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**Category:** Department of Medical Engineering

**Faculty:** Faculty of Rehabilitative Sciences

**Year of Study:** 3

**Semester:** 1

Module 4: Mathematics I

Code: MAT 106 Hours: 60

Credit: 6 4.1

This module is designed to enable the learner acquire mathematical knowledge and skills in solving problems related to Medical Engineering.

By the end of this module, the learner should;

1. Solve mathematical problems involving permutations and combinations, Partial fractions, complex numbers, hyperbolic functions and inverse trigonometric functions.

**Module Content**

define the term permutation, define the term factorial, the notation for the number of permutations of n objects taking r at a time without repetition, define the term combination, define notation for the number of combinations of n objects taking r at a time, calculate the number of combination of n objects taking r objects at a time with repetition.**Permutations and Combinations**;; denominator containing linear factor, denominator containing repeated linear factors, denominator containing a quadratic factor.**Partial Fraction**define complex numbers, conjugate number in its three forms (cartesian, polar, exponential), argand diagram, arithmetic operation on complex numbers (addition and subtraction, multiplication, division), De Moivre’s theorem, application of De Moivre’s theorem is calculating (roots of numbers, derivation of trigonometric identities), application of complex numbers to engineering problem (impedances, forces, loci, zero of functions).**Complex Numbers;**define hyperbolic ratios (cosh 𝑥, sinh 𝑥, tanh 𝑥, sech𝑥, cosech𝑥and coth𝑥), graphs of hyperbolic functions, properties of hyperbolic functions, simple hyperbolic functions, state Obsorne’s rule, use Obsorne’s rule to translate trigonometric identities to hyperbolic identities, derive series expansions for ch𝑥 and sh𝑥, apply hyperbolic identities to solve engineering problems.**Hyperbolic Functions;**define of inverse trigonometric functions (arcos 𝑥, arcsin𝑥, arctan𝑥, arcsec𝑥, arccosec𝑥,arccot𝑥), graphs of the inverse functions, solutions of inverse trigonometric functions, explain the “principle value” of inverse trigonometric functions, inverse hyperbolic functions (arccosh𝑥, arcsinh𝑥, arctanth𝑥,arcsech𝑥, arccoth𝑥), graphs of the inverse hyperbolic functions, describe the “principle – value” of inverse hyperbolic functions.**Inverse Functions;**

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Introduction to Permutations and Combinations;

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