals and understand how to find the area under a curve.
The course delves into the profound Fundamental Theorem of Calculus, which bridges the concepts of differentiation and integration, and equips you with techniques like u-substitution and integration by parts to tackle a wide range of integration problems.
You will then explore various integration techniques, including trigonometric substitution, partial fractions, and reduction formulas.
You will gain a comprehensive understanding of improper integrals, which involve infinite limits or discontinuities.
The course then shifts its focus to the fascinating world of sequences and series.
You will learn about geometric and telescoping series and master various convergence tests to determine if an infinite series converges or diverges.
You will explore the power of power series, Taylor series, and Maclaurin series, which enable you to represent functions as infinite sums.
The course also illustrates the real-world significance of calculus by demonstrating its applications in physics, economics, and biology.
For instance, you will learn to calculate work, determine the center of mass, analyze growth models, and solve other practical problems.
Finally, you will explore the realm of parametric and polar curves.
You will learn to work with these curves, including finding tangent lines, calculating areas, and understanding their calculus.
The course culminates with a comprehensive final exam, allowing you to test your understanding of all the topics covered.
Become a Calculus 3 Master
This Calculus 3 course thoroughly explains multivariable calculus.
You’ll begin with the foundations of three-dimensional coordinate systems, learning to plot points and calculate distances in 3D space.
Building upon this, you’ll learn about equations of spheres and how to describe regions in space using inequalities.
The course then introduces the concept of level curves, helping you visualize multivariable functions.
You’ll then dive into the world of lines and planes, discovering how to represent them using vector, parametric, and symmetric equations.
You’ll develop the ability to analyze their relationships, determining if they are parallel, intersecting, or skew.
The course equips you with the tools to find the equations of planes, points of intersection, and angles between these geometric objects.
Next, you will learn about cylinders and quadric surfaces and how to visualize them in three dimensions.
Then you’ll develop a strong understanding of limits and continuity for multivariable functions.
You’ll learn how to find partial derivatives, which are crucial for understanding rates of change in multiple dimensions.
You’ll master techniques like the chain rule and implicit differentiation, essential for tackling complex multivariable function problems.
This course will teach you how to find the directional derivative, which helps determine the rate of change of a function in any given direction.
You’ll then explore optimization, a cornerstone of calculus.
You’ll learn how to find critical points, use the second derivative test, and distinguish between local and global extrema.
You will be able to solve real-world optimization problems using powerful techniques like Lagrange multipliers.
The journey continues with multiple integrals, where you’ll learn to calculate areas and volumes in higher dimensions.
The course guides you through different coordinate systems, including polar, cylindrical, and spherical coordinates, providing you with a versatile toolkit for solving a wide array of integration problems.
Lastly, you’ll explore the fascinating world of vectors.
You’ll learn about dot and cross products, discover how to represent curves and surfaces using vector functions, and gain a deep understanding of concepts like arc length, curvature, and velocity/acceleration in three dimensions.
The course concludes with an exploration of Green’s Theorem, Stokes’ Theorem, and the Divergence Theorem, which provide powerful connections between different calculus concepts.
Calculus 1 with the Math Sorcerer
The “Calculus 1 with the Math Sorcerer” course guides you through the essential concepts of calculus, starting with the foundation of limits.
You will learn to compute limits from graphs and apply techniques to calculate limits of various functions, including rational functions, absolute value functions, and piecewise functions.
The course delves into the squeeze theorem and how to prove limits using the delta-epsilon definition.
You then transition to continuous functions, discovering how to determine if a function is continuous at a point or on an interval.
You will also learn to identify different types of discontinuities and understand the Intermediate Value Theorem.
The course then tackles infinite limits and vertical asymptotes before diving into derivatives.
You will explore various differentiation formulas, including the product rule, quotient rule, and chain rule, and practice finding higher-order derivatives.
The course extends beyond the basics, exploring implicit differentiation, related rates, and optimization.
