# Calculus of Science and Engineering

Course code MATH2310
Available in 2016

## Description

Provides the essential mathematical techniques of Physical Science and Engineering. These are the methods of Multivariable Calculus and Differential Equations. Multivariable Calculus involves a study of the differential and integral calculus of functions of two or more variables. In particular it covers introductory material on the differential calculus of scalar and vector fields, and the integral calculus of scalar and vector functions. Differential Equations arise from mathematical models of physical processes. Also includes the study of the main analytical and numerical methods for obtaining solutions to first and second order differential equations. The course also introduces students to the use of mathematical software in the investigation of problems in multivariable calculus and differential equations.

### Availability

#### Callaghan

• Semester 1 - 2016
• Semester 2 - 2016
• Semester 1 - 2017
• Semester 2 - 2017

#### UoN Singapore

• Trimester 2 - 2016 (Singapore)
• Trimester 2 - 2017 (Singapore)

### Learning Outcomes

On successful completion of the course students will be able to:

1. Demonstrate a sound grounding in the differentiation and integration of functions of several variables and in the methods of solution of ordinary differential equations.

2. Demonstrate skills in solving a range of mathematical problems involving functions of many variables.

3. Demonstrate basic skills in modelling real world problems involving multivariable calculus and ordinary differential equations, and in interpreting their solutions as they relate to the original problem.

4. Demonstrate skills in the application of computer software in the exploration of mathematical systems and in the solution of real-world problems relevant to the content of the course.

### Content

• Real valued functions of several variables.
• The differential operator "del".
• Cylindrical and spherical coordinates.
• General curves and surfaces.
• Normals, tangents and tangent planes.
• Double integrals.
• Iterated integrals.
• Triple integrals.
• Line integrals.
• Surface integrals.
• Vector valued functions.
• Divergence and Curl.
• Line integrals of vector fields.
• Green's theorem.
• Stokes' theorem.
• Divergence theorem.
• Formulation of differential equations for simple physical processes.
• Finding solutions to first order separable and linear differential equations.
• Interpreting solutions for first order differential equations using appropriate software.
• Solving linear second order differential equations with constant coefficients, with applications.
• Finding numerical solutions using Runge-Kutta methods via computer software.
• Laplace transform methods for initial value problems.
• Solving second order initial value problems with step function forcing terms.
• Power series solutions to second order differential equations.
• Boundary-value problems for partial differential equations.

### Assumed Knowledge

MATH1120 or MATH1220

### Assessment Items

Quiz: Quiz - Class

Tutorial / Laboratory Exercises: Laboratory Workshop Exercises

Formal Examination: Examination

Online Learning Activity: Homework - Online assessment

In Term Test: Mid Semester Test

### Contact Hours

#### Callaghan and UoN Singapore

##### Lecture

Face to Face On Campus 4 hour(s) per Week for Full Term

Students enrolled in the part-time evening program at UoN Singapore will receive equivalent instruction delivered in a block mode of 7 teaching weeks. Some tutorials will be conducted in a computer laboratory.

##### Workshop

Face to Face On Campus 11.5 hour(s) per Term

1.5 hour workshops for weeks 2, 3, 6, 7, 10, 11 and 12 and 1 hour tutorials for weeks 4, 5, 8, and 9. Week 6 will consist of an In Term Test.