## APPLIED MATHEMATICS I

 SHE Level 1 SCQF Credit Points 20.00 ECTS Credit Points 10.00 Module Code M1G121961 Module Leader Faridon Amdjadi School School of Computing, Engineering and Built Environment Subject Mechanical Engineering Trimesters A (September start)-B (January start) B (January start)

### Pre-Requisite Knowledge

SCE Higher Mathematics or equivalent

### Summary of Content

Basic Algebra, Coordinate Geometry, Trigonometry, Calculus, Matrices, Complex Numbers

### Syllabus

Algebra: Application of algebraic techniques to the manipulation of mathematical expressions including indices, trigonometrical, logarithmic and exponential functions; transposition of formulae and equations, analytical and numerical solutions of simple equations. Trigonometry: Radian measure, trigonometrical identities, sine and cosine rules; selected examples of solution of trigonometrical equations with the aid of identities. Co-ordinate Geometry: Determination of equations of straight lines and circles, equations of tangents and normals, determination of points of intersection. Complex numbers: properties of complex numbers in Cartesian form and polar form; addition, subtraction, multiplication and division; the Argand diagram; application of phasors, subtraction and addition of phasors Matrices: Addition, subtraction, multiplication; inverse of a matrix, determinants; solution of equations. Calculus: First and second order derivatives of algebraic, trigonometrical, exponential and logarithmic functions including function of a function, product and quotient rules; applications to problems involving gradients of curves, rates of change and optimisation; standard integrals involving algebraic, trigonometrical and exponential functions; applications to indefinite and definite integrals.

### Learning Outcomes

On successful completion of this module students should be able to:1. Manipulate mathematical expressions, formulae and equations by applying the basic rules of algebra2. Solve linear, quadratic and simultaneous equations3. Solve trigonometrical equations with the aid of identities4. Derive the equations of straight lines and circles and thereby solve problems of co-ordinate geometry5. Solve systems of linear equations using matrices and determinants6. Manipulate expressions involving complex numbers;7. Solve problems by the application of complex number techniques;8. Differentiate mathematical expressions by using standard rules9. Apply differential calculus to rates of change and maximisation/minimisation problems10. Integrate mathematical expressions by using standard rules11. Solve problems involving the application of indefinite and definite integrals.

### Teaching / Learning Strategy

Traditional lectures will be supported by tutorials/seminars/computer laboratories with continuous assessment in the form of coursework/class tests.

Croft A and Davidson R, Mathematics for Engineers, 2nd edition, Addison Wesley.

### Transferrable Skills

Knowledge of Basic Calculus

### Module Structure

Activity Total Hours
Tutorials (FT) 24.00
Tutorials (PT) 12.00
Assessment (PT) 18.00
Lectures (FT) 42.00
Assessment (FT) 18.00
Seminars (PT) 6.00
Seminars (FT) 6.00
Independent Learning (FT) 110.00
Independent Learning (PT) 122.00
Lectures (PT) 42.00

### Assessment Methods

Component Duration Weighting Threshold Description
Exam (Exams Office) 2.00 70.00 35% Exam
Coursework 1 n/a 30.00 35% Class Test