Analytical Geometry for University Students
Description
Analytical Geometry for University Students is a comprehensive and rigorous treatment of coordinate-based approaches to geometry, designed specifically for undergraduate mathematics and engineering students. Professor Jan Wójcik, a respected Polish mathematician, has created a text that seamlessly connects analytical geometry to linear algebra, calculus, and advanced mathematics.
This definitive work has been a cornerstone of mathematical education in Polish technical universities for over a decade and is now available in a carefully translated English edition. The book stands out for its methodical development of concepts, its wealth of worked examples, and its focus on developing a geometric intuition that serves students throughout their mathematical careers.
Key Features:
- Systematic development from basic coordinate systems to complex geometric structures
- Strong connections to linear algebra, providing a unified perspective on both subjects
- Extensive treatment of conic sections, quadric surfaces, and higher-dimensional analogs
- Applications to optimization, dynamical systems, and computational geometry
- Over 700 exercises ranging from computational practice to theoretical explorations
- Detailed solutions to selected problems
- Historical notes on the development of analytical methods
This translation preserves Professor Wójcik's clear explanations and logical progression while adapting terminology to align with English-language conventions in mathematical education. The book is ideal for mathematics and engineering students as well as instructors seeking a comprehensive resource for teaching analytical geometry.
Table of Contents
- Coordinate Systems
- Cartesian Coordinates in the Plane
- Polar Coordinates
- Three-Dimensional Coordinate Systems
- Cylindrical and Spherical Coordinates
- Coordinate Transformations
- Vectors and Vector Spaces
- Vector Algebra
- Linear Independence and Bases
- Dot Product and Orthogonality
- Cross Product and Geometric Applications
- Triple Scalar and Vector Products
- Lines and Planes
- Equations of Lines in the Plane
- Lines in Three Dimensions
- Planes: Representations and Properties
- Intersections and Angles
- Distance Problems
- Conic Sections
- Circles and Ellipses
- Hyperbolas
- Parabolas
- General Second-Degree Equations
- Rotations and Principal Axes
- Quadric Surfaces
- Ellipsoids and Hyperboloids
- Paraboloids
- Cones and Cylinders
- Classification of Quadric Surfaces
- Reduction to Canonical Form
- Transformations and Invariants
- Linear Transformations
- Orthogonal Transformations
- Projective Transformations
- Invariant Properties
- Advanced Topics
- Curves in Space
- Curvature and Torsion
- Surfaces: Parametric Representations
- Differential Geometry Elements
- Introduction to Tensors
- Applications
- Optimization Problems
- Mechanics Applications
- Computer Graphics Fundamentals
- Robotics and Motion Planning
- Appendices
- Linear Algebra Review
- Calculus Concepts
- Solutions to Selected Exercises
About the Author
Professor Jan Wójcik is a distinguished mathematician who has dedicated his career to the development and teaching of analytical and computational geometry. Born in Gdańsk, Poland in 1962, he completed his doctoral studies at the Warsaw University of Technology with a dissertation on "Computational Methods in Projective Geometry."
As a Professor of Mathematics at the Warsaw University of Technology for over 25 years, Prof. Wójcik has taught thousands of students and supervised numerous doctoral dissertations. His research focuses on the interface between classical analytical geometry and modern computational approaches, with particular emphasis on applications in engineering, computer graphics, and robotics.
Prof. Wójcik has published over 70 papers in international journals and is the author of four textbooks that are standard references in Polish technical universities. He has been awarded the Golden Medal for Teaching Excellence by the Polish Ministry of Science and Higher Education (2016) and has served as a visiting professor at universities in Germany, the United States, and Japan.
His approach to teaching analytical geometry, which emphasizes both theoretical rigor and practical application, has influenced a generation of Polish mathematicians and engineers. This book represents a distillation of his teaching methodology and research insights, making his expertise accessible to an international audience.
