MATHS 2101 - Multivariable & Complex Calculus II

North Terrace Campus - Semester 1 - 2021

The mathematics required to describe most "real life" systems involves functions of more than one variable, so the differential and integral calculus developed in a first course in Calculus must be extended to functions of more variables. In this course, the key results of one-variable calculus are extended to higher dimensions: differentiation, integration, and the link between them provided by the Fundamental Theorem of Calculus are all generalised. The machinery developed can be applied to another generalisation of one-variable Calculus, namely to complex calculus, and the course also provides an introduction to this subject. The material covered in this course forms the basis for mathematical analysis and application across an extremely broad range of areas, essential for anyone studying the hard sciences, engineering, or mathematical economics/finance. Topics covered are: introduction to multivariable calculus; differentiation of scalar- and vector-valued functions; higher-order derivatives, extrema, Lagrange multipliers and the implicit function theorem; integration over regions, volumes, paths and surfaces; Green's, Stokes' and Gauss's theorems; differential forms; curvilinear coordinates; an introduction to complex numbers and functions; complex differentiation; complex integration and Cauchy's theorems; and conformal mappings.

  • General Course Information
    Course Details
    Course Code MATHS 2101
    Course Multivariable & Complex Calculus II
    Coordinating Unit School of Mathematical Sciences
    Term Semester 1
    Level Undergraduate
    Location/s North Terrace Campus
    Units 3
    Contact Up to 3.5 hours per week
    Available for Study Abroad and Exchange Y
    Prerequisites MATHS 1012
    Incompatible MATHS 2202, ELEC ENG 2106
    Course Description The mathematics required to describe most "real life" systems involves functions of more than one variable, so the differential and integral calculus developed in a first course in Calculus must be extended to functions of more variables. In this course, the key results of one-variable calculus are extended to higher dimensions: differentiation, integration, and the link between them provided by the Fundamental Theorem of Calculus are all generalised. The machinery developed can be applied to another generalisation of one-variable Calculus, namely to complex calculus, and the course also provides an introduction to this subject. The material covered in this course forms the basis for mathematical analysis and application across an extremely broad range of areas, essential for anyone studying the hard sciences, engineering, or mathematical economics/finance.

    Topics covered are: introduction to multivariable calculus; differentiation of scalar- and vector-valued functions; higher-order derivatives, extrema, Lagrange multipliers and the implicit function theorem; integration over regions, volumes, paths and surfaces; Green's, Stokes' and Gauss's theorems; differential forms; curvilinear coordinates; an introduction to complex numbers and functions; complex differentiation; complex integration and Cauchy's theorems; and conformal mappings.
    Course Staff

    Course Coordinator: Associate Professor Sanjeeva Balasuriya

    Course Timetable

    The full timetable of all activities for this course can be accessed from Course Planner.

  • Learning Outcomes
    Course Learning Outcomes
    1. Demonstrate understanding of the basic concepts of calculus involving more than one real variable.
    2. Demonstrate understanding of the basic concepts of calculus for one complex variable.
    3. Be able to state and apply the major results in the course.
    4. Apply the theory in the course to solve a variety of problems at an appropriate level of difficulty.
    5. Demonstrate skills in communicating mathematics orally and in writing.
    University Graduate Attributes

    This course will provide students with an opportunity to develop the Graduate Attribute(s) specified below:

    University Graduate Attribute Course Learning Outcome(s)
    Deep discipline knowledge
    • informed and infused by cutting edge research, scaffolded throughout their program of studies
    • acquired from personal interaction with research active educators, from year 1
    • accredited or validated against national or international standards (for relevant programs)
    all
    Critical thinking and problem solving
    • steeped in research methods and rigor
    • based on empirical evidence and the scientific approach to knowledge development
    • demonstrated through appropriate and relevant assessment
    all
    Teamwork and communication skills
    • developed from, with, and via the SGDE
    • honed through assessment and practice throughout the program of studies
    • encouraged and valued in all aspects of learning
    3,5
    Career and leadership readiness
    • technology savvy
    • professional and, where relevant, fully accredited
    • forward thinking and well informed
    • tested and validated by work based experiences
    5
    Self-awareness and emotional intelligence
    • a capacity for self-reflection and a willingness to engage in self-appraisal
    • open to objective and constructive feedback from supervisors and peers
    • able to negotiate difficult social situations, defuse conflict and engage positively in purposeful debate
    5
  • Learning Resources
    Required Resources
    • Textbook: Multivariable and Complex Calculus, Matt Finn and Sanjeeva Balasuriya, University of Adelaide (2021).
    • Purpose built video lecture recordings for each section of the textbook.
    Both these primary learning resources will be made available to enrolled students via the course's MyUni page.
    Recommended Resources
      • External videos relevant to the course material. 

