Mathematics A (Classroom & Asynchronous e-learning)
About This Course
This course aims to provide a mathematical foundation for learners, covering key concepts such as vectors, limits, derivatives, integrals, differential equations, sequences, and series. These topics are fundamental in calculus and analysis, equipping learners with essential skills to enhance their problem-solving and analytical capabilities.
Learners will develop proficiency in solving geometrical problems using vectors, as well as in differentiating and integrating functions to tackle real-world challenges related to rates of change, optimization, and calculating areas and volumes. These mathematical skills are highly relevant across engineering and data analytics disciplines, and the course equips learners with versatile tools that lay the groundwork for their academic and professional advancement.
What You'll Learn
1. Use vectors to solve geometrical problems in two- and three-dimensional space.
2. Evaluate limits of functions using different methods.
3. Evaluate derivatives and apply Chain Rule and Implicit differentiation and L'Hopital's Rule.
4. Apply differentiation to solve problems related to rate of change and optimization.
5. Evaluate integrals using different techniques and apply integration to find areas and volumes.
6. Classify and solve Ordinary Differential Equations.
7. Give examples of convergent and divergent sequences and series, and perform various convergence tests for series.
8. Describe how a function can be expressed as a power series, determine the radius of convergence of a power series.
9. Represent certain functions by manipulating geometric series or by differentiating or integrating known series.
10. Find Taylor/Maclaurin series of a given function using definition.
11. Evaluate partial derivatives and apply Chain Rule and Implicit Differentiation for functions of more than one variable.
12. Apply the properties of directional derivatives and gradient vectors to solve problems related to rate of change of functions of more than one variable.
13. Interpret the meaning of double integrals, and evaluate double integrals via iterated integrals and change of order.
14. Evaluate double integrals in polar coordinates.
Entry Requirements
Learners are required to have a relevant part-time diploma issued from local polytechnics.