This study guide is designed for students taking a Calculus III course. The textbook includes examples, questions, and practice problems that will help students to review and sharpen their knowledge of the subject and enhance their performance in the classroom. The material covered in the book includes linear algebra and analytical geometry; lines, surfaces, and vector functions in three-dimensional coordinate systems; multiple-variable functions; multiple integrals and their applications; line integrals and their applications. Offering detailed solutions, multiple methods for solving problems, and clear explanations of concepts, this hands-on guide will improve students’ problem-solving skills and foster a solid understanding of calculus, which will benefit them in all of their calculus-based courses.

Table of Contents

1: Problems: Linear Algebra and Analytical Geometry

2: Solutions of Problems: Linear Algebra and Analytical Geometry

3: Problems: Lines, Surfaces, and Vector Functions in Three-Dimensional Coordinate System

4: Solutions of Problems: Lines, Surfaces, and Vector Functions in Three-Dimensional Coordinate System

5: Problems: Multivariable Functions

6: Solutions of Problems: Multivariable Functions

7: Problems: Double Integrals and Their Applications

8: Solutions of Problems: Double Integrals and Their Applications

9: Problems: Triple Integrals and Their Applications

10: Solutions of Problems: Triple Integrals and Their Applications

11 : Problems: Line Integrals and Their Applications

12: Solutions of Problems: Line Integrals and Their Applications

About the Author

Dr. Mehdi Rahmani-Andebili is an Assistant Professor in the Electrical Engineering Department at Arkansas Tech University, AR, US. He received his first M.Sc. and Ph.D. degrees in Electrical Engineering (Power System) from Tarbiat Modares University and Clemson University in 2011 and 2016, respectively, and his second M.Sc. (Ph.D.) degree in Physics and Astronomy from the University of Alabama in Huntsville in 2019. Moreover, he was a Postdoctoral Fellow at the Sharif University of Technology during 2016-2017. As a professor, he has taught many courses and labs, including Power System Analysis, Power Electronics, DC and AC Electric Machines, Feedback Control Systems Analysis and Design, Renewable Distributed Generation and Storage, Industrial Electronics, Analog Electronics, Electrical Circuits and Devices, AC Electrical Circuits Analysis, DC Electrical Circuits Analysis, Essentials of Electrical Engineering Technology, and Algebra and Calculus-Based Physics. Dr. Rahmani-Andebili has over 200 single-author and first-author publications, including journal papers, conference papers, textbooks, books, and book chapters. He is an IEEE Senior Member and a permanent reviewer for many reputable international journals. His research areas include Smart Grid, Power System Operation and Planning, Integration of Renewables and Energy Storages into Power Systems, Energy Scheduling and Demand-Side Management, Plug-in Electric Vehicles, Distributed Generation, and Advanced Optimization Techniques in Power System Studies.