## CIVE1619 Preparatory Mathematics For Engineers

### 10 creditsClass Size: 180

Module manager: Dr P A Sleigh
Email: P.A.Sleigh@leeds.ac.uk

Taught: Semester 1 View Timetable

Year running 2007/08

This module is not approved as an Elective

### Objectives

To prepare students without A Level Mathematics for the Modules Engineering Mathematics 1.1 & 1.2.

### Syllabus

Algebra and Functions:
- Simplification of rational algebraic expressions including factorising and cancelling, and dividing one polynomial by another,
- Rational functions and partial fractions,
- The Remainder Theorem.Co-ordinate geometry in the (x,y)-plane,
- Co-ordinate geometry of the circle, standard equation of the circle,
- Cartesian and parametric representations of curves and the conversion between them. Sequences and Series Expansions;
- The expansion of (1+x)^n, the notations n! and ,
- Binomial expansion of (1+x)^q where q is a rational number. Trigonometry;
- The secant, cosecant and cotangent functions,
- Inverse trigonometric functions, their graphs and their restricted domains and their relationship with the sine cosine and tangent functions,
- Knowledge and use of double angle formulas, the formulas for sin(A +/- B), cos(A +/- B and tan(A +/- B),
- Expression of a.cosq + b.sinq in the forms r.cos(q+a) and r.sin(q+a). Exponentials and logarithms;
- Exponential growth and decay,
- The solution of equations of the form a^x=b. Differentiation;
- The derivatives of the trigonometric functions,
- Application of differentiation to tangents and normals,
- Differentiation using the product, quotient and chain rules, and the formula dx/dy=1/(dy/dx),
- Differentiation of functions defined implicitly or parametrically,
- Formation of simple differential equations. Integration;
- Integration of sinx and cosx,
- Simple cases of integration by parts and using substitutions,
- Simple cases of integration using partial fractions,
- Analytical solution of first order differential equations with separable variables.

### Teaching methods

 Delivery type Number Length hours Student hours Lecture 22 1.00 22.00 Practical 11 1.00 11.00 Seminar 11 1.00 11.00 Private study hours 56.00 Total Contact hours 44.00 Total hours (100hr per 10 credits) 100.00

### Private study

33 hours - 1 hour reading per lecture, 2 hours per example sheet
23 hours - exam preparation

### Opportunities for Formative Feedback

- 4 marked problem sheets during semester

### Methods of assessment

Coursework
 Assessment type Notes % of formal assessment Problem Sheet Problem sheet 1 5.00 Problem Sheet Problem sheet 2 5.00 Problem Sheet Problem sheet 3 5.00 Problem Sheet Problem sheet 4 5.00 Total percentage (Assessment Coursework) 20.00

Normally resits will be assessed by the same methodology as the first attempt, unless otherwise stated

Exams
 Exam type Exam duration % of formal assessment Standard exam (closed essays, MCQs etc) 2 hr 00 mins 80.00 Total percentage (Assessment Exams) 80.00

Normally resits will be assessed by the same methodology as the first attempt, unless otherwise stated