Enroll Course: https://www.coursera.org/learn/calculus-diferansiyel-hesap
Coursera’s ‘Multivariable Calculus II: Applications’ is the second part of a two-course series designed to build upon the foundational concepts of derivatives and integrals introduced in the first course. This installment truly shines by delving into more advanced topics and showcasing their real-world applications, adopting a content-rich approach that makes abstract concepts tangible.
The course begins with a concise yet effective recap of Multivariable Calculus I, focusing on essential concepts like partial derivatives, double integrals, and their geometric interpretations. It quickly moves into coordinate transformations, the Jacobian, divergence, curl, and the Laplacian, providing a solid bridge to more complex applications. The syllabus highlights the generalization of these concepts from two to three and even ‘n’ variables, which is crucial for understanding phenomena in physics, engineering, and data science.
A significant portion of the course is dedicated to optimization problems, including finding maximum and minimum values (both local and absolute, and under constraints) and the powerful Lagrange multiplier method. This section is particularly valuable for anyone involved in economics, operations research, or any field requiring optimization.
The latter half of the course tackles surface and volume integrals in space, exploring parametric representations of surfaces, curvilinear coordinates, and the calculation of triple integrals in Cartesian, cylindrical, and spherical coordinates. The introduction to vector fields, line integrals, and surface integrals sets the stage for understanding fundamental laws of nature. The course culminates in a thorough exploration of Green’s Theorem in the plane, Stokes’ Theorem in space, and the Divergence Theorem (Green-Gauss Theorem), demonstrating their applications in conservation laws for mass, electric charge, and heat energy.
The ‘Applications’ in the course title are not just an afterthought; they are woven throughout the curriculum. The explanations are clear, and the solved examples are illustrative, making complex mathematical machinery understandable. Whether you’re a student pursuing a STEM degree, a professional looking to refresh or deepen your calculus knowledge, or simply a curious mind eager to understand the mathematical underpinnings of the world around us, this course is a highly recommended resource. It provides a robust understanding of multivariable calculus and its practical utility.
Enroll Course: https://www.coursera.org/learn/calculus-diferansiyel-hesap