Vector algebr and analytical geometry textbook

In summary, the conversation revolves around a comprehensive textbook in Portuguese about vector algebra and analytical geometry. The individual is looking for English textbooks that cover the same syllabus, including topics such as defining a vector, coordinate systems, conics, and quadrics. They mention that they have found several textbooks that cover some of the topics, but none that cover all of them in one book. They also note that the cross product symbol used in the textbook is different from the commonly used X symbol. Overall, they are curious about why American textbooks tend to merge calculus and analytical geometry, unlike Brazilian textbooks.
  • #1
0kelvin
50
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.
 
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  • #2
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.
 

Related to Vector algebr and analytical geometry textbook

What is vector algebra and analytical geometry?

Vector algebra and analytical geometry are mathematical disciplines that deal with the study of vectors and their properties, as well as the use of algebraic equations and coordinates to represent geometric figures and solve geometric problems.

What topics are typically covered in a vector algebra and analytical geometry textbook?

A vector algebra and analytical geometry textbook usually covers topics such as vector operations (addition, subtraction, multiplication), vector components, vector equations, dot and cross products, lines and planes in 3-dimensional space, and applications of vectors in physics and engineering.

What are some real-world applications of vector algebra and analytical geometry?

Vector algebra and analytical geometry have numerous applications in various fields, including physics, engineering, computer graphics, and navigation. They are used to describe and analyze the motion of objects in space, design structures and machines, and create visual representations of 3D objects and environments.

Do I need a strong background in math to understand vector algebra and analytical geometry?

A basic understanding of algebra and geometry is necessary to comprehend vector algebra and analytical geometry. However, with patience and practice, anyone can learn these concepts and their applications.

Are there any common misconceptions about vector algebra and analytical geometry?

One common misconception is that vector algebra and analytical geometry are only used in advanced mathematics and have no real-world applications. In reality, these concepts are widely used in various fields and have practical applications in everyday life.

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