Calculus of Science and Engineering

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.

Learning Outcomes

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

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

3. 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. 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 Exercises
Formal Examination: Examination
Online Learning Activity: Homework - Online assessment