### Subject details

At the completion of this subject students will be able to:

1. sketch, differentiate and integrate functions and understand the application of these
2. solve differential equations and understand their derivation and basic application
3. solve higher order differential equations and understand how they arise in practice
4. test for convergence and sum series
5. derive series representation for basic functions using Taylor series
6. understand basics of vectors and matrices
7. understand matrix operations, eigenvalues and eigen vectors and applications in modelling
8. use level curves and level surfaces to represent functions of several variables
9. use partial derivatives to derive basic properties of function of several variables.
• Functions and differentiation revision
• Integration by parts, substitution and trigonometric substitution
• 1st-order differential equations and applications
• Complex numbers
• 2nd-order differential equations
• Infinite sequences and series
• Vectors and geometry in space
• Linear algebra for calculus
• Functions of several variables and partial derivatives
• Study resources

• Instructional methods

• Discussion forum/Discussion Board
• Standard Media
• Podcasting/Lecture capture
• Online materials

• Printable format materials

You must have successfully completed the following subject(s) before starting this subject:

MUR-MAS120-Applied Mathematics , or MON-MAT14

#### Others

Or equivalent of advanced high school calculus.

#### Special requirements

No special requirements

Calculus and matrix algebra form the basis of the mathematical knowledge required to model physical, environmental, biological and engineering systems and investigate their behaviour. This subject assumes an understanding of the basic topics and develops them further. Vector and matrix operations, determinants, inverses and eigenvalues will be considered along with differentiation, integration, sequences and series, differential equations, and introductory multivariable calculus. Applications will be considered, with computer algebra packages used to reduce tedious calculations and present results.

• Assignments x 5 (30%)
• Invigilated Exam (70%)

Textbook information is pending.

Textbook information is pending.