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  2. Calculus 1 [MAT1236]

School: Science

This unit information may be updated and amended immediately prior to semester. To ensure you have the correct outline, please check it again at the beginning of semester.

  • Unit Title

    Calculus 1

  • Unit Code

    MAT1236

  • Year

    2018

  • Enrolment Period

    1

  • Version

    3

  • Credit Points

    15

  • Full Year Unit

     N

  • Mode of Delivery

    On Campus

  • Unit Coordinator

    Dr Steven James RICHARDSON

Description

This unit is intended for students who already have a basic level of understanding of differential and integral calculus and its applications. Students will be introduced to more advanced techniques of calculus and its application required for foundational study in engineering and applied science. Although students with ATAR Mathematics Methods will be given the option to enroll directly into MAT1236 Calculus 1 they need to be aware that they will not have all of the assumed knowledge if they have not completed ATAR Mathematics Specialist. To cover this content gap, students will be provided with bridging material on the unit Blackboard site. Students who are not mathematically strong (e.g. who do not have a mark of at least 70% in ATAR Mathematics Methods), or who struggle with the essential skills exercises, are encouraged to enroll in MAT1137 Introductory Applied Mathematics before progressing to MAT1236 in a later semester.

Prerequisite Rule

Students must have passed MAT1137 or must have a scaled score >49.99 in ATAR Mathematics Methods or ATAR Mathematics Specialist or WACE MAT3C/3D or equivalent.

Learning Outcomes

On completion of this unit students should be able to:

  1. Apply appropriate differentiation and integration techniques to solve applied problems.
  2. Communicate their understanding of concepts, and explain their solutions to problems involving the application of calculus techniques, in a coherent written form.
  3. Demonstrate competence in differentiation of implicit, inverse and hyperbolic functions.
  4. Demonstrate competence in vector calculus and its application to curvilinear motion.
  5. Demonstrate competence incomplex arithmetic.
  6. Identify and apply appropriate integration techniques.
  7. Identify key features of functions of two variables, evaluate partial derivatives, and apply optimisation techniques in applied problems.
  8. Solve first order separable and linear differential equations in both abstract and applied contexts.
  9. Utilise Fourier and Taylor series in approximating functions.

Unit Content

  1. Applied Calculus - Utilise techniques for differentiation and integration and solving differential equations in applied contexts.
  2. Calculus - Review of derivatives and differentiability; implicit differentiation; derivatives of parametric equations; inverse trigonometric functions and their derivatives; hyperbolic functions and their derivatives; review of integration and the fundamental theorem of calculus; trigonometric integrals; integration by substitution, by parts, by completing the square and by partial fractions; improper integrals; integration using tables.
  3. Complex numbers - Definition of 'i'; complex solutions of quadratics; complex plane; Cartesian form (addition, subtraction, multiplication and division); polar form (multiplication and division); conjugates (properties and location in complex plane); reciprocal of non-zero complex number; defining regions of the complex plane with equations and inequalities; De Moivres's theorem; solutions of z^n=C in the complex plane; Euler's formula.
  4. Differential Equations - First order separable differential equations; first order linear differential equations; applications.
  5. Functions - Review of Algebra, review of functions (domain, range, composition, exponentials and logarithms); inverse functions; limits and continuity; piece-wise defined functions; L'Hopitals rule.
  6. Functions of Several Variables - Domain and range; partial derivatives; critical points and classification; maxima and minima (second derivative test); optimisation.
  7. Series - Taylor series approximations of functions; Fourier series approximations to functions; differentiation and integration of series.
  8. Vector Calculus - Vector functions (domain and range); differentiation and integration; curvilinear motion.

Learning Experience

Students will attend on campus classes as well as engage in learning activities through ECU Blackboard.

JoondalupMount LawleySouth West (Bunbury)
Semester 113 x 2 hour lectureNot Offered13 x 2 hour lecture
Semester 213 x 2 hour lectureNot OfferedNot Offered

For more information see the Semester Timetable

Additional Learning Experience Information

Lectures and tutorials.

Assessment

GS1 GRADING SCHEMA 1 Used for standard coursework units

Students please note: The marks and grades received by students on assessments may be subject to further moderation. All marks and grades are to be considered provisional until endorsed by the relevant Board of Examiners.

ON CAMPUS
TypeDescriptionValue
Exercise ^Essential skills exercises5%
ExercisePractice exercises10%
AssignmentProblem solving assignment10%
TestIn-semester test25%
Examination ^End of semester exam50%

^ Mandatory to Pass

Disability Standards for Education (Commonwealth 2005)

For the purposes of considering a request for Reasonable Adjustments under the Disability Standards for Education (Commonwealth 2005), inherent requirements for this subject are articulated in the Unit Description, Learning Outcomes and Assessment Requirements of this entry. The University is dedicated to provide support to those with special requirements. Further details on the support for students with disabilities or medical conditions can be found at the Access and Inclusion website.

Academic Misconduct

Edith Cowan University has firm rules governing academic misconduct and there are substantial penalties that can be applied to students who are found in breach of these rules. Academic misconduct includes, but is not limited to:

  • plagiarism;
  • unauthorised collaboration;
  • cheating in examinations;
  • theft of other students' work;

Additionally, any material submitted for assessment purposes must be work that has not been submitted previously, by any person, for any other unit at ECU or elsewhere.

The ECU rules and policies governing all academic activities, including misconduct, can be accessed through the ECU website.

