Subject Code:  EMT1016 
Objective:  To provide various mathematical concepts and analysis methods in calculus, algebra, vectors, complex functions and Fourier analysis in the engineering context. 
PreRequisite:  None 
Credit Hours:  3 
Contact Hours:  49 hours (Lecture Hours = 35 and Supervised Tutorial Hours = 14) 
Assessment:  Test/Quiz/Assignment: 40% Final Examination: 60% 
References: 

Calculus
Calculus of One Variable
Elementary functions: polynomials, rational functions, exponential and logarithm functions, trigonometric functions and their inverses, principal values, hyperbolic functions and their inverses, graphs. Limits: intuitive approach and computation, end behaviour of a function. Continuity and differentiability. Techniques of differentiation: product, quotient and chain rules. Implicit differentiation. Meanvalue theorem. L’Hôpital’sRule.Applications of differentiation.Maximum and minimum values. Techniques of Integration. Applications of integration.
Partial Differentiation
Functions of several variables: graphs of functions of two variables, level curves and surfaces.Limits, continuity and partial derivatives. Higherorder partial derivatives, equality of mixed partials.Differentiability, total differentials, approximations using differentials and their applications to engineering problems.Chain rule. Implicit differentiation. Extremum problems, without and with constraints, Lagrange multipliers, global extremum. Applications of extremum problems.
Complex Function and Vector Algebra
Sequences and Series
Fourier Series
At the completion of the subject, students should be able to perform the following tasks:
Learning Outcomes  Level of Emphasis 
LO1  Compute the limits, derivatives, integrals and extrema of singlevariable and/or multivariable functions. (cognitive  applying, level 3)  High 
LO2  Perform basic vector operations and calculate the powers and roots of complex numbers. (cognitive  applying, level 3)  Medium 
LO3  Determine the convergence of a sequence or series and the interval of convergence of a power series. (cognitive  evaluating, level 5)  Medium 
LO4  Construct the Fourier series representations of periodic functions. (cognitive  creating, level 6)  Medium 
Programme Outcomes  Level of Emphasis 
PO1  Acquire and apply knowledge of mathematics, science and engineering fundamentals to solve complex engineering problems.  High 