      Links to these will be provided via the course's MyUni page.
      Online Learning
      This course uses MyUni exclusively for providing electronic resources, such as the textbook, videoed lectures, tutorial questions, assignments, sample solutions, quizzes (for self-testing) discussion boards, sample test/examination etc. Students must make appropriate use of all these resources to succeed in this course.
    1. Learning & Teaching Activities
      Learning & Teaching Modes
      Course delivery will occur on a weekly timetable.  Each week typically consists of a variety of learning activities.  All asynchronous activities/resources will be released at the beginning of each week, to enable students to personalise their schedules.  Weekly tasks include:
      • Reading the relevant sections of the textbookViewing video-recorded lecture material which complements rather than mimics the textbook.
      • Participation in a synchronous scheduled (face-to-face or remote) tutorial session, which is designed for active learning.
      • Attempting the extra practice problems which are released with the tutorial sheets.
      • Reviewing whether the learning outcomes -- listed at the end of each relevant section in the textbook -- have been achieved.
      • Completing a short online quiz to strengthen understanding of the relevant weekly material.
      • Review released solutions from the previous week's tutorial questions.
      • Attend the online consulting sessions as necessary, particularly if the student is having difficulty in achieving the learning outcomes.
      The Weekly Tasks are designed to provide complementary activities which carefully work with each other in helping students achieve the learning outcomes for the relevant sections for each week.  The design ensures that each student has the opportunity to take responsibility for their own learning.  
      Workload

      The information below is provided as a guide to assist students in engaging appropriately with the course requirements.


      Activity Quantity Workload Hours
      Engaging with the written (textbook) and oral/visual (lecture recordings) course material 88
      Tutorials and Practice Problems 11 22
      Quizzes 10 5
      Assignments 5 10
      Revising and studying 31
      Total 156
      Learning Activities Summary
      The learning activities are centred around the course content, given below in terms of the relevant chapters of the textbook:
      1. Functions of many variables: preliminaries
      2. Differentiation of multivariable functions
      3. Integration of multivariable functions
      4. Fundamental theorems of multivariable calculus
      5. Complex calculus
      Each chapter has sections, which are the basis for partitioning the course material.The weekly task schedule (with each week consisting of reading the textbook, viewing lecture recordings, participating in active tutorials, completing the online quiz questions for self-learning, reviewing practice problems, etc) is approximately as follows:


      • Week 1:  Course introduction, Section 1.1
      • Week 2:  Sections 1.2, 2.1
      • Week 3: Sections 2.2, 2.3
      • Week 4: Sections 2.4, 2.5
      • Week 5: Sections 2.6, 3.1
      • Week 6: Sections 3.2, 3.3
      • Week 7: Section 3.4
      • Week 8: Sections 3.5, 4.1
      • Week 9: Sections 4.2, 4.3
      • Week 10: Sections 5.1, 5.2
      • Week 11: Sections 5.3, 5.4
      • Week 12: Section 5.5
      • Week 13: No new material, Course Review and Examination Preparation
      Small Group Discovery Experience
      In the tutorials.
    2. Assessment

      The University's policy on Assessment for Coursework Programs is based on the following four principles:

      1. Assessment must encourage and reinforce learning.
      2. Assessment must enable robust and fair judgements about student performance.
      3. Assessment practices must be fair and equitable to students and give them the opportunity to demonstrate what they have learned.
      4. Assessment must maintain academic standards.

