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MA30213 Applied Mathematics

Supplementary Subject Learning area of Mathematics
Level M.6 Semester 1 60 periods: 1.5 credits

The learning area of this course is aimed at introducing the foundations of calculus. Topics include
the study of limits, derivatives, definite and indefinite integrals, and the Fundamental Theorem of Calculus.
This course also provides an introduction to probability theory, random variables and probability
distributions of random variables. 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. Calculate the limit of a function of two variables, understand that a function of two variables can
approach different values at a boundary point, depending on the path of approach.
2. Know the conditions for continuity of a function of two variables and verify the continuity of a
function of two variables at a point.
3. Understand that the gradient at a point is the limit of the gradients of a suitable sequence of chords;
use the notation for the first and second derivatives.
4. Use the power rule of differentiation together with constant multiples, sums, differences of
functions, and of composite functions using the chain rule.
5. Apply differentiation to gradients, tangents, normals and apply differentiation to increasing and
decreasing functions and to identify stationary points.
6. Understand integration as the reverse of differentiation, and integrate (ax+b)n, together with
constant multiples, sums and differences..
7. Solve problems involving the evaluation of a constant of integration and evaluate definite integrals.
8. Use definite integration to find the area of a region bounded by a curve and a line, find the volume
of revolution of a curve about the x or y axes.
9. Construct a probability distribution table for a discrete random variable; calculate the expectation
value and variance of a discrete random variable.
10. Know the conditions for a discrete random variable to follow a binomial distribution, calculate
binomial probabilities and find the expectation and variance of a binomial distribution.
11. Know the conditions for a continuous random variable to follow a normal distribution and how to
use the normal distribution to approximate the binomial distribution.
12. Use the normal distribution table to find probabilities and identify the critical values of a given
normal distribution.
Total: 14 Learning Outcomes

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