# Okoampa

## Contents

## SECOND SEMESTER COURSES 2010/2011 ACADEMIC YEAR

**APPLIED MATHEMATICS**

**Mathematics for Computing course outline**

**COURSE CODE**, CSD 102**CONTACT HOURS**, 3HOURS PER WEEK

**Introduction to the course**

1. COMPLEX NUMBERS a) Introduction of Complex numbers; (complex variables, algebraic properties,…)

b) The Argand Diagram i) Modulus – argument form/trigonometric form/Polar form of a complex

c) De moivre’s Theorem Euler’s Relation. These would be covered in two weeks, (At the end of week three)

2. BOOLEAN ALEBRA (a) i) Classes and Element ii) Venn Diagram (Basic expressions) (b) Boolean Functions i) Truth table

AND OR Truth tables

Three variables etc. ii) Optimisation of Boolean Function (c) Algebraic Manipulation of Boolean Expressions

3. DIGITAL LOGIC GATES (a) Introduction: i) AND – OR Gates ii) Simplifying Logic Circuits (Mapping)

iii) Minterm iv) Maxterm

(b) Karnaugh Maps i) Don’t Cares on Karnaugh maps

**At the end of seventh week the above topics and subtopics would be covered**.

MID SE MESTER REVISION (ONE WEEK) MID SEMESTER EXAMINATION

4. Finite Differential Equation i) With Characteristics Polynomial ii) With Complex Roots

- Above Topics covered in the 12th week.

5. Multinomial Coefficient . 13 – 15 Weeks

- REFERENCE BOOKS.

A. ENGINEERING MATHEMATICS (FIFTH EDITION),By K. A. Stroud.

B. COMPLEX NUMBERS FROM A – Z ,By Dorin Andrica and Titu Andreesku

C. SCHAUM’S OUTLINES DIGITAL PRINCIPLE (THIRD EDITION) By Roger L. Tokheim

D. LESSIONS IN ELECTRICAL CIRCUITS VOLUME IV – DIGITAL By Tony R. Kuphaldt.

E. MATHEMATICS FOR ENGINEERING AND COMPUTING By Mary Attenborough

## COURSE MATERIALS

**THEORY**

1. (a). Consider the differential equation (i) Determine whether it is a homogenous function and state it degree of homogeneity. (ii) Find it general solution by making use of the substitution

- (b). The population of a particular community is observed to increase at a rate Proportional to the number of people present at any one time. In the last five years the population has doubled. Using first order differential equation, determined the number of years it will take the population to triple.

2. (a).(i).Given that and evaluate

- (ii). Solve the equation ,expressing the roots in the form , where Verify that the sum of the roots is 4 and their product is 53.

- (b). using the method of substitution solve the differential equation

C) Draw the logic diagrams for the following expressions

- i. (A + B + C)(D +E)
- ii. A.B.C(D + E)

*...*

**Binary Operations**

*Put your notes, materials and information on the topic here...*

## RESEARCH METHODOLOGY

- CLASS: HND YEAR THREE

- COURSE CONTENT
- WEEK 1