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
Contents & Summary
- 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