F17XE - Mathematics for Engineers and Scientists 1

Course leader(s):

• James Gaunt (Edinburgh, September)

Syllabus

1. Formulae (1.1 Recognise, manipulate, evaluate, and transpose given formulae. These formulae may involve a combination of polynomial, algebraic, fractional, trigonometric, exponential, and logarithmic components.)

2. Logarithms, Exponentials and Hyperbolic Functions (2.1 Definitions and laws of logarithms log and exponentials exp. Graphs of log and exp. Manipulation of expressions involving log and exp. Definition and drawing the graph of hyperbolic functions. Use of identities associated with hyperbolic functions.)

3. Application of linear, log and exponential functions (3.1 Applications of the straight line equation. Linear-linear graphs and linear interpolation. Reduction of algebraic equations. Linear graphs of logarithmic functions. Log-linear scales. Log-log scales)

4. Introduction to differentiation (4.1 Derivatives as rate of change. Definition of a derivative. Derivatives of polynomials, differentiation of other common functions. Higher derivatives. The chain, product and quotient rules. Implicit and Parametric differentiation. Curve sketching, stationary points. Simple rate problems)

5. Introduction to Integration (5.1 Basic ideas and definitions. Anti-derivatives. Definite and indefinite integrals. Fundamental theorem of calculus. Area under a curve. Rules of integration and Table of Standard integrals. Infinite limits)

6. Data Handling and representation (6.1 Data, data averages and variation of data. Elementary probability. Laws of Probability. Probability distributions. Engineering, science and economic applications)

7. Vectors (7.1 Basic Operations. Components. Multiply a vector by a scalar. Three-Dimensional Coordinate Frame. Direction Ratio and Direction Cosine. Scalar Product or dot product. Vector Product or cross product. Triple Vector Product. Vector Equation of a line and a plane)

Learning outcomes

By the end of the course, students should be able to do the following:

• Manipulate and solve mathematical formulae which appear in science and engineering
• Demonstrate fluency in sketching and plotting graphs of given functions and data
• Calculate derivatives of functions of one variable using standard techniques
• Evaluate integrals (definite, indefinite, improper) using standard techniques
• Apply calculations using appropriate basic quantities within statistics and probability
• Apply calculations of vector arithmetic to compute quantities and/or equations of vector objects
• Apply the mathematical concepts from this course to various disciplines in science and engineering

Further details

Curriculum explorer: Click here

SCQF Level: 7

Credits: 15