      Assessment Summary

      Assessment Task type Due Weighting Learning outcomes
      Final Examination Summative Final Examination period 45% All
      Mid-semester Test Summative and Formative Week 8 20% All
      Quizzes (10) Summative and Formative End of Weeks 2, 3, 4, 5, 6, 8, 9, 10, 11, 12 10% All
      Assignments (5) Summative and Formative Weeks 3, 5, 8, 10, 12 25% All
      Assessment Detail
      Assessment Item Distributed Due Weighting
      Quiz 1 Week 2 End of Week 2 1%
      Quiz 2 Week 3 End of Week 3 1%
      Quiz 3 Week 4 End of Week 4 1%
      Quiz 4 Week 5 End of Week 5 1%
      Quiz 5 Week 6 End of Week 6 1%
      Quiz 6 Week 8 End of Week 8 1%
      Quiz 7 Week 9 End of Week 9 1%
      Quiz 8 Week 10 End of Week 10 1%
      Quiz 9 Week 11 End of Week 11 1%
      Quiz 10 Week 12 End of Week 12 1%
      Assignment 1 Week 2 Week 3 5%
      Assignment 2 Week 4 Week 5 5%
      Assignment 3 Week 7 Week 8 5%
      Assignment 4 Week 9 Week 10 5%
      Assignment 5 Week 11 Week 12 5%
      Mid-semester Test Week 8 20%
      The Mid-semester Test will be held synchronously for all students at the specified time which has been set aside on your timetable for this course.   By enrolling in this course, students are signalling their commitment to be available at this time, and must take the test at this time.
      Submission
      All submissions are to be done using MyUni, following the relevant instructions.  Submission deadline will be strictly adhered to.

      1. Any delay in assignment submissions will attract penalties. 
      2. Quizzes not completed by the due time will not be accepted by the system.
      3. The Mid-semester Test must also be strictly completed by the due time.


      Course Grading

      Grades for your performance in this course will be awarded in accordance with the following scheme:

      M10 (Coursework Mark Scheme)
      Grade Mark Description
      FNS   Fail No Submission
      F 1-49 Fail
      P 50-64 Pass
      C 65-74 Credit
      D 75-84 Distinction
      HD 85-100 High Distinction
      CN   Continuing
      NFE   No Formal Examination
      RP   Result Pending

      Further details of the grades/results can be obtained from Examinations.

      Grade Descriptors are available which provide a general guide to the standard of work that is expected at each grade level. More information at Assessment for Coursework Programs.

      Final results for this course will be made available through Access Adelaide.

    3. Student Feedback

      The University places a high priority on approaches to learning and teaching that enhance the student experience. Feedback is sought from students in a variety of ways including on-going engagement with staff, the use of online discussion boards and the use of Student Experience of Learning and Teaching (SELT) surveys as well as GOS surveys and Program reviews.

      SELTs are an important source of information to inform individual teaching practice, decisions about teaching duties, and course and program curriculum design. They enable the University to assess how effectively its learning environments and teaching practices facilitate student engagement and learning outcomes. Under the current SELT Policy (http://www.adelaide.edu.au/policies/101/) course SELTs are mandated and must be conducted at the conclusion of each term/semester/trimester for every course offering. Feedback on issues raised through course SELT surveys is made available to enrolled students through various resources (e.g. MyUni). In addition aggregated course SELT data is available.

    4. Student Support
    5. Policies & Guidelines
    6. Fraud Awareness

      Students are reminded that in order to maintain the academic integrity of all programs and courses, the university has a zero-tolerance approach to students offering money or significant value goods or services to any staff member who is involved in their teaching or assessment. Students offering lecturers or tutors or professional staff anything more than a small token of appreciation is totally unacceptable, in any circumstances. Staff members are obliged to report all such incidents to their supervisor/manager, who will refer them for action under the university's student’s disciplinary procedures.

    The University of Adelaide is committed to regular reviews of the courses and programs it offers to students. The University of Adelaide therefore reserves the right to discontinue or vary programs and courses without notice. Please read the important information contained in the disclaimer.