Calculus 3 (multivariable calculus), part 2 of 2

🎓 Course Title: Calculus 3 (Multivariable Calculus) - Part 2 of 2

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Overview of Calculus 3, Part 2

Towards and through the Vector Fields
📚 Based on chapters from Robert A. Adams & Christopher Essex' "Calculus: A Complete Course" (8th or 9th edition)

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Course Structure

Chapter 14: Multiple Integrals

• S1. Introduction to Multiple Integrals

  • Overview of the chapter and what to expect.

• S2. Repetition (Riemann integrals, sets in the plane, curves)

  • Solidifying foundational concepts before moving forward.

• S3. Double Integrals

  • Computing double integrals over APR using iteration.
  • Understanding x-simple and y-simple domains.
  • Iteration of double integrals through Fubini's theorem.

• S4. Change of Variables in Double Integrals

  • Learning to compute double integrals via polar coordinates and other substitutions.

• S5. Improper Integrals

  • Identifying convergence or divergence of improper integrals.
  • Using the mean-value theorem for double integrals to find mean values.

• S6. Triple Integrals

  • Introducing the concept of triple integration and its applications.

• S7. Change of Variables in Triple Integrals

  • Computing triple integrals using spherical or cylindrical coordinates.
  • Understanding the Jacobian for various change of variables.

• S8. Applications of Multiple Integrals

  • Applying multiple integrals to compute mass, surface area, and find the mass center.

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Chapter 15: Vector Fields

• S9. Vector Fields

  • Exploring vector fields in the plane and in space.

• S10. Conservative Vector Fields

  • Understanding conservative vector fields and their properties.
  • Learning to compute potential functions for conservative vector fields.

• S11. Line Integrals of Functions

  • Calculating line integrals for various applications such as mass, arc length, and work.

• S12. Line Integrals of Vector Fields

  • Mastering three methods to compute line integrals of vector fields.

• S13. Surfaces

  • Learning about surfaces in two and three dimensions.
  • Identifying closed surfaces, understanding their boundaries, and determining normal vectors.

• S14. Surface Integrals

  • Calculating surface integrals for applications like heat transfer.

• S15. Wrap-up Multivariable Calculus / Calculus 3, Part 2 of 2

  • Summarizing the key concepts learned in this course.

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Chapter 16: Vector Calculus and Advanced Topics

• S16. Gradient, Divergence, and Curl

  • Defining and computing gradient, divergence, and curl for vector fields.

• S17. Green's Theorem

  • Understanding Green's Theorem as a connection between line integrals and surface integrals.

• S18. Gauss's Theorem (Divergence Theorem)

  • Applying Gauss's Theorem to convert volume integrals into surface integrals.

• S19. Stokes' Theorem

  • Learning how Stokes' Theorem relates the contour integral of a closed loop to the flux through the bounded surface spanning that loop.

• S20. Extras

  • Exploring additional resources and potential future courses.

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Important Notes

• Professor's Guidance: Always check with your professor which parts of the course are relevant to your final exam, as requirements can vary.

• Comprehensive Material: A detailed outline of all videos and their titles, along with solved problems, is provided in the resource file "001 Outline_Calculus3_part2.pdf" (located under video 1, "Introduction to the course"). This material also covers topics in depth.

• Stay Updated: Keep an eye on our offerings for upcoming courses and hypothetical release dates.

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Dive into the fascinating world of multivariable calculus with this comprehensive course, where you'll master the intricacies of multiple integrals, vector fields, and their applications. Embark on this mathematical adventure today! 🧮🚀

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Overview of the Course:

Global course rating: 4.69

This online course on Multivariable Calculus and Vector Calculus has garnered a high level of satisfaction among its students, with recent reviews all rating it positively. The course is designed to be comprehensive, covering classical material that is fundamental to physics, engineering, and applied mathematics. It is technical in nature but is presented in a way that makes the complex content accessible and potentially enjoyable for learners.

Pros:

• Quality of Exposition: The course is praised for its high-quality explanations, with attention to detail that allows students to grasp difficult concepts.
• Comprehensive Material: It offers a thorough coverage of Calculus 3 topics, including classical material and advanced concepts.
• Clear and Detailed Examples: Students appreciate the abundance of clear examples and step-by-step solutions provided in the course.
• Effective Learning Tools: The course is structured topic-wise with a good balance of theory and practice, making online learning efficient.
• Technical Proficiency: The course lays out technical concepts clearly and systematically, with illustrative examples that enhance understanding.
• Rich Content Selection: Hania Uscka-Wehlou has been recognized for the careful selection of content, which is both rich and relevant to the subject matter.
• Excellent Production Quality: The course boasts high production values, including clear sound and recording quality.
• Engaging Teaching Style: The instructor's approach to teaching is engaging and comfortably matched to the content, making it a pleasure to learn.
• Visual Aids: The use of colorful illustrations and visualizations is noted as particularly helpful for conceptual understanding.
• Practical Application: The course not only covers theoretical aspects but also prepares students effectively for standard exams in the subject.
• Additional Resources: Extra notes on technical details are provided for advanced learners who require a deeper dive into the subject matter.
• Student Support: The instructor is praised for her clear explanations, patient manner, and responsiveness in discussion threads.
• Overall Thoroughness: The course is commended for its thorough coverage of the syllabus, with no areas left unaddressed.

Considerations:

• Technical Issues: A few users mentioned occasional lag in the course interface, which may affect the user experience.

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Course Highlights:

• Expert Instructor: Professor Hania Uscka-Wehlou demonstrates her expertise effectively throughout the course.
• Visual Learning: The course stands out for its exceptional use of visual aids to help students understand complex geometric concepts.
• Practical Exercises: Students are encouraged to engage with try-yourself examples, which helps solidify their understanding and overcome bad habits in derivation.
• Thorough Justification: Each step in computational processes is carefully justified, providing a strong foundation for learners.

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Conclusion:

This Multivariable Calculus and Vector Calculus course is highly recommended based on the overwhelmingly positive reviews from students. Its comprehensive approach to teaching complex mathematics, coupled with high production values and an engaging presentation style, makes it an excellent resource for anyone looking to deepen their understanding of Calculus 3 or prepare for exams in the field. The course's thoroughness and the instructor's clear explanations set it apart as one of the best offerings on Udemy for this subject.