## 15 Points

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

### Staff

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#### Lecturer(s)

: rachael.foote@waikato.ac.nz

#### Librarian(s)

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.
• For extensions starting with 5: dial +64 7 858 extension.
• For extensions starting with 9: dial +64 7 837 extension.
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### Paper Description

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These papers extend the one–variable calculus from MATHS101 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 MATHS102). The mathematics studied is of fundamental and equal importance to engineers and non-engineers. Therefore, MATHS201 and ENGEN201 are substantially the same, and share the same classroom during the first 8 weeks. During the last 4 weeks, the ENGEN201 stream is joined by MATHS203 class, and continues with Fourier series, PDEs, and systems of ODEs (used to be taught in ENGG284).

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### Paper Structure

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Five contact hours per week -- roughly 4 lectures and 1 tutorial.
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### Learning Outcomes

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Students who successfully complete the course should be able to:

• First 8 weeks:

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.

• Last 4 weeks:

7. Compute Fourier series.

8. Solve PDEs by the method of separation of variables.

9. Solve systems of ODEs.

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### Assessment

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

The internal assessment will consist of five assignments (worth 2% 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 25 July 3pm

Assignment 2: Wednesday 8 August 3pm

Assignment 3: Wednesday 5 September 3pm

Assignment 4: Wednesday 19 September 3pm

Assignment 5: Wednesday 3 October 3pm

Late assignments will not be accepted (any time after 3pm is considered late).

Tests will be held as follows:

Tuesday 4 September 6:15-8:00pm in PWC, ELT.G.01 and MSB.1.01

Tuesday 9 October 6:15-8:00pm in PWC, ELT.G.01 and MSB.1.05

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 3-hour final examination will be arranged by the University.

#### Assessment Components

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The internal assessment/exam ratio (as stated in the University Calendar) is 50:50. 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 50:50 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. 5x Assignments (2% 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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(available in the University Library)

Calculus by James Stewart. (Highly recommended)

Thomas’ Calculus by George B. Thomas Jr. et al. (Highly recommended)

Schaum's Outline of Calculus by Frank Ayres Jr. and Elliot Mendelson.

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.

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.

Last 4 weeks:

Library books on differential equations are listed under QA371 and QA372.

I recommend Elementary Differential Equations and Boundary Value Problems by Boyce & DiPrima.

#### 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

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10-12 hours per week, including 5 contact hours.

This paper is a prerequisite for many higher level engineering papers.

#### Prerequisite(s)

Prerequisite papers: (ENGEN183 or ENGG183 or MATH102 or MATHS102) and (ENGEN184 or ENGG184 or MATH101 or MATHS101)

#### Restriction(s)

Restricted papers: ENGG284, ENGG285, MATH251, MATH255, MATHS201, MATHS203