You gain experience with integrals, beginning with Riemann sums and progressing to the Fundamental Theorem of Calculus.
You will even explore Simpson’s rule for approximating definite integrals.
The course concludes by equipping you with the skills to find derivatives and integrals involving logarithmic and exponential functions, including those with bases other than e.
INTUITION MATTERS! Applied Calculus in Engineering: Complete
This course takes you step-by-step through calculus, focusing on how it’s used in engineering.
You’ll begin with a review of functions, tackling straight lines, parabolas, and even cubic functions.
The course then throws you into the world of trigonometric functions, where you’ll learn how sine, cosine, and tangent functions are used in real-life scenarios, like mapping out the flight path of an airplane.
Next, you’ll dive into multidimensional functions and see how they’re used in real-world problems.
For example, you’ll discover how a 3-variable function can model a simple airplane.
You’ll also explore limits and derivatives using examples like a falling sphere.
The course teaches you how to use the chain rule, how to work with derivatives of trigonometric functions, and even how to figure out the least amount of material needed to make a can – a practical application of minimizing materials.
Vectors are up next.
You’ll learn about vectors in two and multiple dimensions, including vector magnitudes, components, and operations like dot and cross products.
A water tank example, complete with a Python simulation, shows how these concepts work together.
You’ll also learn how to differentiate vectors and understand the connection between distance, position, displacement, velocity, and acceleration.
Finally, the course wraps up with an introduction to differential equations and how they’re used in control engineering.
You’ll learn about the different types of differential equations, how to represent waves, and how to use a PID controller to control systems.
The course even provides Python code examples so you can experiment with simulations and exercises, putting your newfound knowledge into practice.
You’ll learn how to install and use Python on Windows, macOS, and Linux, giving you a well-rounded understanding of how calculus is used in real-world engineering.
Math 0-1: Calculus for Data Science & Machine Learning
This course guides you through calculus, focusing on how it’s used in data science and machine learning.
You begin with the basics of functions and limits, crucial for understanding how functions behave.
You then explore derivatives, learning different rules to calculate them and solve real-world problems, like finding rates of change.
You also learn about optimization, using calculus to find minimums and maximums of functions.
Next, you delve into integration, the inverse of differentiation.
You discover the fundamental theorem of calculus and learn to calculate definite and indefinite integrals.
You even use Python libraries like Scipy and Numpy for numerical integration.
The course then introduces vector calculus, extending calculus to multiple dimensions.
You learn about partial derivatives, gradients, and the Jacobian, using these concepts to optimize functions of multiple variables.
Throughout the course, you use Python libraries like TensorFlow and Theano, essential for machine learning.
The syllabus helps you set up your Python environment and offers practical tips, including how to leverage YouTube for learning calculus.
You even tackle exercises like calculating Gaussian variance and entropy, solidifying your understanding.
Calculus 2 with the Math Sorcerer
“Calculus 2 with the Math Sorcerer” takes you on a deep dive into advanced calculus concepts, equipping you with the tools for higher-level math.
You begin by mastering inverse trigonometric functions, learning to calculate their derivatives and apply them to find tangent lines.
You then explore integration techniques, tackling intricate problems using methods like integration by parts and tabular integration.
The course introduces you to the unique properties of hyperbolic functions.
You will discover how to differentiate and integrate them, and then apply these skills to real-world scenarios like calculating the area between curves.
You’ll also delve into techniques for calculating volume using the disk/washer and shell methods, essential for understanding solids of revolution.
You then shift gears to explore the fascinating world of infinite series.
You learn to determine if a series converges or diverges using tests like the ratio test and comparison test.
The course culminates with Taylor and Maclaurin series, powerful tools for approximating functions, providing a strong foundation for future mathematical endeavors.
Calculus 3 (multivariable calculus), part 1 of 2
This Calculus 3 course begins with the fundamentals of vectors and their various products, including the dot product, cross product, and scalar triple product.
