# Çok değişkenli Fonksiyon II: Uygulamalar / Multivariable Calculus II: Applications

Koç University

Embark on a comprehensive journey through multivariable calculus with a focus on advanced applications and problem-solving techniques. This course is the second installment in a series, building upon the foundational knowledge established in the first course. With a content-based approach, it presents a wide array of real-life examples and practical scenarios.

• Explore the summary of Multivar I and integral in circular coordinates
• Dive into derivative applications, including absolute extremum problems and Lagrange multipliers
• Gain a deep understanding of chain derivatives, Jacobians, and complex functions
• Examine surface and volume integrals in space and flux integrals in the plane
• Learn about Green, Stokes, and Green-Gauss theorems in both 2D and 3D spaces
• Delve into the fundamental partial differential equations and conservation laws in nature
• Conclude with a comprehensive final exam to test your understanding and knowledge

Immerse yourself in the intricacies of multivariable calculus and elevate your problem-solving skills with this engaging and practical course.

Certificate Available ✔

##### Course Modules

This course comprises seven modules that delve into advanced topics of multivariable calculus, emphasizing real-life applications and problem-solving. From integral concepts to conservation laws, students will gain comprehensive knowledge and practical skills.

#### Multivar 1'in Özeti, Dairesel Koordinatlarda Entegraller

Explore the summary of Multivar I and integral in circular coordinates, delving into two-fold integrals and solved problems within circular coordinates. Gain insights into key concepts and fundamental techniques.

#### Türev Uygulamalarından Seçme Konular

Dive into derivative applications, including absolute extremum problems, Lagrange multipliers, and the calculus of changes. Grasp the intricacies of gradients and fundamental equations in nature.

#### Çok Değişkenle Zincirleme Türev ve Jakobiyan

Gain a deep understanding of chain derivatives, Jacobians, and the structures of complex functions. Explore infinite small areas, volumes, and representations of surfaces.

#### Uzayda Yüzey ve Hacım Entegralleri

Examine surface and volume integrals in space, solving complex problems and gaining practical insights into comparison coordinate applications. Delve into the intricacies of space and volume integrals.

#### Düzlemde Akı Entegralleri

Learn about flux integrals in the plane and delve into vector fields, line integrals, and potential. Explore core concepts and engage in solving problems utilizing residual value theorems.

#### Düzlemde Green, Uzayda Stokes ve Green-Gauss Teoremleri

Delve into the extension of Green theorems to Green-Gauss and Stokes theorems, exploring solved problems in 3D space. Gain insights into the decompositions of vectors and fundamental theorems.

#### Stokes ve Green-Gauss teoremleri ve doğanın korunum yasaları

Explore the fundamental partial differential equations and conservation laws in nature, covering momentum, heat, electric charge, and electromagnetic wave equations. Gain practical knowledge of conservation laws.

#### Dönem Sonu Sınavı

Conclude with a comprehensive final exam to test your understanding and knowledge. Prepare to showcase your mastery of multivariable calculus and problem-solving techniques.

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