# MATH 1019 Mathematics for Engineers 2

Credit Points 10

Legacy Code 200238

Coordinator Wei Xing Zheng Opens in new window

Description This subject is the second of two mathematics subjects to be completed by students enrolled in an Engineering degree during their first year of study. The content covers a number of topics that build on the calculus knowledge from Mathematics for Engineers 1. The subject matter includes: ordinary differential equations, Laplace transforms and multi-variable calculus.

School Computer, Data & Math Sciences

Discipline Mathematics

Student Contribution Band HECS Band 1 10cp

Check your fees via the Fees page.

Pre-requisite(s) MATH 1016

Equivalent Subjects -

Incompatible Subjects MATH1035

## Learning Outcomes

On successful completion of this subject, students should be able to:

1. Recognise and solve various types of first and second order differential equations and some higher order ordinary differential equations
2. Set up a linear 2D system of differential equations and investigate its solution and the nature of its critical points
3. Apply Laplace transforms in solving problems
4. Use multivariable calculus techniques competently
5. Evaluate multiple (double and triple) integrals.

## Subject Content

First Order Ordinary Differential Equations - Separable and linear equations and applications.
Second Order Linear ODEs- both homogeneous and non homogeneous with constant coefficients and applications, Euler Cauchy and Power series solutions.
Higher Order ODEs - homogeneous and non homogeneous with constant coefficients and Euler-Cauchy.
2D linear constant coefficient homogeneous systems, phase plane, critical points and criteria for critical points.
Laplace Transforms and solving ODEs using Laplace transforms.
Level curves and sketching regions in space
Limits and continuity of functions of two variables
Partial differentiation
Chain rule
Equations of normal lines and tangent planes
Lagrange multipliers
Double integrals in rectangular and polar coordinates and applications
Triple integrals in rectangular, cylindrical and spherical coordinates and applications.
1. First Order Ordinary Differential Equations - Separable and linear equations and applications.
2. Second Order Linear ODEs- both homogeneous and non homogeneous with constant coefficients and applications, Euler Cauchy and Power series solutions.
3. Higher Order ODEs - homogeneous and non homogeneous with constant coefficients and Euler-Cauchy.
4. 2D linear constant coefficient homogeneous systems, phase plane, critical points and criteria for critical points.
5. Laplace Transforms and solving ODEs using Laplace transforms.
6. Level curves and sketching regions in space
7. Limits and continuity of functions of two variables
8. Partial differentiation
9. Chain rule
10. Gradient vectors and directional derivatives
11. Equations of normal lines and tangent planes
12. Maxima, minima and saddle points
13. Lagrange multipliers
14. Double integrals in rectangular and polar coordinates and applications
15. Triple integrals in rectangular, cylindrical and spherical coordinates and applications
15. Triple integrals in rectangular, cylindrical and spherical coordinates and applications.

## Assessment

The following table summarises the standard assessment tasks for this subject. Please note this is a guide only. Assessment tasks are regularly updated, where there is a difference your Learning Guide takes precedence.

Type Length Percent Threshold Individual/Group Task
Quiz 30 minutes per quiz 10 N Individual
Intra-session Exam 60 minutes 20 N Individual
Intra-session Exam 60 minutes 20 N Individual
Final Exam 120 minutes 50 Y Individual

### Summer On-site

The following table summarises the standard assessment tasks for this subject. Please note this is a guide only. Assessment tasks are regularly updated, where there is a difference your Learning Guide takes precedence.

Type Length Percent Threshold Individual/Group Task
Numerical Problem Solving 60 minutes 20 N Individual
Numerical Problem Solving 60 minutes 20 N Individual
Final Exam 120 minutes 50 Y Individual
Quiz 30 minutes (per quiz) 10 N Individual

Teaching Periods

## Autumn (2024)

### Penrith (Kingswood)

#### On-site

Subject Contact Wei Xing Zheng Opens in new window

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### Parramatta - Victoria Rd

#### On-site

Subject Contact Wei Xing Zheng Opens in new window

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## Sydney City Campus - Term 1 (2024)

### Sydney City

#### On-site

Subject Contact Peter Lendrum Opens in new window

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## Sydney City Campus - Term 2 (2024)

### Sydney City

#### On-site

Subject Contact Peter Lendrum Opens in new window

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## Spring (2024)

### Penrith (Kingswood)

#### On-site

Subject Contact Wei Xing Zheng Opens in new window

View timetable Opens in new window

### Parramatta - Victoria Rd

#### On-site

Subject Contact Wei Xing Zheng Opens in new window

View timetable Opens in new window

## Sydney City Campus - Term 3 (2024)

### Sydney City

#### On-site

Subject Contact Peter Lendrum Opens in new window

View timetable Opens in new window

## Summer (2024)

### Parramatta City - Macquarie St

#### On-site

Subject Contact Wei Xing Zheng Opens in new window

View timetable Opens in new window