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### Course Overview

The course presents fundamental mathematical ideas useful in the study of Engineering. A major focus of the course is on differential and integral calculus. Applications to Engineering problems involving rates of change and averaging processes are emphasized. Complex numbers are introduced and developed. The course provides the necessary mathematical background for other engineering courses in level 2.

### Course Details

Study Type Level Undergraduate 1 Second Sub Session 15 credits (7.5 ECTS credits) Aberdeen No Dr Mark Grant

### Qualification Prerequisites

• Either Programme Level 1 or Programme Level 2

### What courses & programmes must have been taken before this course?

• Engineering (EG)

None.

No

### Course Description

1. Complex Numbers: the arithmetic of complex numbers.  Argand diagrams. Modulus, conjugate, argument etc. Polar form and de Moivre's theorem.  Solution of zn = 1. Theory of polynomial equations: roots and factors of polynomials. Fundamental theorem of Algebra. Complex roots of real polynomials occur in conjugate pairs.

2. Revision of differential calculus: derivatives, sum and product rule. Higher derivatives. Classification of critical (stationary) points, sign test and 2nd derivative tests, maxima and minima.  Higher derivatives.

3. Further differential calculus: chain and quotient rule. Inverse functions. The functions arcsin, arccos, arctan and their derivatives. The exponential function and natural logarithms. Hyperbolic functions.

4. Approximation & Taylor Series: The idea of approximating one function by another. Linear (first) approximation. Second and higher approximations. Infinite series and Taylor series.

5. Revision of integral calculus:  indefinite and definite integrals, integration of some simple functions.

6. Further integral calculus: integration by substitution and by parts. Applications of integration.

### Contact Teaching Time

Information on contact teaching time is available from the course guide.

### Teaching Breakdown

• 1 Tutorial during University week s 26 - 30, 32 - 34, 38 - 39
• 1 Workshop during University week s 26 - 30, 32 - 34, 38 - 39

### Summative Assessments

1. Online timed test 1 (35%)

2. Online timed test 2 (35%)

3. Online timed test 3 (30%)

Resit

Re-sit of only the failed assessment component(s)

### Formative Assessment

There are no assessments for this course.

### Course Learning Outcomes

Knowledge LevelThinking SkillOutcome
FactualRememberILO’s for this course are available in the course guide.

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