You will discover how these tools can be used to describe real-world scenarios, particularly in the realm of physics.
You will then delve into conic sections, exploring circles, ellipses, parabolas, and hyperbolas, and learn how to represent them mathematically.
Building upon this, you will explore quadric surfaces, which are three-dimensional shapes like spheres, cylinders, cones, ellipsoids, and paraboloids.
The course then ventures into the concept of topology, teaching you about different types of sets and how to identify them in multidimensional spaces.
You will learn about different coordinate systems, such as polar, cylindrical, and spherical coordinates, and discover how to choose the most suitable system for different problems.
The course then shifts its focus to vector-valued functions.
You will learn about parametric curves, how to analyze their properties like smoothness and continuity, and calculate their derivatives.
The concept of arc length will be introduced, and you will learn how to calculate it and re-parametrize curves in terms of arc length.
You will then explore real-valued functions of multiple variables, learning about their domains, graphs, level curves, limits, continuity, and partial derivatives.
The course also introduces essential tools like the chain rule, linear approximation, and directional derivatives, highlighting their applications in solving real-world problems.
You will understand how to find the direction of maximum change of a function and use gradients to find tangent planes and normal lines.
Finally, the course delves into optimization in multivariable calculus.
You will explore how to find the extreme values of functions using methods like critical points and Lagrange multipliers, equipping you with practical tools to solve optimization problems involving constraints.
Advanced Calculus/Real Analysis with the Math Sorcerer
This course equips you with the fundamental tools of advanced calculus, starting with sets and notations.
You then explore essential inequalities like the Triangle Inequality and Bernoulli’s Inequality, learning to construct rigorous proofs that underpin the rest of the course.
The Archimedean Principle is introduced, laying the groundwork for understanding limits and sequences.
You delve into the behavior of sequences, mastering techniques to determine convergence or divergence.
You utilize tools like the Squeeze Theorem and explore the intricacies of Cauchy Sequences.
The course then guides you through the rigorous world of delta-epsilon proofs, enabling you to define and prove limits for various functions, including trigonometric and polynomial functions.
Building upon this, you investigate the concept of continuity and its connection to differentiability.
You learn to discern whether a function is differentiable, exploring examples of both differentiable and non-differentiable functions.
The intriguing realm of infinite series is demystified, with explorations of Zeno’s Paradox and Dirichlet’s Test for convergence.
Finally, the course introduces multivariable limits and delves into the nuanced concepts of pointwise and uniform convergence.
You learn to differentiate between these convergence types, solidifying your understanding through examples and proofs.
The curriculum culminates in a deep understanding of core calculus concepts, empowering you to tackle complex mathematical problems across various fields like physics, engineering, and computer science.
Calculus - Math for AI Data Science & Machine Learning
This calculus course equips you with a strong understanding of calculus and its applications in AI, data science, and machine learning.
You will begin with the fundamentals of calculus, mastering derivatives through methods like the delta method, product rule, and chain rule.
You will then delve into multi-variate calculus, learning to differentiate functions with multiple variables and understand concepts like Jacobians and Hessians.
This section prepares you to work with multi-dimensional datasets, crucial for machine learning projects.
The course then transitions into the exciting realm of neural networks, where you uncover the role of calculus in building and optimizing these powerful models.
You will learn about bias in neural networks, how to update parameters using techniques like gradient descent, and explore the Newton Raphson method.
This knowledge forms the bedrock for understanding how calculus powers AI.
You will then shift from theory to practice, using Python libraries like TensorFlow and Keras to build and train machine learning models.
Hands-on exercises and projects solidify your skills.
You will dive into linear regression, deep learning, and multi-class classification, gaining practical experience in these critical areas.
This course provides a comprehensive understanding of how to apply calculus to real-world problems, preparing you for a future in AI, data science, and machine learning.
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