|Objective:||To provide various mathematical concepts and analysis methods in calculus, algebra, vectors, complex functions and Fourier analysis in the engineering context.|
|Contact Hours:||49 hours (Lecture Hours = 35 and Supervised Tutorial Hours = 14)|
Final Examination: 60%
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. Mean-value 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. Higher-order 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
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 single-variable and/or multi-variable 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|