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MA30211 Applied Mathematics

Supplementary Subject Learning area of Mathematics
Level M.5 Semester 1 60 periods: 1.5 credits

The learning area of this course is aimed at introducing the foundations of analysis designed to
precede the calculus sequence with emphasis on functions and graphs. Topics include trigonometric
functions and graphs, techniques for solving problems in trigonometry, matrices, vectors, permutation and
combination, sequences and series and an introduction to complex analysis. Students will be able to apply
mathematical concepts and principles to identify and solve problems and develop their thinking skills
towards the 21st century.
The teaching procedures introduced in this course focus on the mathematical learning process;
lectures by the teacher; collaborative learning groups; student-led facilitation of topics; online learning;
games; and activities in order to allow students to develop themselves to their highest potentiality.
Throughout the course, students should be able to use mathematical skills, including the ability to use
technology, critical thinking and problem solving to become well-rounded and fully developed in all
respects; physically, intellectually, emotionally and socially.

The course also enables students to instill the desirable characteristics, including honesty and
integrity; self-discipline; avidity for learning; dedication and commitment to work; public-mindedness; and
being healthy and well-balanced.

Course Learning Outcomes
1. Understand the definition of a radian and use the relationship between radians and degrees.
2. Sketch and use graphs of the sine, cosine and tangent functions (for any size using degrees or
radians).
3. Use the exact values of the sine, cosine and tangent of 30, 45, 90 degrees and related angles. Find
all solutions of simple trigonometric equations lying in a specific interval.
4. Understand the relationship between the secant, cosecant and cotangent functions to cosine, sine
and tangent. Use trigonometric identities for the simplification and exact evaluation of expressions
and in the course of solving equations.
5. Understand the idea of a complex number, recall the meaning of the modulus, argument and
conjugate of a complex number. Carry out operations of addition, subtraction, multiplication and
division of two complex numbers.
6. Represent complex numbers geometrically by means of an Argand diagram. Carry out operations
of multiplication and division of two complex numbers expressed in polar form.
7. Multiply a matrix by a scalar; add, subtract and multiply two matrices up to order 4.
8. Find the determinant and inverse of a matrix and use matrices to solve systems of linear equations.
9. Add and subtract vectors, multiply a vector by a scalar and interpret these operations geometrically.
10. Find the vector equation of a line, find and use the scalar and vector product of two vectors.
11. Understand the definitions and be able to calculate permutations and combinations.
12. Apply permutations and combinations to solve problems involving probability.
13. Recognize arithmetic and geometric progressions and use the binomial expansion.
14. Use the formulae for the nth term and first sum of the first n terms to solve problems involving
arithmetic and geometric progressions.
Total: 14 Learning Outcomes

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