Vector algebr and analytical geometry textbook

Click For Summary
SUMMARY

The discussion centers on the search for English textbooks covering vector algebra and analytical geometry, specifically a comprehensive syllabus that includes topics such as vector addition, dot product, and conics. The user references a Portuguese textbook lacking a bibliography and lists several English titles that partially cover the required material. Notable recommendations include "Analytic Geometry with an Introduction to Vectors and Matrices" by David Murdoch and "Schaum's Outline of Vector Analysis." The user highlights a gap in American textbooks that combine calculus with analytical geometry, unlike Brazilian texts.

PREREQUISITES
  • Understanding of vector algebra concepts
  • Familiarity with analytical geometry principles
  • Knowledge of coordinate systems and transformations
  • Basic proficiency in mathematical notation and symbols
NEXT STEPS
  • Research "Schaum's Outline of Vector Analysis" for supplemental exercises
  • Explore "Analytic Geometry: A Vector Approach" by Charles Wexler for a comprehensive overview
  • Investigate "The Elements of Analytic Geometry" by Percy F. Smith for historical context
  • Examine modern textbooks that integrate calculus with analytical geometry
USEFUL FOR

Students and educators in mathematics, particularly those focusing on vector algebra and analytical geometry, as well as anyone seeking comprehensive resources in English on these topics.

0kelvin
Messages
50
Reaction score
5
Vector algebra and analytical geometry textbook

I have a very comprehensive textbook written in portuguese about vector algebra and analytical geometry, but the author didn't include a bibliography at the book's end. What textbooks, in english, contains these syllabus (I'm pasting the list of chapters)?

  1. Defining a vector
  2. Vector addition
  3. Multiplication of vector by real number
  4. Adding points and vectors
  5. Geometric applications
  6. Linear dependence
  7. Basis
  8. Change of basis
  9. Dot product (or scalar product)
  10. Orientation of V3
  11. Cross product (or vector product)
  12. Mixed product (or triple product)
  13. Coordinate system
  14. Equation of line and plane
  15. Intersection of planes and lines
  16. Relative position of lines and planes
  17. Perpendicularity and orthogonality
  18. Measuring angles
  19. Measuring distance
  20. Changing the coordinate system
  21. Ellipse, hyperbola and parabola
  22. Conics
  23. Espherical surfaces
  24. Quadrics

PS: For some reason the cross product symbol in this textbook is ^, not the X used in notes and books that I've found in english.

In Brazil no author merges calculus and analytical geometry in one textbook, I don't know why most american authors (or is it the publishers?) do.

The textbook has 500+ pages, almost as large as a calculus textbook alone.
 
Last edited:
Physics news on Phys.org
Found textbooks that cover what I asked for:

Analytic Geometry with an introduction to vectors and matrices - David Murdoch
Analytic geometry - Charles Lehman
The elements of analytic geometry - Percey F. Smith and Arthur Sullivan Gale
Analytic Geometry : A Vector Approach - Charles Wexler (coincidentally, the title is the same as the book in portuguese that I know)
Vector geometry - Gilbert de B. Robinson
A vector space approach to geometry - Melvin Hausner
Elementary vectory geometry - Seymour Schuster
Vectors and their applications - Anthony J. Pettofrezzo
Schaum's outline of vector analysis
Schaum's outline of analytic geometry

Seems that no textbook contains all the chapters I posted in one book. Most of the books that I've found are really old.
 

Similar threads

  • · Replies 18 ·
Replies
18
Views
18K
Replies
7
Views
2K
  • Sticky
  • · Replies 16 ·
Replies
16
Views
13K
Replies
7
Views
4K
  • · Replies 4 ·
Replies
4
Views
3K
  • · Replies 1 ·
Replies
1
Views
1K
  • · Replies 50 ·
2
Replies
50
Views
5K
  • · Replies 7 ·
Replies
7
Views
2K
  • · Replies 3 ·
Replies
3
Views
4K
  • · Replies 8 ·
Replies
8
Views
2K