Last modified: 16 Nov 2016 17:46
The course presents fundamental mathematical ideas useful in the study of Engineering. A major focus of the course is on differential and integral calculus. Applications to Engineering problems involving rates of change and averaging processes are emphasized. Complex numbers are introduced and developed. The course provides the necessary mathematical background for other engineering courses in level 2.
|Session||Second Sub Session||Credit Points||15 credits (7.5 ECTS credits)|
1. Complex Numbers: the arithmetic of complex numbers. Argand diagrams. Modulus, conjugate, argument etc. Polar form and de Moivre's theorem. Solution of zn = 1. Theory of polynomial equations: roots and factors of polynomials. Fundamental theorem of Algebra. Complex roots of real polynomials occur in conjugate pairs.
2. Revision of differential calculus: derivatives, sum and product rule. Higher derivatives. Classification of critical (stationary) points, sign test and 2nd derivative tests, maxima and minima. Higher derivatives.
3. Further differential calculus: chain and quotient rule. Inverse functions. The functions arcsin, arccos, arctan and their derivatives. The exponential function and natural logarithms. Hyperbolic functions.
4. Approximation & Taylor Series: The idea of approximating one function by another. Linear (first) approximation. Second and higher approximations. Infinite series and Taylor series.
5. Revision of integral calculus: indefinite and definite integrals, integration of some simple functions.
6. Further integral calculus: integration by substitution and by parts. Applications of integration.
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