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Analytical Geometry \& Linear Algebra -- I

• Course name: Analytical Geometry \& Linear Algebra -- I
• Course number: XYZ

Course Characteristics

Key concepts of the class

• fundamental principles of vector algebra,
• concepts of basic geometry objects and their transformations in the plane and in the space

What is the purpose of this course?

This is an introductory course in analytical geometry and linear algebra. After having studied the course, students get to know fundamental principles of vector algebra and its applications in solving various geometry problems, different types of equations of lines and planes, conics and quadric surfaces, transformations in the plane and in the space. An introduction on matrices and determinants as a fundamental knowledge of linear algebra is also provided.

Course objectives based on Bloom’s taxonomy

- What should a student remember at the end of the course?

By the end of the course, the students should be able to

• List basic notions of vector algebra,
• recite the base form of the equations of transformations in planes and spaces,
• recall equations of lines and planes,
• identify the type of conic section,
• recognize the kind of quadric surfaces.

- What should a student be able to understand at the end of the course?

By the end of the course, the students should be able to

• explain the geometrical interpretation of the basic operations of vector algebra,
• restate equations of lines and planes in different forms,
• interpret the geometrical meaning of the conic sections in the mathematical expression,
• give the examples of the surfaces of revolution,
• understand the value of geometry in various fields of science and techniques.

- What should a student be able to apply at the end of the course?

By the end of the course, the students should be able to

• Perform the basic operations of vector algebra,
• use different types of equations of lines and planes to solve the plane and space problems,
• represent the conic section in canonical form,
• compose the equation of quadric surface.