Multivariable Calculus by M Usman Hamid and M Zeeshan Ahmad

Multivariable calculus is a fundamental subject that extends the concepts of single-variable calculus to higher-dimensional spaces. It provides a powerful framework for analyzing and modeling complex phenomena in fields such as physics, engineering, economics, and computer science. This textbook is designed to provide a comprehensive introduction to multivariable calculus, covering topics such as Vectors, Functions, partial derivatives, multiple integrals, and differential equations, Laplace and Fourier Transformations, Sequence, Series and Complex Integration. Through a combination of theoretical foundations, practical applications, and numerous examples and exercises, we aim to equip students with a deep understanding of the subject matter and its relevance to real-world problems.

Throughout the book, we emphasize the development of problem-solving skills, critical thinking, and mathematical maturity. We also highlight the connections between multivariable calculus and other areas of mathematics, such as linear algebra and differential equations.

• Name: Multivariable Calculus
• Author: M Usman Hamid and M Zeeshan Ahmad
• Pages: 70 pages
• Format: PDF
• Size: 4.56 MB

• MULTI VARIABLE FUNCTIONS AND PARTIAL DERIVATIVES
  • Functions of Several Variables
  • Limits and Continuity
  • Partial Derivatives
  • Differentiability
  • Tangent Planes and Linear Approximations
  • The Chain Rule
  • Partial Derivatives with Constrained Variables
  • Directional Derivatives and the Gradient Vector
  • Maximum and Minimum Values
  • Extreme Values, Saddle Points, Stationary Points, Critical Points
  • Lagrange Multipliers
  • Taylor’s Formula

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