**Programs **Common Second Year Engineering (NQF Level 8)

**Subject**** ****Name **Engineering Mathematics III

**Subject**** ****Code **EN212

**Duration **13 Lecture Weeks, I Exam Week, 1 Mid-Semester Week

**Contact**** ****Hours **6 Hours/Week (4 Lectures, 1 tutorial, 1 lab)

**Credit Points ** 20

**Delivery**** ****Mode **On campus

**Prerequisites **EN121 Engineering Mathematics II

**Co requisites ** Nil

**Synopsis**

To enable students to acquire further basic mathematical concepts, principles and analytical processes needed for degree studies in Engineering. On completion of this subject students should be able to use numerical methods for approximation of solutions, perform multiple integrals, use advanced mathematical method such as Fourier transforms and Laplace transform to solve ordinary and partial differential equations of the 1st and 2nd order and work with line and surface integrals.

# Subject Topics

**Topic****1: Numerical Methods**

Solution of equations – bisection, Newton -Raphson. Numerical methods of integration using trapezoidal Rule and Simpson’s Rule. Numerical solutions of differential equations using, Euler, Heun, and Runge-Kutta techniques.

# 2. Topic 2: Multivariable Calculus

Partial differentiation: Applications including tangent planes, total derivatives, directional derivatives, gradient, maxima/minima.Introduction to partial differential equations. Multiple Integrals: Double integrals over rectangular and non-rectangular regions. Triple integrals. Applications including surface areas, centroids, and centre of gravity.

# 3. Topic 3: Partial Differential Equations

Fourier’s series, integrals and transforms. Solving PDEs, the One Dimensional Wave and Heat Equations, The Two Dimensional Wave and Heat equations, Higher Order PDE.

# 4. Topic 4: Vector Calculus

- Inverse square fields, Divergence and curl, The del operator, The Laplacian operator.Evaluation of line integrals in 2D and in3D space, Change of parameter, Applications to the evaluation of a mass of a wire, arc length and work.

The Fundamental theorem of work Integrals, Independence of path, Recognition of conservative vector fields in 2 and 3 dimensional spaces.Finding work using Green’s Theorem, Greens Theorem for multiply connected regions.

- Evaluation of surface integrals, Applications to the evaluation of a mass of a curved lamina, surface area and to vector fields associated with fluid flow and electrostatic forces.Oriented surfaces, usingthe Divergence Theorem to find flux, Sources and sinks, Gauss’s Law for inverse square fields.

Relative orientation of curves and surfaces, using Stokes’ Law to calculate work, Relationship between Green’s Theorem and Stokes’ Theorem, Curl viewed as circulation.

# Subject Learning Outcomes (SLOs)

After completing this unit students will be able to:

- Use numerical techniques to solve equations, calculate definite integrals, and solve differential equations.
- Find the integral of a function of several variables,
- Apply Fourier series to solve Ordinary Differential equations and Partial Differential equations.
- Evaluate lines and surface integrals in two and three dimensional space.

# Assessment Tasks and Weightings

**To**** ****obtain**** ****a pass grade in this Unit 50% overall must be achieved and at least 50% achieved in the final examination.**

**Students**** ****must also refer to the Subject Assessment Details.**

Unit Assessment consists of three assignments, three tests and a final examination summarised below.

**AT1 Assignment1 **The assignment provides student with the opportunity to use numerical techniques to solve equations, calculate definite integrals, and solve differential equations.

It contributes 3% of the total marks for the Subject.

**AT2 Test1 **The test provides student with the opportunity to recall, interpret and solve problems involving numerical techniques it contributes 13% of the total marks for the Subject.

**AT3 Assignment2 **This assignment provides students with the ability to find the integral of functions of several variables. The assignment is worth 3% of the total marks for the Subject.

**AT4 Test2 **The test provides student with the opportunity to recall, interpret and solve problems integral of functions of several variables. It contributes 13% of the total marks for the Subject.

**AT5 Assignment3 **This assignment provides the students with the ability to apply Fourier series to solve Ordinary Differential equations and Partial Differential equations. The assignment is worth 4% of the total marks for the Subject.

**AT6 Test3 **The test provides student with the opportunity to recall, interpret and solve problems involving Vector Calculus. It contributes 14% of the total marks for the Subject.

**AT7 Final Examination: **The final examination is of 3 hours duration. The final exam is worth 50%of the total marks for the Subject.

**It is important that all students familiarise themselves with the University of Technology Assessment Guidelines including those on plagiarism www.unitech.ac.pg. It is also important to note that any software or hardware related damage to the computers or other laboratory facilities attracts severe disciplinary measures.**

**Mapping**

SLO are mapped to each of NQF, CLO, GA and AT. Assessment Tasks are linked with the topics that provide material to enable their completion.

SLO | SLO to NQF8 | SLO to CLO | SLO to GA | SLO to AT | AT to Topics |

1 | Knowledge and skills | 1 | Critical Thinker, Life Long Learner | AT1, AT2, AT7 | Topic 1 All topics |

2 | Knowledge and Skills | 1 | Life Long Learner, Critical Thinker | AT3, AT4, AT7 | Topic 2 All topics |

3 | Knowledge and Skills and Applications | 1 | Life Long Learner, Critical Thinker | AT5, AT7 | Topic 3 All topics |

4 | Knowledge and skills & Application | 1 | Critical Thinker, Life Long Learner | AT6, AT7 | Topic 4 All topics |

Key:

- SLO: Subject Learning Outcomes
- CLO: Course Learning Outcomes

- GA: Graduate Attributes

- AT: Assessment Task

# Graduate Statement

The engineering graduate will have mastery of the principles and methods of mathematics that underpin engineering and be able to apply them theoretically and practically in solving engineering problems.

# Engineering Course Learning Outcome

Course Learning Outcomes | Descriptor |

1. Underpinning Maths and Sciences | Mastery of the principles and methods of the sciences and mathematics that underpin engineering. |

2. Design | Developing creative, sustainable solutions to complex problems. |

3. Engineering Discipline Specialisation | In depth proficiency in applying the tools, methods, concepts, technology and knowledge of an engineering discipline. |

4. Communication and Teamwork | Proficient communication via written, oral and digital means across multiple audiences and within teams |

5. Researching and Evaluating Information | Ability to research, evaluate and synthesise information from varied sources. |

6. Project Management | Manage project conception and operation involving complex technical systems and processes. |

7. Professional Conduct | Conducting oneself in a professional, ethical manner consistent with sustainable economic development and society’s expectations. |

**Student Workload**

The total workload for the subject for the ‘average’ student is a nominal 150 hours, based on a 14 week semester with 13 weeks of lecturing and tutorials, 1 mid-semester week and 1 week of examination as per the PNG National Qualification Framework.

# Subject Text

- Kreyszig E. Advanced Engineering Mathematics, 7th ed. (Wiley, 1993).
- Anton H, Calculus with Analytical Geometry, 6th Edition (Wiley 1999)

# References

1. Stroud K.A .Engineering Mathematics: Programmes and Problems. 6th Edition (ELBS/Macmillan 2000)

# Readings and Resources

Scientific Calculator: student to provide Weekly Tutorial worksheets

Mathematical softwares

# Relevant Unitech Policies

It is important that all students familiarize themselves with the PNGUOT Assessment Guidelines including those on plagiarism and other relevant policies. These policies can be viewed by visiting the PNGUOT website: