MATH 100 - Technical Mathematics for Geomatics

Course Details
Course Code:
MATH 100


Calendar Description:
This course introduces students to technical mathematics with an emphasis on its application to surveying: trigonometric functions of any angle, solution of triangles, identities and trigonometric equations; spherical trigonometry; systems of linear equations; analytic geometry.

Date First Offered:

Total Hours: 105
Lecture Hours: 5
Laboratory Hours: 2

Total Weeks:

This course is offered online:

One of Principles of Math 12, Pre-Calculus 12 or Math 050

Non-Course Pre-Requisites:


Course Content:
Algebra Review
- Elements of geometry
- Right-angled Trigonometry
- Trigonometric functions of any Angle
- Radian Measure

Solution of Oblique Triangles
- Applications of oblique triangles to geomatics

Elements of Descriptive Statistics

Area Calculations
- Volume calculations

Graphs of the Trigonometric Functions
- Trigonometric identities

Trigonometric Equations
- Applications of trigonometric identities and trigonometric equations

Introduction to Spherical Trigonometry
- Solution of right-angled spherical triangles
- Napier’s Rules

Solution of Oblique Triangles
- Introduction to astronomy

Applications of Spherical Trigonometry, Course Notes
- Introduction to Linear Algebra

Introduction to Matrix Algebra

The Circle, Parabola, Ellipse, Hyperbola

Learning Outcomes:
Upon successful completion, the student will be able to:
- Use basic algebraic rules and operations
- Rearrange formulae used in geomatics
- Solve line intersection problems
- Formulate and solve elementary geometric properties of circles
- Solve right-angle triangles using trigonometry
- Use right-angle trigonometry to solve applied surveying problems
- Use radian measure in the solution of surveying problems involving circular arcs
- Use the sine and cosine laws for solving oblique triangles
- Apply the sine and cosine laws to elevation problems and traverses
- Carry out the simplification of trigonometric expressions using trigonometric identities
- Solve simple trigonometric equations
- Demonstrate the use of statistical parameters in reducing surveying measurements
- Apply area formulae to problems such as finding the area contained in a traverse and the area contained within a lot with an irregular boundary.
- Apply volume formulae to problems such as cut and fill.
- Solve right-angled spherical triangles.
- Solve oblique spherical triangles.
- Use spherical triangles for determining azimuth and bearing.
- Carry out matrix operations.
- Use matrix operations to rotate, translate and scale coordinate systems such as is used in transforming from a ground based system to UTM coordinates.
- Solve problems in analytic geometry.
- Use analytic geometry in geomatics applications such as vertical curves.

Grading System:

Passing Grade:
D (50%)

Grading Weight:
Final Exam: 35 %
Quizzes and Tests: 50 %
Assignments: 15 %

Percentage of Individual Work:

Course Offered in Other Programs:

Additional Comments:
Assignments: Late assignments, lab reports or projects will not be accepted for marking. Assignments must be done on an individual basis unless otherwise specified by the instructor.

Makeup Tests, Exams or Quizzes: There will be no makeup tests, exams or quizzes. If you miss a test, exam or quiz, you will receive zero marks. Exceptions may be made for documented medical reasons or extenuating circumstances. In such a case, it is the responsibility of the student to inform the instructor immediately.

Ethics: NLC assumes that all students attending the institution will follow a high standard of ethics. Incidents of cheating or plagiarism may, therefore, result in a grade of zero for the assignment, quiz, test, exam, or project for all parties involved and/or expulsion from the course.

Attendance: Attendance will be taken at the beginning of each session. Students not present at that time will be recorded as absent.

Illness: A doctor’s note is required for any illness causing you to miss assignments, quizzes, tests, projects, or exam. At the discretion of the instructor, you may complete the work missed or have the work prorated.

Attempts: Students must successfully complete a course within a maximum of three attempts at the course. Students with two attempts in a single course will be allowed to repeat the course only upon special written permission from the Dean. Students who have not successfully completed a course within three attempts will not be eligible to graduate from the appropriate program.

Course Outline Changes: The material or schedule specified in this course outline may be changed by the instructor. If changes are required, they will be announced in class.

Course Credit: Applications for course credit or course exemption on the basis of previously completed mathematics courses are assessed on a case-by-case basis by the NLC Geomatics Faculty taking into account all of the following:
• the correspondence between topics, content and level
• recency (generally no more than 3–5 years)
• the grade (generally at least a C+ or 65%)
• the context (course taken as part of a university or college science or engineering program, rather than, for example, an arts or social science program)

Assignment Details: There is a weekly assignment which consists of questions related to the material covered in the lectures of that week. A deadline for submission of these assignments will be established at the beginning of the term..

Other information:
Specify Number of Assignments: 10-12

Text Books:

Required - Washington, A.J., Basic Technical Mathematics with Calculus, 8th Edition (Addison Wesley). Chapters Covered: 1,2,4,6, 7-11, 16, 20-21
Optional - Sheperd, Engineering Surveying Problems with Solutions
Optional - Davis, Foote, Anderson, Mikhail, Surveying, Theory and Practice
Optional - Rice and Knight, Technical Mathematics with Calculus
Optional - Calter, Technical Mathematics with Calculus