Mathematics for Civil Engineering 1

First year Mathematics for Civil Engineering covers fundamentals of arithmetic and algebra, co-ordinate geometry and graphing, algebraic and trigonometric functions, introduction to complex numbers and matrices, differentiation and some applications, integration and some applications, sequences and series and statistics.

Functions can be used to model environmental systems; linear and exponential.  Series can determine the cumulative effect of changes within our environment. Calculus analyses rates of change, students look at practical examples such as sustainability of wildlife, forestry and clean air.   

1. Manipulate algebraic expressions. Solve linear, quadratric, simultaneous, exponential and logarithmic equations, including worded questions. Graph standard functions and solve equations graphically.

2. Apply the basic trigonometric ratios, sine rule and cosine rule to solve unknowns in right-angled and oblique triangles

3. Represent complex numbers in polar form, calculate roots and powers of complex number using De Moivre's Theorem.

4. Perform basic matrix operations: addition, subtraction and multiplication.

5. Differentiate standard functions using a table of derivatives, the sum, product, quotient or chain rule. Calculate maximum, minimum values and rates of change.

6. Recognise integration as the reverse process to differentiation and determine standard indefinite integrals. Evaluate definite integrals and calculate areas under curves.

7. Organise and display data in an appropriate manner and summarise important characteristics of a data set