3D Coordinates and Quadric Surfaces - Analytic Geometry

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.

54

26 hrs

$ 10.00

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.
CHE 305: Engineering Analysis I
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

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

Chapter lessons

1.Cartesian coordinates20:14

An introduction to the Cartesian coordinates system.

2.Distance between two points16:55

Distance between two points in the Cartesian coordinates system.

3.Midpoint of a line segment13:58

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

4.Slope of a line17:46

Calculating the slope (gradient) of a line.

5.Angle between two lines17:11

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

6.Equation of a line I36:57

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

7.Equation of a line II11:09

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

2
Second-Degree Plane Curves

Equations of circles, ellipses, parabolas and hyperbolas.

Chapter lessons

1.Ellipse47:33

Equation of an ellipse.

2.Worked examples I35:21

Worked examples on the equation of an ellipse.

3.Hyperbola33:50

Equation of a hyperbola.

4.Worked examples II22:40

Worked examples on the equation of a hyperbola.

5.Parabola12:36

Equation of a parabola.

6.Worked examples III28:54

Worked examples on the equation of a hyperbola.

7.Circle8:21

Equation of a circle.

8.Worked examples IV14:33

Worked examples on the equation of a circle.

9.General conics and degeneracy33:13

Visualizing the conic sections and degeneracy.

3
Three-Dimensional Rectangular Coordinates

Three-dimensional rectangular coordinates system, graphs.

Chapter lessons

1.Introduction24:08

An introduction to the 3-dimensional Cartesian coordinates system.

2.Worked examples I19:54

Worked examples graphing in 3 dimensions.

3.Worked examples II17:27

More worked examples graphing in 3 dimensions.

4.Worked examples III20:23

More worked examples graphing in 3 dimensions.

4
Coordinates Transformation

Transformation of coordinates by rotation.

Chapter lessons

1.Introduction48:46

Introduction to transformation of coordinates by rotation.

2.Worked examples I21:21

Worked examples on transformation of coordinates.

3.Worked examples II19:47

More worked examples on transformation of coordinates.

5
Quadric Surfaces

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

Chapter lessons

1.Quadric cylinders34:19

Elliptic, circular, hyperbolic and parabolic cylinders.

2.Ellipsoid15:28

Identifying an ellipsoid - graph and equation.

3.Hyperboloids18:16

Identifying hyperboloids - graphs and equations.

4.Cone20:43

Identifying a cone - graph and equation.

5.Paraboloids23:56

Identifying paraboloids - graphs and equations.

6.Overview33:37

An overview of equations of various quadric surfaces.

6
Classifying Quadric Surfaces I

Direct classification of quadric surfaces.

Chapter lessons

1.Direct classification20:40

Direct classification (identification) of quadric surfaces.

2.Worked examples I19:46

Worked examples on direct classification of quadric surfaces.

3.Worked examples II18:38

More worked examples on direct classification of quadric surfaces.

4.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

Classification of quadric surfaces by variable substitution.

Chapter lessons

1.Symmetric and orthogonal matrices24:16

Meaning and examples of symmetric and orthogonal matrices.

2.Eigenvalues and eigenvectors14:17

An overview of eigenvalues and eigenvectors of matrices.

3.Diagonalization of matrices26:35

An overview of diagonal matrices and diagonalization of matrices.

4.Transformation of coordinates30:55

Detecting transformed coordinates with variable substitutions using orthogonal diagonalizing matrices.

5.Classification by variable substitution1:26:33

Classification of quadric surfaces by variable substitution.

6.Worked examples I1:41:39

Worked examples on classification of quadric surfaces by variable substitution.

7.Eigenvalue inspection45:06

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

8.Worked examples II58:51

Worked examples on classification of quadric surfaces by eigenvalue inspection and / or variable substitution.

9.Worked examples III57:15

More worked examples on classification of quadric surfaces by eigenvalue inspection and / or variable substitution.

8
Other Coordinates Systems

The polar, cylindrical and spherical coordinates systems.

Chapter lessons

1.Polar coordinates25:53

An overview of the polar coordinates system.

2.Cylindrical coordinates11:19

An overview of the cylindrical coordinates system.

3.Spherical coordinates19:54

An overview of the spherical coordinates system.

4.Worked examples I8:23

Worked examples on the polar, cylindrical and spherical coordinates.

5.Worked examples II7:08

More worked examples on the polar, cylindrical and spherical coordinates.

6.Worked examples III14:28

More worked examples on the polar, cylindrical and spherical coordinates.