Calculus and Applications
Duration
- One Semester or equivalent
Contact hours
- 60 hours
On-campus unit delivery combines face-to-face and digital learning.
2022 teaching periods
| Hawthorn Higher Ed. Semester 1 |
Hawthorn Higher Ed. Semester 2 | |
|---|---|---|
Dates: Results: Last self enrolment: Census: Last withdraw without fail: |
Dates: Results: Last self enrolment: Census: Last withdraw without fail: |
Prerequisites
Assumed KnowledgeAims and objectives
Offered from 2017
Students who successfully complete this unit will be able to:
2. Apply the induction principle and basic inequalities to verify important relations (K2).
3. Determine the convergence or divergence of sequences. Determine limits of functions of one variable (K2).
4. Determine first and higher order derivatives of functions of one variable. Determine the derivatives of inverse functions of one variable and apply implicit differentiation. Use differentiation for detailed graph drawing of relevant functions. Apply differentiation to determine rates of change, derivation of Taylor polynomials and correct use of de l’Hopital’s rule (K2).
5. Determine indefinite and definite integrals of basic trigonometric, hyperbolic, rational and other functions of one variable, using partial fractions, substitutions and integration by parts. Apply these concepts to evaluate the area under and between curves, arc lengths, volumes of solids of revolution and other examples (K2, S1).
6. Determine the solution to first order separable differential equations and linear differential equations using an integrating factor. Determine the solution to second order homogeneous and non homogeneous linear differential equations with constant coefficients. Apply these methods to simple, fundamental equations (K2, S1).
7. Determine partial derivatives of functions of more than one variable and stationary points (K2).
Unit information in detail
- Teaching methods, assessment, general skills outcomes and content.
Teaching methods
Assessment
| Types | Individual or Group task | Weighting | Assesses attainment of these ULOs |
| Online Assignments | Individual | 15-20% | 1, 2, 3, 4, 5, 6, 7 |
| Test 1 | Individual | 10-15% | 1, 2, 3 and (part of 4) |
| Test 2 | Individual | 10-15% | 4, 5 and (part of) 6 |
| Examination | Individual | 50-60% | 1, 2, 3, 4, 5, 6, 7 |
General skills outcomes
During this unit students will receive feedback on the following key generic skills:
- K2 Maths and IT as Tools: Proficiently uses relevant mathematics and computer science and information science concepts as tools.
- S1 Engineering Methods: Applies engineering methods in practical applications.
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
- Text books, recommended reading and references.
Text books
Recommended reading
The Library has a large collection of resource materials, both texts and current journals. Listed below are some references that will provide valuable supplementary information to this unit.
Croft, A. & Davison, R. (2008). Mathematics for Engineers: A Modern Interactive Approach, 3rd Edn,
Prentice Hall.
James, G. (2010). Modern Engineering Mathematics, 4th Edn, Prentice Hall.
Stroud, K.A. &
Booth, D.J. (2007). Engineering Mathematics, 6th Edn, Industrial Press.
Thomas, G.B., Weir, M.D. & Hass, J. (2009). Thomas’ Calculus, 12th Edn, Addison Wesley.
References
MTH10012 Calculus and Application, Study Guide 2017 (also available on Blackboard, posted under Learning Material).
Texas Instruments 30XB MultiView Calculator. Note that this is the only calculator permitted to be used in some of the assessments in this unit and these assessments will be set on the assumption that students have such a calculator.