Engineering Mathematics 2
Unit code: HMS112
| Credit points | 12.5 Credit Points |
| Duration | 1 Semester |
| Contact hours | 60 hours |
| Campus | Hawthorn, Sarawak |
| Prerequisites | HMS111 or equivalent |
| Corequisites | Nil |
Related course(s)
A unit of study in the;
An elective unit of study in the;
Aims and objectives
This unit of study aims to provide students with mathematical knowledge and skills needed to support their concurrent and subsequent engineering and science studies.
At the completion of this subject, students should be able to:
1. Draw the surface for a given equation and find the gradient and second derivative at any point on the surface. (K2, S1)
2. Calculate small changes in a function of several variables. (K2, S1)
3. Estimate errors of measurement for a function of several variables. (K2, S1)
4. Find derivatives of a function of several variables using relevant chain rules. (K2, S1)
5. Find the directional derivatives at a point on a surface. (K2)
6. Find stationary points on a surface. (K2, S1)
7. Solve first order separable differential equations. (K2, S1)
8. Solve first order linear differential equations using an integrating factor. (K2, S1)
9. Find the orthogonal family to a given family of curves. (K2, S1)
10. Solve second order homogeneous linear differential equations with constant coefficients. (K2, S1)
11. Solve second order nonhomogeneous linear differential equations with constant coefficients. (K2, S1)
12. Do calculations involving binary, octal and hexadecimal numbers. (K2, S1)
13. Design simple switching and logic circuits using Boolean algebra and Karnaugh maps. (K2, S1)
14. Perform simple operations involving matrices and determinants by hand. (K2, S1)
15. Solve simultaneous equations using Cramer’s rule, inverse matrices and Gaussian elimination. (K2, S1)
16. Calculate the paths of projectiles in 2D. (K2, S1)
17. Find the curvature and radius of curvature of a given curve. (K2, S1)
18. Do calculations involving complex numbers. (K2, S1)
1. Draw the surface for a given equation and find the gradient and second derivative at any point on the surface. (K2, S1)
2. Calculate small changes in a function of several variables. (K2, S1)
3. Estimate errors of measurement for a function of several variables. (K2, S1)
4. Find derivatives of a function of several variables using relevant chain rules. (K2, S1)
5. Find the directional derivatives at a point on a surface. (K2)
6. Find stationary points on a surface. (K2, S1)
7. Solve first order separable differential equations. (K2, S1)
8. Solve first order linear differential equations using an integrating factor. (K2, S1)
9. Find the orthogonal family to a given family of curves. (K2, S1)
10. Solve second order homogeneous linear differential equations with constant coefficients. (K2, S1)
11. Solve second order nonhomogeneous linear differential equations with constant coefficients. (K2, S1)
12. Do calculations involving binary, octal and hexadecimal numbers. (K2, S1)
13. Design simple switching and logic circuits using Boolean algebra and Karnaugh maps. (K2, S1)
14. Perform simple operations involving matrices and determinants by hand. (K2, S1)
15. Solve simultaneous equations using Cramer’s rule, inverse matrices and Gaussian elimination. (K2, S1)
16. Calculate the paths of projectiles in 2D. (K2, S1)
17. Find the curvature and radius of curvature of a given curve. (K2, S1)
18. Do calculations involving complex numbers. (K2, S1)
Swinburne Engineering Competencies for this Unit of Study
This Unit of Study will contribute to you attaining the following Swinburne Engineering Competencies:
K2 Maths and IT as Tools: Proficiently uses relevant mathematics and computer and information science concepts as tools.
S1 Engineering Methods: Applies engineering methods in practical applications.
This Unit of Study will contribute to you attaining the following Swinburne Engineering Competencies:
K2 Maths and IT as Tools: Proficiently uses relevant mathematics and computer and information science concepts as tools.
S1 Engineering Methods: Applies engineering methods in practical applications.
Assessment
| Types | Individual or Group Assessment | Weighting |
| Closed Book Examination | Individual | 50% - 60% |
| Test(s) | Individual | 30% |
| Assignments | Individual | 10% - 20% |
Content
- Matrices: determinants, inversion, Cramer's rule, rank, null space, basis, linear independence
- Applications of vectors: straight lines and planes in space, vector product
- Complex numbers: Imaginary numbers, complex numbers, complex conjugates, Argand plane in Cartesian and polar forms; de Moivre’s theorem and roots of complex numbers; complex exponential form.
- Differential equations: First order separable differential equations, first order linear differential equations, orthogonal trajectories, second order linear differential equations with constant coefficients and simple right hand sides.
- Surfaces and partial differentiation: Surfaces, partial derivatives, small increment formula, errors of measurement, chain rule, directional derivatives, stationary points.
- Curves: 2D polar coordinates, 2D parametric curves, parametric differentiation and anti-differentiation, 3D curves, velocity and acceleration, curvature in 2D, application to transition curves, curvature in 3D.
