Calculus and Applications
Duration
- One Semester or equivalentThis unit will be delivered on-line in Semester 2 2020
Contact hours
- 84
On-campus unit delivery combines face-to-face and digital learning.
2023 teaching periods
| Hawthorn Higher Ed. Semester 2 |
||
|---|---|---|
Dates: Results: Last self enrolment: Census: Last withdraw without fail: |
Prerequisites
MTH00005 Applied Engineering MathematicsAims 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.
Unit Learning Outcomes (ULO)
Students who successfully complete this unit will be able to:
1. Apply general concepts of functions and graphs to polynomial, rational, exponential, logarithmic, trigonometric, hyperbolic functions of one variable, their inverses and compositions (K2).
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’Hôpital’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 Learning Outcomes (ULO)
Students who successfully complete this unit will be able to:
1. Apply general concepts of functions and graphs to polynomial, rational, exponential, logarithmic, trigonometric, hyperbolic functions of one variable, their inverses and compositions (K2).
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’Hôpital’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).
Courses with unit
Associate Degree of EngineeringUnit information in detail
- Teaching methods, assessment, general skills outcomes and content.
Teaching methods
*Scheduled face to face: Lectures (48 hours), Tutorials (12 hours), Workshop (24 hours)
*Scheduled synchronous online learning events (N/A)
Non-scheduled online learning events and activities (approx. 40-60 hours)
Non-scheduled learning events and activities including independent study (approx. 10-20 hours)
Assessment
Hawthorn
Type | Hours per week | Number of Weeks | Total |
Live Online Lecture |
2 |
12 |
24 |
On Campus Class |
1 | 12 | 12 |
On Campus Class | 2 | 12 | 24 |
Online Directed Online Learning and Independent Learning | 1 | 12 | 12 |
Unspecified Activities Independent Learning | 5.5 | 12 | 66 |
TOTAL | 150 hours |
General skills outcomes
During this unit students will receive feedback on the following key generic skills:
• Teamwork skills
• Analysis skills
• Problem solving skills
• Communication skills
• Ability to tackle unfamiliar problems
• Ability to work independently
• Teamwork skills
• Analysis skills
• Problem solving skills
• Communication skills
• Ability to tackle unfamiliar problems
• Ability to work independently
Content
• Prerequisites & Fundamental properties of functions. Induction principle and inequalities. Domain, image, composition, inversion and graphs.
• Introduction to sequences, convergence and divergence. Limits of sequences and functions. Fundamental limits and indeterminate forms.
• Continuity: definition, properties, graphing and examples.
• Differentiation of functions of one variable. Rules, properties, applications to derivatives.
• Integration of functions of one variable. Anti-differentiation, substitutions, integration by parts, partial fractions and applications.
• Differential equations. First order separable & linear differential equations, second order linear differential equations with homogenous /particular solutions.
• Functions of two and more variables. Partial and directional derivatives. Properties and stationary points of simple, important surfaces.
• Introduction to sequences, convergence and divergence. Limits of sequences and functions. Fundamental limits and indeterminate forms.
• Continuity: definition, properties, graphing and examples.
• Differentiation of functions of one variable. Rules, properties, applications to derivatives.
• Integration of functions of one variable. Anti-differentiation, substitutions, integration by parts, partial fractions and applications.
• Differential equations. First order separable & linear differential equations, second order linear differential equations with homogenous /particular solutions.
• Functions of two and more variables. Partial and directional derivatives. Properties and stationary points of simple, important surfaces.
Study resources
- Text books, recommended reading and references.
Text books
Recommended reading
References
A list of reading materials and/or required texts will be made available in the Unit Outline.