Mathematics 1A module (MA11001)
This module is part of a series of four modules, Mathematics 1A, 1B, 2A, and 2B, which are the core Mathematics modules in years 1 and 2. These modules provide a solid foundation in calculus, algebra, and geometry required for higher-level mathematics modules.
In this module, you will learn essential ideas and techniques in calculus (single-variable functions and their differentiation) and algebra (complex numbers, polynomials, sequences and series, and conic sections). This module will consolidate and extend the mathematics you covered in high school. You will also develop your skills in communicating results through a group project and report writing.
- Functions - number systems, open and closed intervals, elementary functions, domain, range, composition, inverse. Inequalities. Limits of functions and sequences.
- Differential calculus - derivatives, tangents and rates of change. Simple derivatives by first principles. Higher order derivatives. Implicit differentiation. Revision of index laws and log to base a. Definitions and elementary properties of exp and ln. Solution of equations involving exponential and logarithmic functions. Differentiation of functions involving exponential and logarithmic functions. Logarithmic differentiation. Tangents and normals to curves. Increasing and decreasing functions. Critical points. Curve sketching (including asymptotes).
- Polynomials - quadratic polynomials. Algebraic and geometric representation of complex numbers. Division algorithm, remainder theorem. Roots of polynomials. Techniques of partial fraction decomposition.
- Trigonometry - definitions and properties of the six trigonometric functions. Solution of trigonometric equations.
- Series - series as sequences of partial sums. Summation of series and sigma notation. Convergence of series, geometric series. Examples of finite and infinite series. Binomial theorem.
- Conics - classification, standard forms, parametric representations.
This module is available on following courses: