# MATH06069 2013 Mathematics 1

### General Details

Full Title
Mathematics 1
Transcript Title
Mathematics
Code
MATH06069
Attendance
N/A %
Subject Area
MATH - Mathematics
Department
MENG - Mech. and Electronic Eng.
Level
06 - NFQ Level 6
Credit
05 - 05 Credits
Duration
Semester
Fee
Start Term
2013 - Full Academic Year 2013-14
End Term
9999 - The End of Time
Author(s)
David Mulligan, Grace Corcoran
Programme Membership
SG_EMECL_B07 201300 Bachelor of Engineering in Mechanical Engineering SG_EMECH_B07 201300 Bachelor of Engineering in Engineering in Mechatronics SG_EELEC_C06 201500 Higher Certificate in Engineering in Engineering in Electronics SG_EMTRN_C06 201500 Higher Certificate in Engineering in Mechatronics SG_EMECL_C06 201500 Higher Certificate in Engineering in Mechanical Engineering SG_EMECH_B07 201300 Bachelor of Engineering in Mechanical Engineering SG_EMECL_B07 201600 Bachelor of Engineering in Mechanical Engineering SG_EMANU_B07 201700 Bachelor of Engineering in Engineering SG_ETRON_B07 201600 Bachelor of Engineering in Electronic Engineering SG_EMECH_B07 201700 Bachelor of Engineering in Engineering Mechatronics Systems Engineering SG_EELCO_B07 201700 Bachelor of Engineering in Electronic and Computer Engineering SG_EELCO_C06 201700 Higher Certificate in Engineering in Engineering in Electronic and Computer Engineering SG_EMTRN_C06 201500 Higher Certificate in Engineering in Mechatronics SG_EGENE_X07 201700 Bachelor of Engineering in Engineering in General SG_EGENE_X06 201700 Higher Certificate in Engineering in Engineering in General SG_EELCO_C06 201800 Higher Certificate in Engineering in Electronic and Computer Engineering SG_EELCO_B07 201800 Bachelor of Engineering in Electronic and Computer Engineering SG_EMECH_C06 201900 Higher Certificate in Engineering in Engineering in Mechatronics
Description

Mathematics for 1st year Mechanical, Mechatronic and Electronic Engineers

### Learning Outcomes

On completion of this module the learner will/should be able to;

1.

Add, subtract, divide Natural Numbers, Integers, Rational Numbers and Real Numbers and demonstate knoweledge of the indice rules and riles of logs

2.

Solve linear, quadratic and simultaneous equations; expand (a+b)n for n between 2 and 8; Solve equations with fractions; Manipulate formulae; State, prove and use the factor theorem.

3.

Use the ratio’s sine, cosine and tangent to calculate the side or an angle of a right angled triangle; Use pythagoras’ Theorem to calculate a side of a right angle d triangle; Become familiar with the sine, cosine and tangent of 30,45,60,90,180 etc. ; Use sine and cosine rule to calculate sides and angles of a triangle; Become familiar with standard trigonometric identities; Become familiar with compound and double angle formulae; Convert Degree’s to Radians and Radians to Degree’s.

4.

Add, subtract, divide complex numbers; calculate the complex conjugate, modulus and argument of a complex number; Be familiar with polar and exponential form;  Multiply and divide complex numbers in polar form; Use De Moivre’s Theorem to calculate (a+bi)^n and find roots.

5.

Add, subtract, scalar multiply and multiply matrices. Become familiar with the Zero and Identity matrix and their properties.  Invert 2x2. Solve equations with matrices and a system of linear equations.

6.

Become familiar with the basic rules of diferentations (xn,  ex,sin(x), cos(x), ln(x), etc.);Differentiate using 1st principles; Be able to differentiate using the product, quotient and chain rule; Calculate the equation of a tangent to a curve; Use differentiation to find the Max/Min of a function.

7.

Add, subtract and scalar multiply vectors; Calculate the length and unit vector of a vector; Be familiar with their properties.

### Indicative Syllabus

1. Revision of computation, algebraic operations, transposition of formulae, solution of algebraic equations, laws of indices and logs
2. Elementary set theory, relations, functions and their graphs
3. Solution of right-angled and other triangles, sin and cos rules, trigonometric identities, degrees and radians, area and circumference of circles
4. Addition and subtraction of vectors and scalar multiples of vectors. Lengths and unit vectors of a vector.
5. Addition, subtraction and multiplication of matrices. Scalar multiples of a matrix. The Zero and Identity matrix and their properties. Inversion of 2x2 matrices. Solution a system of linear equations with matrices.
6. Add, subtract, divide complex numbers, and calculate the complex conjugate modulus and argument of a complex number. Be familiar with polar and exponential form. Multiply and divide complex numbers in polar form, DE Moivre’s Theorem
7. Differentiation of polynomial, trigonometric, exponential and logarithmic functions. Differentiation using first principles. Differentiation using the product, quotient and chain rules. Equation of a tangent to a curve. Maxima and minima of a function. Rates of change, velocity and acceleration as derivatives.

### Coursework & Assessment Breakdown

Coursework & Continuous Assessment
40 %
End of Semester / Year Formal Exam
60 %

### Coursework Assessment

Title Type Form Percent Week Learning Outcomes Assessed
1 Continuous Assessment Continuous Assessment UNKNOWN 10 % OnGoing 4,5
2 Continuous Assessment Christmas written Continuous Assessment UNKNOWN 10 % Week 12 1,2,3
3 Continuous Assessment Easter written Continuous Assessment UNKNOWN 10 % Any 5,6
4 Continuous Assessment Continuous Assessment UNKNOWN 10 % OnGoing 1,2,3

### End of Semester / Year Assessment

Title Type Form Percent Week Learning Outcomes Assessed
1 Final Exam Final Exam UNKNOWN 60 % End of Year 1,2,3,4,5,6,7

Type Location Description Hours Frequency Avg Workload
Tutorial Not Specified Tutorial 1 Weekly 1.00
Lecture Not Specified Theory 2 Weekly 2.00
Independent Learning Not Specified Independent Learning 3 Weekly 3.00
Total Full Time Average Weekly Learner Contact Time 3.00 Hours

Type Location Description Hours Frequency Avg Workload
Lecture Distance Learning Suite Lecture 2 Weekly 2.00
Lecture Not Specified Independent Learning 4 Weekly 4.00
Total Part Time Average Weekly Learner Contact Time 6.00 Hours

### Module Resources

Non ISBN Literary Resources

Engineering Mathematics by K.A Stroud

Other Resources

None