## Mathematics 1M1

 Unit code: MATH19661 Credit Rating: 10 Unit level: Level 1 Teaching period(s): Semester 1 Offered by School of Mathematics Available as a free choice unit?: N

None

#### Aims

The course unit aims to provide a basic course in calculus and algebra to students with A-level mathematics or equivalent in school of MACE.

#### Learning outcomes

Knowledge and understanding: Be familiar with functions and geometry, differentiation, integration, basic numerical methods, vectors and complex numbers, simple ordinary differential equations.

Intellectual skills: Be able to carry out routine operations involving the topics in the syllabus.

Transferable skills and personal qualities: Have a set of tools and methods that can be applied in the courses given in the host department or in subsequent years.

#### Assessment methods

• Other - 20%
• Written exam - 80%

#### Assessment Further Information

Diagnostic Followup Coursework (week 4) Weighting within unit 10%

Coursework 2 (week 11) Weighting within unit 10%

2 hour examination (semester 1) Weighting within unit 80%

#### Syllabus

4 lectures: Intermediate Calculus.
Review of product, quotient and chain rules for differentiation. Partial differentiation in 2 variables. Review of methods of integration (by parts, substitution and partial fractions.

4 lectures: Double integrals and line integrals.
Double integrals over rectangles and disks. Line integrals and integrals with respect to arc-length. Relation through Green's theorem.

2 lectures: Basic Numerical Methods.
Trapezoidal and Simpson's rule, inc. estimation of error. Bisection and Newton-Raphson methods for solving nonlinear equations.

4 lectures: Vectors.
Review of vectors in component form; vector addition, parallelogram and triangle of vectors. Vector equation of straight line.  Scalar and vector products. Triple Products. Applications including vector products and areas.

3 lectures: Complex numbers.
Definition, algebraic operations, modulus and argument.   Argand
Diagram, De Moivre's theorem.

4 lectures: Ordinary Differential Equations (ODEs).
Examples of First and Second order ODEs. Role of arbitrary constants.
Solution of first-order separable, linear and exact ODEs.  First order linear ODEs and integrating factors.

3 lectures: Probability.
Deterministic vs random (probabilistic) models. Random experiments and sample spaces. Definition and properties of probability; finite sample spaces. Conditional probability, independent events.

KA Stroud, Engineering Mathematics, Palgrave

Croft et al., Mathematics for Engineers, Pearson

#### Study hours

• Lectures - 24 hours
• Tutorials - 11 hours
• Independent study hours - 65 hours

#### Teaching staff

Sean Holman - Unit coordinator