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Updated in [October 18th, 2023]
What does this course tell?
(Please note that the following overview content is from the original platform)
Change is an essential part of our world and calculus helps us quantify it multivariable calculus continues the story of calculus Learn how tools like the derivative and integral generalize to functions depending on several independent variables and discover some of the exciting new realms in physics and pure mathematics they unlock
We considered the value of this course from many aspects, and finally summarized it for you from two aspects: skills and knowledge, and the people who benefit from it:
(Please note that our content is optimized through artificial intelligence tools and carefully reviewed by our editorial staff.)
What skills and knowledge will you acquire during this course?
During this course, students will acquire the following skills and knowledge in multivariable calculus:
1. Understanding of functions with several independent variables: Students will learn how to work with functions that depend on multiple independent variables, extending their understanding of calculus beyond single-variable functions.
2. Partial derivatives: Students will learn how to calculate partial derivatives, which measure the rate of change of a function with respect to each independent variable while holding the others constant. This skill is crucial in various fields, including physics, economics, and engineering.
3. Gradient vector: Students will learn about the gradient vector, which provides information about the direction and magnitude of the steepest ascent of a function. This concept is essential in optimization problems and vector calculus.
4. Multiple integrals: Students will learn how to evaluate multiple integrals, which involve integrating functions over regions in multiple dimensions. This skill is fundamental in calculating volumes, areas, and solving problems in physics and engineering.
5. Line integrals: Students will learn how to calculate line integrals, which involve integrating a function along a curve. This concept is crucial in physics, particularly in the study of vector fields and work done by forces.
6. Surface integrals: Students will learn how to evaluate surface integrals, which involve integrating a function over a surface. This skill is important in physics, especially in the study of flux and flow.
7. Vector calculus: Students will learn the fundamental concepts of vector calculus, including divergence, curl, and the theorems of Green, Stokes, and Gauss. These concepts are widely used in physics, engineering, and fluid dynamics.
8. Applications in physics and engineering: Students will explore various applications of multivariable calculus in physics and engineering, such as finding electric fields, calculating fluid flow, and solving optimization problems.
Overall, this course in multivariable calculus equips students with the necessary skills and knowledge to understand and solve problems involving functions with multiple independent variables, opening up new realms in physics and pure mathematics.
Who will benefit from this course?
Mathematics Enthusiasts: Those with a strong interest in mathematics who want to delve deeper into calculus and explore its applications in multi-dimensional spaces.
Physics and Engineering Students: Students pursuing degrees in physics and engineering will find this course essential as it provides the mathematical foundation for understanding complex physical phenomena.
Data Scientists and Analysts: Professionals in the field of data science and analytics who require a solid grasp of advanced mathematical concepts for data modeling and analysis.
Academics and Researchers: Academic researchers and scholars in the fields of mathematics and physics seeking to expand their knowledge in multivariable calculus and its applications.
Anyone Interested in Advanced Calculus: Individuals looking to challenge themselves with a more intricate understanding of calculus and its relevance in various scientific disciplines.
Course Syllabus
Limits with Many Variables: Uncover unexpected function properties with limits.
Searching Square Lake: Begin to uncover the mysteries of limits with the search for a mythical beast.Derivatives: Measuring rates of change is just the beginning...
Multivariable Limits: Connect limits with many variables to limits with just one.Optimization: Put derivatives to work finding and classifying extreme values.
Shock Waves and Discontinuities: Learn to visualize limits and apply them to the real world.Multiple Integrals: Become a master of multivariable integration.
Extreme Value Theorem (Part I): Get a bird's-eye view of a crucial calculus theorem.
