MTH110 - Mathematics

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Last revision date Jul 31, 2018 9:20:35 AM
Last review date Jul 31, 2018 9:20:52 AM

Subject Title

Subject Description
This course, along with mathematics courses MTH200 and MTH300, provides the knowledge of calculus and other topics in mathematics required by the engineering courses in the Flight Program. MTH110 begins with a review of some high school mathematics: trigonometric functions; systems of simultaneous linear equations; vector geometry; exponential and logarithmic functions; complex numbers. The remainder of the course consists of an introduction to the differential calculus of functions of one variable. Topics covered include: limits; the derivative; derivatives of some basic functions; higher order derivatives; the derivatives of functions defined implicitly.

Credit Status
One Credit

Learning Outcomes
Upon successful completion of this subject the student will be able to:

1. Define the trigonometric functions, evaluate trigonometric functions for any angle and plot trigonometric functions.

2. Define the frequency, period, angular velocity and phase angle of trigonometric functions where the angle is a function of time.

3. Calculate the unknown angles and or sides of a given arbitrary triangle using the sine law and/or cosine law.

4. Define a vector and determine the sum of two or more vectors and the difference of two vectors graphically and analytically.

5. Calculate the dot product of two vectors and the cross product of two vectors.

6. Write down the equations of three-dimensional geometrical objects such as spheres, planes etc. when given sufficient information to define them.

7. Solve systems of linear equations consisting of two equations in two unknowns and three equations in three unknowns using determinants. The student should be able to identify those systems which do not have a unique solution, describe the nature of those non-unique solutions if they exist and explain the geometrical significance of those situations where there is no unique solution.

8. Define the terms logarithm and exponent and in particular define the natural logarithm "ln" and the transcendental number e. Write down the properties of logarithms and exponents and use "ln" and e to solve equations containing logarithms or exponents.

9. Define complex numbers, write down the rectangular form and polar form of a given complex number and perform the basic operations of addition, subtraction, multiplication and division with complex numbers. The student will also be able to calculate the integral power of any complex number.

10. Define a limit and evaluate the limits of a variety of algebraic and trigonometric functions of one variable. In particular, the student will be able to calculate the limits of such functions when the independent variable approaches.

11. Define what is meant by the continuity of a function at a point and prove continuity, or lack of it, at a given point for a variety of algebraic and trigonometric functions.

12. Define the derivative of a function, describe the geometric significance of the derivative and evaluate the derivatives of given functions at given points from first principles.

13. Use the rules of differentiation to calculate the first and higher derivatives of algebraic and trigonometric functions. Students will also be able to calculate the derivatives of functions defined implicitly.

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