On successful completion of this subject, students should be able to:

1. Perform arithmetic operations and manipulate algebraic symbols as required in solving mathematical problems set in an engineering context
2. Solve mathematical problems using trigonometry, logarithmic and exponential functions
3. Apply correctly the techniques of both differential and integral calculus to solve problems that may involve transcendental functions.
4. Communicate mathematical ideas using standard practices

1. Arithmetic and Algebra: Rational and irrational numbers, indices, manipulation of algebraic expressions, factorisation, linear equations and quadratic expressions, simultaneous equations.
2. Relations and Functions: Domain and range, linear functions, quadratic functions, roots of quadratic equations
3. Logarithmic and Exponential Functions: Definition and properties of exponentials, graphing exponentials, differentiation and integration of exponentials, exponential growth and decay. Definition and properties of logarithms, graphing logarithms, differentiation and integration of logarithms.
4. Trigonometry: Trigonometric ratios, exact ratios, Sine and Cosine rules, reciprocal ratios, angles of any magnitude
5. Trigonometric Functions: Radian measure, graphing, properties of functions, differentiation, integration
6. Further Trigonometric Functions: Applied trigonometry, sums and differences of angles, equation solving, general solutions to trigonometric equations.
7. Inverse Functions and Inverse Trigonometric Functions: y'logax and y'ax as inverse functions, inverse trigonometric functions, differentiation and integration of inverse functions.
8. Differentiation: Limits and continuity - the derivative from first principles; differentiation formulae; implicit differentiation, tangents and normals to curves, stationary points, higher order derivatives, curve sketching, problems involving maxima and minima, differentiation of trigonometric functions, logarithmic and exponential functions, and inverse trigonometric functions
9. Integration: Primitive functions, definite integrals, areas between curves; integration of trigonometric functions, logarithmic and exponential functions, and inverse trigonometric functions.
8. Differentiation: Limits and continuity; the derivative from first principles; differentiation formulae; implicit differentiation, tangents and normals to curves, stationary points, higher order derivatives, curve sketching, problems involving maxima and minima, differentiation of trigonometric functions, logarithmic and exponential functions, and inverse trigonometric functions
9. Integration: Primitive functions, definite integrals, areas between curves; integration of trigonometric functions, logarithmic and exponential functions, and inverse trigonometric functions