## APPLICABLE MATHEMATICS I (CCE)

 SHE Level 1 SCQF Credit Points 20.00 ECTS Credit Points 10.00 Module Code M1H124707 Module Leader Calum MacDonald School School of Computing, Engineering and Built Environment Subject SCEBE - School Office Trimesters A (September start) B (January start)

### Summary of Content

The module provides grounding in a range of mathematical topics including expansion of binomial, polynomial equations and inequalities, partial fractions,vector algebra, Cartesian components, trigonometry, introduction to co-ordinate geometry, differential and integral calculus. Applications of the mathematics are considered whenever appropriate.

### Syllabus

Algebra: Partial fractions, Inequalities, Binomial expansion, Vector algebra-vectors and scalars, Cartesian components, scalar and vector products and their applications. Trigonometry: Trigonometric identities and equations, solutions of trigonometric equations, sine and cosine formulae and applications, combining waves. Matrices & Determinants : Basic operations of matrices, determinants, inverse of a matrix, solving simultaneous linear equations using Cramer's rule and inverse technique. Co-ordinate Geometry: Equations of straight lines and circles, equations of tangents and normal, determination of points of intersection, polar form. Differential Calculus: Limits and Continuity, Methods of differentiation, differentiation of parametric equations, implicit functions and logarithmic differentiation, Tangent and normal, velocity, acceleration, turning points, maxima and minima, partial differentiation. Integral Calculus: Indefinite and definite integrals, integration by parts and by substitution methods, Areas under and between curves, Length of curve, Volume of solids and Surface area.

### Learning Outcomes

On completion of this module the students should be able to 1. Manipulate mathematical expressions which are relevant to engineering(AM1, AM5)2. Perform operations using vectors(AM1, AM5)3. Solve simple trigonometric equations with the aid of identities (AM1, AM5)4. Determine solution of triangles and its applications(AM1, AM5)5. Solve the system of equations by matrices & determinants(AM1, AM5)6. Derive equations of straight lines and circles(AM1) 7. Differentiate functions using the chain, product and quotient rules(AM1)8. Apply the knowledge of derivatives in determining the nature of turning points of a curve and in other applications(AM1)9. Compute partial derivatives of functions of several variables and apply on homogeneous functions(AM1)10. Evaluate definite and indefinite integrals using appropriate rules (AM1)11. Apply the knowledge of integration in application problems (AM1).

### Teaching / Learning Strategy

Combination of lectures and tutorials: Lectures: 4 hours/week and Tutorials: 2 hours/week Lectures will be used to convey basic concepts and principles with explanatory examples. Tutorial hours will be used to reinforce the module material taught during the lectures.

### Indicative Reading

John Bird, Engineering Mathematics, Elsevier Ltd., 2010.

### Transferrable Skills

Through the study of a variety of mathematical techniques, the student will develop his/her analytical and problem-solving skills

### Module Structure

Activity Total Hours
Tutorials (FT) 28.00
Lectures (FT) 56.00
Assessment (FT) 16.00
Independent Learning (FT) 100.00

### Assessment Methods

Component Duration Weighting Threshold Description
Exam (School) 1.50 20.00 35% Midterm Test - Unseen written exam for 1½ hours duration
Exam (Exams Office) 2.00 50.00 45% Final Examination - Unseen written examination for 2 hours duration
Coursework 1 n/a 30.00 35% Quizzes - FormativeWritten Assignment with questions Summativ