IU:TestPage

Analytical Geometry & Linear Algebra – I

• Course name: Analytical Geometry & Linear Algebra – I
• Code discipline:
• Subject area: ['fundamental principles of vector algebra,', 'concepts of basic geometry objects and their transformations in the plane and in the space']

Course Topics

Course Sections and Topics

Section	Topics within the section
Vector algebra	Vector spaces Basic operations on vectors (summation, multiplication by scalar, dot product) Linear dependency and in-dependency of the vectors Basis in vector spaces
Introduction to matrices and determinants	Relationship between Linear Algebra and Analytical Geometry Matrices 2x2, 3x3 Determinants 2x2, 3x3 Operations om matrices and determinants The rank of a matrix Inverse matrix Systems of linear equations Changing basis and coordinates
Lines in the plane and in the space	General equation of a line in the plane General parametric equation of a line in the space Line as intersection between planes Vector equation of a line Distance from a point to a line Distance between lines Inter-positioning of lines
Planes in the space	General equation of a plane Normalized linear equation of a plane Vector equation of a plane Parametric equation a plane Distance from a point to a plane Projection of a vector on the plane Inter-positioning of lines and planes Cross Product of two vectors Triple Scalar Product
Quadratic curves	Circle Ellipse Hyperbola Parabola Canonical equations Shifting of coordinate system Rotating of coordinate system Parametrization
Quadric surfaces	General equation of the quadric surfaces Canonical equation of a sphere and ellipsoid Canonical equation of a hyperboloid and paraboloid Surfaces of revolution Canonical equation of a cone and cylinder Vector equations of some quadric surfaces

Intended Learning Outcomes (ILOs)

What is the main 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.

ILOs defined at three levels

Level 1: What concepts should a student know/remember/explain?

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.

Level 2: What basic practical skills should a student be able to perform?

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.

Level 3: What complex comprehensive skills should a student be able to apply in real-life scenarios?

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.