Calculus and Applications
Duration
- One Semester or equivalent
Contact hours
- 60 hours face to face + Blended
On-campus unit delivery combines face-to-face and digital learning.
2023 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
Aims and objectives
This unit of study aims to provide students with mathematical knowledge and skills needed to support their concurrent and subsequent engineering and science studies
Students who successfully complete this unit will be able to:
2. Apply the induction principle and basic inequalities to verify important propositions (K2)
3. Appraise and apply standard approaches for determining the existence of limits of sequences and functions, quantifying these as point values where appropriate (K2)
4. Apply techniques of differential calculus to functions of one variable, interpreting in the context of equations, graphs and real-world applications (K2)
5. Apply techniques of integral calculus to functions of one variable, interpreting in the context of equations, graphs and real world applications (K2, S1)
6. Formulate separable and linear differential equations in abstract and real-world settings, appraising and applying solution schemas in simple, fundamental equations (K2, S1)
Unit information in detail
- Teaching methods, assessment and content.
Teaching methods
Type | Hours per week | Number of Weeks | Total |
Face to Face Contact Lecture (2 x 2hr lectures) Tutorial | 4 1 | 12 12 | 48 12 |
Unspecified Learning Activities Independent Learning | 9.5 | 12 | 90 |
TOTAL | 150 hours |
Assessment
| Types | Individual or Group task | Weighting | Assesses attainment of these ULOs |
| Assignments | Individual | 15-20% | 1,2,3,4,5,6,7 |
| Test 1 | Individual | 10-15% | 1,2,3 |
| Test 2 | Individual | 10-15% | 3,4,5 |
| Examination | Individual | 50-60% | 1,2,3,4,5,6,7 |
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, text books, recommended reading and references.
Reading materials
Text books