Calculus and Applications
Overview
This unit of study aims to provide students with mathematical knowledge and skills needed to support their concurrent and subsequent engineering and science studies.
Requisites
Rule
Admission into a Bachelor of Engineering (Honours), Bachelor of Aviation or Bachelor of Science, and all related Professional or double degrees
OR
MTH00005 Applied Engineering Mathematics
OR
MTH00007 Preliminary Mathematics
Assumed Knowledge
A study score of at least 20 in VCE Units 3 and 4 Mathematical Methods, or equivalent
27-October-2024
Learning outcomes
Students who successfully complete this unit will be able to:
- Recognise algebraic and graphical forms of standard functions, convert between these forms and calculate their inverses and compositions (K2)
- Apply the induction principle and basic inequalities to verify important propositions (K2)
- Appraise and apply standard approaches for determining the existence of limits of sequences and functions, quantifying these as point values where appropriate (K2)
- Apply techniques of differential calculus to functions of one variable, interpreting in the context of equations, graphs and real-world applications (K2)
- Apply techniques of integral calculus to functions of one variable, interpreting in the context of equations, graphs and real world applications (K2, S1)
- Formulate separable and linear differential equations in abstract and real-world settings, appraising and applying solution schemas in simple, fundamental equations (K2, S1)
- Determine partial derivatives of functions of more than one variable and use these to identify and classify their stationary points (K2)
Teaching methods
Hawthorn
| Type | Hours per week | Number of weeks | Total (number of hours) |
|---|---|---|---|
| On-campus Lecture | 4.00 | 12 weeks | 48 |
| On-campus Class | 1.00 | 12 weeks | 12 |
| Unspecified Activities Independent Learning | 7.50 | 12 weeks | 90 |
| TOTAL | 150 |
Assessment
| Type | Task | Weighting | ULO's |
|---|---|---|---|
| Assignment | Individual | 15 - 20% | 1,2,3,4,5,6,7 |
| Examination | Individual | 50 - 60% | 1,2,3,4,5,6,7 |
| Test | Individual | 10 - 15% | 1,2,3 |
| Test | Individual | 10 - 15% | 3,4,5 |
Hurdle
As the minimum requirements of assessment to pass a unit and meet all ULOs to a minimum standard, an undergraduate student must have achieved:
(i) an aggregate mark of 50% or more, and(ii) at least 40% in the final exam.Students who do not successfully achieve hurdle requirement (ii) will receive a maximum of 45% as the total mark for the unit.
Content
- Overview of some prerequisites. The induction principle and some basic inequalities
- Fundamental properties of functions. Domain, image, composition, inversion and graph. Inverse trigonometric functions, hyperbolic functions and their inverses
- Introduction to sequences, convergence and divergence. Limits of sequences and functions: definition, meaning and properties. Fundamental limits and indeterminate forms
- Continuity: definition, properties, graphing and examples
- Differentiation of functions of one variable: rules, properties, inverse functions, implicit differentiation, applications to graphing of functions. Differentials, higher derivatives, rates of change, Taylor polynomials, de l’Hopital rule
- Integration of functions of one variable: anti-differentiation, properties, substitutions, integration by parts and partial fractions. Application to areas, volumes, arc lengths and other examples
- Differential equations: first order separable differential equations, first order linear differential equations, orthogonal trajectories, second order linear differential equations with constant coefficients and simple right hand sides. Applications to relevant, simple models
- Functions of two and more variables. Differentiation: partial and directional derivatives, higher derivatives, gradients and differentials. Properties and stationary points of simple, important surfaces
Study resources
Reading materials
A list of reading materials and/or required textbooks will be available in the Unit Outline on Canvas.