MAT1236|3|1

School: Science

This unit information may be updated and amended immediately prior to semester. To ensure you have the correct outline, please check it again at the beginning of semester.

  • Unit Title

    Calculus 1

  • Unit Code

    MAT1236

  • Year

    2018

  • Enrolment Period

    2

  • Version

    3

  • Credit Points

    15

  • Full Year Unit

     N

  • Mode of Delivery

    On Campus

  • Unit Coordinator

    Dr Steven James RICHARDSON

Description

This unit is intended for students who already have a basic level of understanding of differential and integral calculus and its applications. Students will be introduced to more advanced techniques of calculus and its application required for foundational study in engineering and applied science. Although students with ATAR Mathematics Methods will be given the option to enroll directly into MAT1236 Calculus 1 they need to be aware that they will not have all of the assumed knowledge if they have not completed ATAR Mathematics Specialist. To cover this content gap, students will be provided with bridging material on the unit Blackboard site. Students who are not mathematically strong (e.g. who do not have a mark of at least 70% in ATAR Mathematics Methods), or who struggle with the essential skills exercises, are encouraged to enroll in MAT1137 Introductory Applied Mathematics before progressing to MAT1236 in a later semester.

Prerequisite Rule

Students must have passed MAT1137 or must have a scaled score >49.99 in ATAR Mathematics Methods or ATAR Mathematics Specialist or WACE MAT3C/3D or equivalent.

Learning Outcomes

On completion of this unit students should be able to:

  1. Apply appropriate differentiation and integration techniques to solve applied problems.
  2. Communicate their understanding of concepts, and explain their solutions to problems involving the application of calculus techniques, in a coherent written form.
  3. Demonstrate competence in differentiation of implicit, inverse and hyperbolic functions.
  4. Demonstrate competence in vector calculus and its application to curvilinear motion.
  5. Demonstrate competence incomplex arithmetic.
  6. Identify and apply appropriate integration techniques.
  7. Identify key features of functions of two variables, evaluate partial derivatives, and apply optimisation techniques in applied problems.
  8. Solve first order separable and linear differential equations in both abstract and applied contexts.
  9. Utilise Fourier and Taylor series in approximating functions.

Unit Content

  1. Applied Calculus - Utilise techniques for differentiation and integration and solving differential equations in applied contexts.
  2. Calculus - Review of derivatives and differentiability; implicit differentiation; derivatives of parametric equations; inverse trigonometric functions and their derivatives; hyperbolic functions and their derivatives; review of integration and the fundamental theorem of calculus; trigonometric integrals; integration by substitution, by parts, by completing the square and by partial fractions; improper integrals; integration using tables.
  3. Complex numbers - Definition of 'i'; complex solutions of quadratics; complex plane; Cartesian form (addition, subtraction, multiplication and division); polar form (multiplication and division); conjugates (properties and location in complex plane); reciprocal of non-zero complex number; defining regions of the complex plane with equations and inequalities; De Moivres's theorem; solutions of z^n=C in the complex plane; Euler's formula.
  4. Differential Equations - First order separable differential equations; first order linear differential equations; applications.
  5. Functions - Review of Algebra, review of functions (domain, range, composition, exponentials and logarithms); inverse functions; limits and continuity; piece-wise defined functions; L'Hopitals rule.
  6. Functions of Several Variables - Domain and range; partial derivatives; critical points and classification; maxima and minima (second derivative test); optimisation.
  7. Series - Taylor series approximations of functions; Fourier series approximations to functions; differentiation and integration of series.
  8. Vector Calculus - Vector functions (domain and range); differentiation and integration; curvilinear motion.

Learning Experience

Students will attend on campus classes as well as engage in learning activities through ECU Blackboard.

JoondalupMount LawleySouth West (Bunbury)
Semester 113 x 2 hour lectureNot Offered13 x 2 hour lecture
Semester 213 x 2 hour lectureNot OfferedNot Offered

For more information see the Semester Timetable

Additional Learning Experience Information

Lectures and tutorials.

Assessment

GS1 GRADING SCHEMA 1 Used for standard coursework units

Students please note: The marks and grades received by students on assessments may be subject to further moderation. All marks and grades are to be considered provisional until endorsed by the relevant Board of Examiners.

ON CAMPUS
TypeDescriptionValue
Exercise ^Essential skills exercises5%
ExercisePractice exercises10%
AssignmentProblem solving assignment10%
TestIn-semester test25%
Examination ^End of semester exam50%

^ Mandatory to Pass

Disability Standards for Education (Commonwealth 2005)

For the purposes of considering a request for Reasonable Adjustments under the Disability Standards for Education (Commonwealth 2005), inherent requirements for this subject are articulated in the Unit Description, Learning Outcomes and Assessment Requirements of this entry. The University is dedicated to provide support to those with special requirements. Further details on the support for students with disabilities or medical conditions can be found at the Access and Inclusion website.

Academic Misconduct

Edith Cowan University has firm rules governing academic misconduct and there are substantial penalties that can be applied to students who are found in breach of these rules. Academic misconduct includes, but is not limited to:

  • plagiarism;
  • unauthorised collaboration;
  • cheating in examinations;
  • theft of other students' work;

Additionally, any material submitted for assessment purposes must be work that has not been submitted previously, by any person, for any other unit at ECU or elsewhere.

The ECU rules and policies governing all academic activities, including misconduct, can be accessed through the ECU website.

MAT1236|3|2