Calculus, Volume 2

The second volume of the textbook ‘Calculus’ meets thedemanding academic standards of engineering and science students. It offers a comprehensive exploration of calculus, designed not only to teach computational techniques but also to foster a deeper conceptual understanding of the subject. What distinguishes this volume is its clear, student-friendly exposition and its emphasis on foundational thinking. The problems are thoughtfully graded—from routine exercises to challenging conceptual puzzles—many inspired by actual coursework and examinations. The book aims to prioritize intuitive explanations and geometric interpretations, helping students develop a strong visual and logical framework for calculus. To enhance engagement, the book also includes real-world applications and historical insights that contextualize mathematical concepts. The book focuses on multivariable calculus, covering limits, continuity, differentiation, and extrema of scalar fields; differentiation and integration of functions of several variables; vector fields and line integrals; Green’s theorem and its applications; surface integrals, the divergence theorem, and Stokes’ theorem with applications.