MATH251-17A (HAM)

Multivariable Calculus

10 Points

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Faculty of Computing and Mathematical Sciences
Rorohiko me ngā Pūtaiao Pāngarau
Department of Mathematics and Statistics

Staff

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Convenor(s)

Woei Chet Lim

Woei Chet Lim
5148
G.3.05
To be advised
wclim@waikato.ac.nz

Lecturer(s)

Woei Chet Lim

Woei Chet Lim
5148
G.3.05
To be advised
wclim@waikato.ac.nz

Administrator(s)

Placement Coordinator(s)

Tutor(s)

Student Representative(s)

Lab Technician(s)

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You can contact staff by:

  • Calling +64 7 838 4466 select option 1, then enter the extension.
  • Extensions starting with 4, 5 or 9 can also be direct dialled:
    • For extensions starting with 4: dial +64 7 838 extension.
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Paper Description

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These papers extend the one–variable calculus from MATH101 Introduction to Calculus to the calculus of functions of more than one variable. Many of the topics covered provide a synthesis of calculus and geometry (from MATH102). The mathematics studied is of fundamental and equal importance to engineers and non-engineers. Therefore, MATH251 and ENGG285 are substantially the same. Some of the examples and assessment items will differ, to reflect the different slant on the material for the two groups of students.

Both papers are worth 10 points.

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Paper Structure

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Three contact hours per week -- roughly 2.5 lectures and 0.5 tutorial.
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Learning Outcomes

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Students who successfully complete the course should be able to:

  • 1. Compute the tangent line, arc length and work integrals over a parametrized curve.

    2. Calculate the gradient vector of a multivariable function, and apply the chain rule.

    3. Calculate the Taylor expansion of a multivariable function.

    4. Solve unconstrained and equality constrained optimization problems in up to three variables.

    5. Compute multivariable integrals (in Cartesian and polar coordinates).

    6. Use integration to compute volumes and moments of solid bodies.

    Linked to the following assessments:
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Assessment

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The internal assessment:final examination ratio is 1:1.

The internal assessment will consist of FOUR assignments (worth 2.5% each) and TWO tests (worth 20% each).

Assignments should be submitted via the slot under the G.3.19 Mathematics Reception counter.

Assignment due dates:

Assignment 1: Wednesday 15 March 3pm SHARP

Assignment 2: Wednesday 5 April 3pm SHARP

Assignment 3: Wednesday 10 May 3pm SHARP

Assignment 4: Wednesday 31 May 3pm SHARP

LATE assignments WILL NOT be accepted (any time after 3pm is considered late).

TESTS will be held as follows:

Thursday 27 April 6:30-7:30pm in PWC

Tuesday 23 May 6:30-7:30pm in PWC

An unrestricted pass will be awarded only to students who achieve both a final mark of at least 50% AND an examination mark of at least 40%.

The time, date and place of the FINAL examination will be arranged by the University.

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Assessment Components

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The internal assessment/exam ratio (as stated in the University Calendar) is 1:1. There is no final exam. The final exam makes up 50% of the overall mark.

The internal assessment/exam ratio (as stated in the University Calendar) is 1:1 or 0:0, whichever is more favourable for the student. The final exam makes up either 50% or 0% of the overall mark.

Component DescriptionDue Date TimePercentage of overall markSubmission MethodCompulsory
1. 4x Assignments (2.5% each)
10
2. Test 1
20
3. Test 2
20
4. Exam
50
✔
Assessment Total:     100    
Failing to complete a compulsory assessment component of a paper will result in an IC grade
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Required and Recommended Readings

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Recommended Readings

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RECOMMENDED TEXTBOOKS (available in the University Library)

Calculus by James Stewart.

Thomas’ Calculus by George B. Thomas Jr. et al.

Calculus with analytic geometry by G.F. Simmons.

Calculus gems by G.F. Simmons.

For ENGINEERING students:

Modern Engineering Mathematics by Glyn James.

Advanced Engineering Mathematics by Peter O'Neil.

Engineering Mathematics by Stroud & Booth.

Advanced Engineering Mathematics by Stroud.

Advanced Engineering Mathematics by Kreyszig.

For PHYSICS students:

Mathematical Methods in the Physical Sciences by Mary L. Boas.

For PURE MATH students:

Calculus Vol. 2 by Tom M. Apostol.

Calculus on Manifolds by Michael Spivak.

Differential and Integral Calculus Vol. 2 by Richard Courant.

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Other Resources

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LECTURE NOTES

A PDF of these notes will be posted on Moodle - not available from Campus Printery.

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Online Support

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NOTICES, MOODLE AND RETURN OF ASSESSED WORK

All notices about this paper, as well as your internal assessment marks, will be posted on Moodle. Such notices are deemed to be official notifications. Please check frequently for any updates.

It is your responsibility to check your marks are entered correctly.

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Workload

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7 hours per week, including 3 contact hours.
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Linkages to Other Papers

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This paper is a prerequisite for MATH311 Advanced Calculus, MATH329 Topics in Applied Mathematics, MATH331 Methods in Applied Mathematics.
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Prerequisite(s)

Both MATH101 and MATH102

Corequisite(s)

Equivalent(s)

Restriction(s)

ENGG285

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