# Course Title: Advanced Engineering Mathematics 2

## Part B: Course Detail

Teaching Period: Term1 2012

Course Code: MATH5155

Course Title: Advanced Engineering Mathematics 2

School: 155T Life & Physical Sciences

Campus: City Campus

Program: C6011 - Advanced Diploma of Engineering (Aerospace)

Course Contact : Selva Venkatesan

Course Contact Phone: +61 3 9925 4964

Course Contact Email:selva.venkatesan@rmit.edu.au

Name and Contact Details of All Other Relevant Staff

Raymond Rozen

51.4.05

Nominal Hours: 60

Regardless of the mode of delivery, represent a guide to the relative teaching time and student effort required to successfully achieve a particular competency/module. This may include not only scheduled classes or workplace visits but also the amount of effort required to undertake, evaluate and complete all assessment requirements, including any non-classroom activities.

Pre-requisites and Co-requisites

Course Description

The purpose of this course is to provide participants with the skills, knowledge and attitudes required to further extent the concepts learned in Advanced Mathematics 1. Areas of study include Integral Calculus, Complex Numbers, Differential Equations, Statistics and Linear Algebra. The course aims to show the relevance of mathematics to engineering and applied science.

National Codes, Titles, Elements and Performance Criteria

 National Element Code & Title: VBH625 Advanced Engineering Mathematics 2

Learning Outcomes

1. Apply the principles of Integral Calculus to solve a variety of practical problems in Engineering and Applied Science.
2. Express Complex Numbers in Cartesian, Polar, Trigonometric, Exponential and Logarithmic form, and use the theory of complex numbers to solve various practical problems in Engineering and Applied Science.
3. Apply the theory of first and Second Order Differential Equitations to solve various practical problems involving the Kinematics and Kinetics of Resisted Gravitational, Simple Harmonic and Vibratory Motion.
4. Describe and represent graphically statistical data in terms of measures of Central Tendency and measures of Dispersion.
5. Use a variety of Matrix and Numerical methods, including the use of appropriate computer software to solve Systems of Equations

Details of Learning Activities

Learning Activities
The learning activities for this course include:
• Attending lectures at which the course content will be presented and taught with appropriate examples
• Completing the assigned questions during class time
• Private study, consolidating the material provided/recommended in class and completing all required exercises and other tasks.

1. Use a variety of Matrix and Numerical methods, including the use of appropriate computer software to solve Systems of Equations
2. Apply the principles of Integral Calculus to solve a variety of practical problems in Engineering and Applied Science.

3. Apply the theory of first and Second Order Differential Equations to solve various practical problems involving the Kinematics and Kinetics of Resisted Gravitational, Simple Harmonic and Vibratory Motion.

Teaching Schedule

Aerospace Math 5155

Week No.    Date                 Topics Teaching Schedule

1            10th February       Matrix Theory and Linear Algebra:
Definition of matrix, special matrices, matrix algebra: addition, subtraction, scalar multiplication, multiplication.

2            17th February      Solving system of linear equations, Graphical method, Cramer’s rule, Matrix, singular and invertible (non-singular) matrices. Inverse Matrix Method.

3           24th February        Solving system of linear equations: Gaussian elimination.

4            2nd March           Transpose, determinant, cofactor, adjoint and inverse of a 3x3 matrix. Symmetric, skew-symmetric, orthogonal.

5            9th March            Eigenvalues and Eigenvectors.

6           16th March          Eigenvalues and Eigenvectors, Modal matrix and Diagonalization.

7           23rd March          Revision Brief overview of Integral calculus with applications.

8           30th March          Mid-Semester Test worth 40% of the total assessment marks

9            6th April 9           Easter Break

10           13th April           Differential Equations and Applications: Classification of differential equations. Solving First order Differential Equations, Type I, II and III. Variables separable equations.

11          20th April           Applications of differential equations, growth and decay problems, Newton’s law of cooling and Electrical problems.

12          27th April           Linear equations, Integrating factor, Solving First order Differential Equations: Homogeneous equations.

13          4th May             Second order Differential Equations: Second order homogeneous equations with constant coefficients

14         11th May            Second order non-homogeneous equations with constant coefficients , Applications to electrical circuits.

15         18th May            Revision

16         25th May           End of Semester Test worth 50% of the total assessment marks

NOTE: Dates and activities may change, students will be advised of any changes.

Learning Resources

Prescribed Texts

References

 The resources include the lecture notes, a recommended text, and other references available in the library . Recommended Text: Mathematical Methods for Engineers and Scientists By G.F. Fitzgerald and I.A. Peckham Publishers: Pearson Education Australia

Other Resources

References:
1. Advanced Engineering Mathematics 9th Ed.
By Erwin Kreyszig
Publishers: John Wiley and Sons 2.Advanced Engineering Mathematics
By K.A. Stroud with additions by Dexter J. Booth; 4th Ed.
Publishers: Palgrave MacMillan

Overview of Assessment

Assessment consists of a Mid-Semester test, and Assignment and a Final Examination.