This book is a concise yet complete calculus textbook covering all essential topics in multi-variable calculus, including geometry in three-dimensional space, partial derivatives, maximum/minimum, multiple integrals and vector calculus as well as a chapter for ODE. All the chapters are constructed in a logical way to outline the essence of each topic and to address potential difficulties arising from learning.

The book is a comprehensive yet compressed entry-level introduction on single variable calculus, focusing on the concepts and applications of limits, continuity, derivative, defi nite integral, series, sequences and approximations. Chapters are arranged to outline the essence of each topic and to address learning diffi culties, making it suitable for students and lecturers in mathematics, physics and engineering. Contents Prerequisites for calculus Limits and continuity The derivative Applications of the derivative The definite integral Techniques for integration and improper integrals Applications of the definite integral Infinite series, sequences, and approximations