# Calculus II

Griffith University

## Course Description

Calculus II

• ### Host University

Griffith University

• ### Location

Gold Coast, Australia

Calculus

• ### Language Level

Taught In English

• ### Prerequisites

1201BPS Mathematics 1A and 1202BPS Mathematics 1B OR 1201SCG Linear Algebra and 1202SCG Calculus I.

• ### Course Level Recommendations

Upper

ISA offers course level recommendations in an effort to facilitate the determination of course levels by credential evaluators.We advice each institution to have their own credentials evaluator make the final decision regrading course levels.

### Hours & Credits

• Credit Points

10
• Recommended U.S. Semester Credits
3 - 4
• Recommended U.S. Quarter Units
4 - 6
• ### Overview

Course Description:
This course provides some of the essential mathematical techniques to mathematicians and physical scientists, and applies them to scientific problems. The course covers basic material on multiple integrals of scalar functions as well as line and surface integrals of vector fields, the theorems of Gauss, Green and Stokes, Fourier series and integrals. It also introduces some of the common partial differential equations of applied mathematics and methods of solution mostly based on separation of variables. It also covers some topics on ordinary differential equations.

Course Introduction
The course covers multiple integrals of scalar functions as well as line and surface integrals of vector fields, the theorems of Gauss, Green and Stokes. Some topics relating to the solution of ordinary differential equations are covered, and the partial derivative and partial differential equations are introducted. We look at some of the common partial differential equations of applied mathematics, and methods of solution mostly based on separation of variables. This leads us to consider the representation of functions using Fourier series and integrals.

Course Aims
This course provides some of the essential mathematical techniques to mathematicians, physical scientists and engineers, and applies them to scientific and engineering problems. It is a compulsory course for the Applied Mathematics major.

The course covers basic material on multiple integrals of scalar functions as well as line and surface integrals of vector fields, the theorems of Gauss, Green and Stokes, Fourier series and integrals. It also introduces some of the common partial differential equations of applied mathematics and methods of solution mostly based on separation of variables, and covers some topics on the solution of ordinary differential equations.

Learning Outcomes
After successfully completing this course you should be able to:

1  Evaluate 2 and 3 dimensional integrals of scalar functions in Cartesian and polar coordinates; Calculate partial derivatives for functions of more than one variable; Calculate and interpret the gradient of scalar functions; Evaluate line integrals of vector fields in 2D; State and use Green's theorem in 2D; Evaluate surface integrals involving vector fields in 2D and 3D; Calculate and interpret the divergence of a vector field in 2D and 3D; State and use Gauss's theorem in 2D and 3D; State Stokes's theorem in 3D.
2  Set up and solve simple systems of linear differential equations; Apply the power series method to appropriate first and second order ODEs.
3  Solve simultaneous first-order partial differential equations (PDEs); Understand the derivation of the 1D wave and diffusion equation; Solve the wave equation in 1D on infinite and finite intervals to match initial and boundary conditions; Use the method of separation of variables to find the separated solutions for linear PDEs; Match separated solutions to homogeneous boundary conditions;
4  Define and interpret Fourier series for periodic functions in 1D; Calculate the Fourier coefficients of appropriate periodic functions; Define and interpret Fourier integrals of functions in one dimension; State and use various theorems related to the evaluation of Fourier series and integrals; Define and manipulate the Dirac delta function in one dimension.

### Course Disclaimer

Courses and course hours of instruction are subject to change.

Eligibility for courses may be subject to a placement exam and/or pre-requisites.

Credits earned vary according to the policies of the students' home institutions. According to ISA policy and possible visa requirements, students must maintain full-time enrollment status, as determined by their home institutions, for the duration of the program.