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

1. Find solutions to problems involving logarithmic, exponential, inverse trigonometric, hyperbolic and inverse hyperbolic functions.
2. Apply correctly the techniques of both differential and integral calculus to solve problems that may involve transcendental functions.
3. Solve problems involving matrices and determinants.
4. Perform operations on vectors, both in 2-D and 3-D.
5. Define i and operate with complex numbers.
6. Define a random variable and find its probability distribution and calculate probabilities based on the Binomial distribution, the Poisson distribution and the Normal distribution.
7. Appreciate the relevance of mathematics in an engineering context.
8. Communicate mathematical ideas using common conventions.

1. Functions and Inverse Functions: Revision - inverse functions, logs, exponentials; trig and inverse trig functions; hyperbolic and inverse hyperbolic functions.
2. Differential Calculus: Revision- limits; continuity; definition of the first derivative, differentiation rules; implicit differentiation including inverse trig functions and inverse hyperbolic functions.
3. Applications of Differential Calculus: L'Hopital's Rule; properties of curves; differentials; related rates.
4. Matrix Algebra: Determinants; matrices; solution of simultaneous equations using matrices and determinants; Gaussian elimination; eigenvalues and eigenvectors.
5. Vectors: definition; basic operations; dot product; cross product; angle between two vectors; equations of lines and planes.
6. Complex Numbers: Basic operations; polar coordinates; Euler's formula; powers and roots of complex numbers.
7. Integration: Indefinite/definite integrals, standard integrals.
8. Techniques of Integration: Method of substitution; method of partial fractions; integration by parts, reduction formula; trig functions; inverse trig and inverse hyperbolic functions; completing the square.
9. Applications of Integration: Revision - areas and volumes; length of curves; mass and moments; power series.
10. Descriptive statistics: Revision - Measures of central tendency and dispersion, mean, mode, median, standard deviation, variance.
11. Random Variables and Probability Distributions: Random variables, discrete random variable distributions, the binomial distribution, the Poisson distribution; definition of a continuous random variable, probability distribution of a continuous random variable, and the Normal distribution.