3D Coordinates and Quadric Surfaces - Analytic Geometry (Undergraduate Advanced)

Learn to analyze the three-dimensional Euclidean space using coordinates and equations with pin-point precision. Designed for students, researchers, and professionals in fields such as engineering, computer graphics, physics, astronomy, medicine, biology, architecture, and building technology, this course provides a thorough understanding of coordinate systems, equations, and quadric surfaces. On completing this course, you will have mastered: - One-dimensional coordinate system and locating points - Two-dimensional coordinate system, lines, and curves - Conic sections and their equations - Three-dimensional coordinate system and quadric surfaces - Computer-aided visualization using Geogebra - Coordinate transformation and rotation - Equations in polar, cylindrical, and spherical coordinates Throughout the course, you'll engage with high-quality video lessons, completely-solved examples, free-hand sketching techniques, and computer-aided visualizations. Multiple-choice quizzes will keep you focused and help reinforce your learning. Prerequisites: This course is designed for first-year undergraduate students in engineering and sciences. Prior knowledge of basic trigonometric ratios, determinants, and elementary row operations on matrices is helpful but not required, as the course is designed to be accessible to learners with varying backgrounds. Once enrolled, you have access to dynamic video lessons, interactive quizzes, and live chat support for an immersive learning experience. You engage with clear video explanations, test your understanding with instant-feedback quizzes and interact with our expert instructor and peers in the chat room. Join a supportive learning community to exchange ideas, ask questions, and collaborate with peers as you master the material, by enrolling right away.

56

26 hrs

Payment required for enrolment
Enrolment valid for 12 months
This course is also part of the following learning track. You may join the track to gain comprehensive knowledge across related courses.
[OAU, Ife] CHE 305: Engineering Analysis I
[OAU, Ife] CHE 305: Engineering Analysis I
Advanced engineering mathematics covering solid analytical geometry, integrals, scalar and vector fields, matrices and determinants and complex variables. Curated for third-year students of engineering at Obafemi Awolowo University, Ile-Ife, Nigeria. Students and professionals with similar learning goal will also find this learning track useful.

Advanced engineering mathematics covering solid analytical geometry, integrals, scalar and vector fields, matrices and determinants and complex variables. Curated for third-year students of engineering at Obafemi Awolowo University, Ile-Ife, Nigeria. Students and professionals with similar learning goal will also find this learning track useful.

Course Chapters

1. Two-Dimensional Rectangular Coordinates
7

Points, distances, lines, angles, gradients, etc., on the two-dimensional coordinates system.

Chapter lessons

1-1. Cartesian coordinates
20:14

An introduction to the Cartesian coordinates system.

1-2. Distance between two points
16:55

Distance between two points in the Cartesian coordinates system.

1-3. Midpoint of a line segment
13:58

Calculating the coordinates of the midpoint of a line segment in a Cartesian coordinates system.

1-4. Slope of a line
17:46

Calculating the slope (gradient) of a line.

1-5. Angle between two lines
17:11

Calculating the angle between two lines in a two-dimensional Cartesian coordinates system.

1-6. Equation of a line I
36:57

Equation of a line in a two-dimensional cartesian coordinates system.

1-7. Equation of a line II
11:09

Equation of a line in a two-dimensional cartesian coordinates system.

2. Second-Degree Plane Curves
5
4

Equations of circles, ellipses, parabolas and hyperbolas.

Chapter lessons

2-1. Ellipse
47:33

Equation of an ellipse.

2-2. Hyperbola
33:50

Equation of a hyperbola.

2-3. Parabola
12:36

Equation of a parabola.

2-4. Circle
8:21

Equation of a circle.

2-5. General conics and degeneracy
33:13

Visualizing the conic sections and degeneracy.

3. Three-Dimensional Rectangular Coordinates
1
3

Three-dimensional rectangular coordinates system, graphs.

Chapter lessons

3-1. Introduction
24:08

An introduction to the 3-dimensional Cartesian coordinates system.

4. Coordinates Transformation
1
2

Transformation of coordinates by rotation.

Chapter lessons

4-1. Introduction
48:46

Introduction to transformation of coordinates by rotation.

5. Quadric Surfaces
6

Graphs of second-degree equations in three variables - ellipsoids, cones, cylinders, hyperboloids, paraboloids, etc.

Chapter lessons

5-1. Quadric cylinders
34:19

Elliptic, circular, hyperbolic and parabolic cylinders.

5-2. Ellipsoid
15:28

Identifying an ellipsoid - graph and equation.

5-3. Hyperboloids
18:16

Identifying hyperboloids - graphs and equations.

5-4. Cone
20:43

Identifying a cone - graph and equation.

5-5. Paraboloids
23:56

Identifying paraboloids - graphs and equations.

5-6. Overview
33:37

An overview of equations of various quadric surfaces.

6. Classifying Quadric Surfaces I
2
2

Direct classification of quadric surfaces.

Chapter lessons

6-1. Direct classification
20:40

Direct classification (identification) of quadric surfaces.

6-2. What if cross-product terms exist?
7:03

The implication, and how to identify surfaces, when defined with cross-product terms.

7. Classifying Quadric Surfaces II
6
3

Classification of quadric surfaces by variable substitution.

Chapter lessons

7-1. Symmetric and orthogonal matrices
24:16

Meaning and examples of symmetric and orthogonal matrices.

7-2. Eigenvalues and eigenvectors
14:17

An overview of eigenvalues and eigenvectors of matrices.

7-3. Diagonalization of matrices
26:35

An overview of diagonal matrices and diagonalization of matrices.

7-4. Transformation of coordinates
30:55

Detecting transformed coordinates with variable substitutions using orthogonal diagonalizing matrices.

7-5. Classification by variable substitution
1:26:33

Classification of quadric surfaces by variable substitution.

7-6. Eigenvalue inspection
45:06

Predicting the nature of a quadric surface by inspection of the eigenvalues of its symmetric coefficient matrix.

8. Other Coordinates Systems
3
3

The polar, cylindrical and spherical coordinates systems.

Chapter lessons

8-1. Polar coordinates
25:53

An overview of the polar coordinates system.

8-2. Cylindrical coordinates
11:19

An overview of the cylindrical coordinates system.

8-3. Spherical coordinates
19:54

An overview of the spherical coordinates system.