# Mathematics 1A

** 20 **

** MA11001 **

### About the module

This module consists of a Calculus and Algebra component. It is part of a series of four modules, Mathematics 1A, 1B, 2A, 2B, which are the core Mathematics modules in years 1 and 2, and provide the foundations in Calculus, Algebra and Geometry for all mathematics modules in higher levels. This module is mandatory for all Level 1 students on Mathematics (including Mathematics combined) degrees. The module is also suitable for students on non-mathematics degrees and recommended for students on physics and computing degrees. If you have questions about this module please contact our Undergraduate Admissions Tutor.

### Prerequisites

Students taking this module should typically have at least a B in Mathematics in Scottish Highers, AS-, or A-Level, or an equivalent qualification.

### Indicative Content

#### Functions

Number systems (N, Z, Q, R), open and closed intervals, elementary functions, domain, range, composition, inverse. Inequalities. Idea of a limit for functions and for sequences.

#### Differential Calculus

Derivatives, tangents and rates of change. Simple derivatives by first principles. Treatment of (f + g)′ , (fg)′, (f/g)′, (f ? g)′ and inverse functions. 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. Algebra 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, including formulae for sin(A + B), sin A sin B, sin A + sin B, etc. Solution of trigonometric equations (including a cos(x) + b sin(x) = c).

#### 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.

### Delivery and Assessment

The module is delivered in the form of lectures and workshops/tutorials and assessed via coursework (100%) consisting of homeworks, projects and tests.

### Credit Rating

This module is a Scottish Higher Education Level 1 or SCQF level 7 module and is rated as 20 SCOTCAT credits or 10 ECTS credits.