The first aim of Mathematics 1 is to allow a thorough revision and consolidation of key basic mathematical topics that have been encountered by students prior to entry to higher education. The second aim is to deepen the students understanding of key mathematical ideas regarding engineering functions, iteration and calculus in such a way as to support other engineering modules.
Review Material:
Arithmetic: Arithmetic of real numbers, indices, fractions, scientific form. Negative and fractional indices. Algebraic expressions and formulae: Precedence rules. Manipulation of algebraic expressions. Manipulation of algebraic fractions. Factorisation of quadratic expressions. Functions: Basic concepts/notation. Domain and range. Recognition of the graphs of simple quadratic forms. Transposition of formulae. Solution of linear equations. Co-ordinate geometry: Cartesian co-ordinates. Equation of a straight line. Plotting simple linear laws, y-intercept and slope. Distance in 2D. Area of a triangle. Complex numbers: Definition of a complex numbers. Conjugate of a complex number. Argand diagram representation. Addition and subtraction of complex numbers.Trigonometry: Radian measure. Right-angled triangles. Sin, cos and tan. Sectors and arcs. Sin, cos and tan as lengths in the unit circle. Pythagoras’ theorem. Solution of right-angled triangles. Sine and cosine rules.
Further Algebra:
Simultaneous equations. Rewriting a quadratic expression by completion of the square. Graphs of a general quadratic expression. Solution of quadratic equations. Graphs of cubics.
Vectors:
Scalars and vectors. Addition and subtraction of vectors. Modulus of a vector. Unit vectors. Resolution into component form. Scalar product.
Functions:
Plotting functions. Alteration of a functional description as a result of transformations in the plane. Function inverses. Limit of a function. Power law, exponential and logarithmic functions. Solving equations involving logarithmic and exponential functions. Definition of periodic functions. Graphs of trigonometric functions. Trigonometric functions: sin, cos and tan. Compound angle formulae. Solving trigonometric equations in an engineering context.
Rate of change and differentiation:
Average and instantaneous rate of change. Definition of derivative of a function at a point. Geometric interpretation of the derivative. The chain rule. The equations of tangent and normal to the graph of a function.Differentiation: Use of a table of derived functions. Use of the multiple, sum, product and quotient rules.
Complex Numbers:
Modulus and argument of a complex number. Multiplication and division of complex numbers in both Cartesian and polar forms. De Moivre Theoerm
Software Skills:
File management: Managing Files and the Computer Interface: Directory structure. Searching for files. Copy and rename. Spreadsheets: Basic concepts. Entering data to cells. Selecting cells, rows, columns and ranges. Copying/moving cells. Inserting/deleting cells, rows and columns. Entering formulae. Cell referencing. Using the function wizard. Plotting charts & graphs: line/curve fitting.
| Module Content & Assessment | |
|---|---|
| Assessment Breakdown | % |
| Other Assessment(s) | 30 |
| Formal Examination | 70 |