 ## 15 Points

Division of Health Engineering Computing & Science
School of Computing and Mathematical Sciences
Department of Mathematics and Statistics

### Staff

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#### Convenor(s)  #### Librarian(s)

You can contact staff by:

• Calling +64 7 838 4466 select option 1, then enter the extension.
• Extensions starting with 4, 5, 9 or 3 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.
• For extensions starting with 3: dial +64 7 2620 + the last 3 digits of the extension e.g. 3123 = +64 7 262 0123.
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### Paper Description

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The paper introduces the use of applied mathematics in science and engineering. The focus is on how ordinary and partial differential equations are used to formulate mathematical models and obtain concrete results.
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### Paper Structure

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3 lectures a week, plus a tutorial each week.
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### Learning Outcomes

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Students who successfully complete the paper should be able to:

• integrate first-order ordinary differential equations (separable, linear, exact, with homogeneous coefficients, Bernoulli)
• use Picard's theorem to establish existence and uniqueness of solutions to first-order differential equations
• integrate homogeneous linear second-order ordinary differential equations with constant coefficients
• integrate inhomogeneous linear second-order ordinary differential equations by the method of undetermined coefficients
• solve linear second-order ordinary differential equations using the method of variation of parameters
• solve second-order ordinary differential equations using reduction of order if one variable is missing or a particular solution is known
• solve second-order Cauchy-Euler equations
• Solve first-order linear systems of ordinary differential equations by the method of elimination
• Solve first-order linear systems of ordinary differential equations by matrix methods
• expand elementary functions in Fourier series
• solve the basic equations of mathematical physics (heat, wave, Laplace) in terms of Fourier series
• integrate first-order partial differential equations by the method of characteristics
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### Assessment

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10 weekly assignments, two tests, and a final exam.

#### 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. assignments
18
2. test 1
16
3. test 2
16
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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S. Imhoff. Differential equations in 24 hours.

G.F. Simmons. Differential equations with applications and historical notes.

E.D. Rainville, P.E. Bedient. Elementary differential equations.

I. Savov. No bullshit guide to math & physics.

### Online Support

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Moodle will be used for communication, including posting of assignment sheets.
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10 hours per week, including 4 contact hours.

#### Prerequisite(s)

Prerequisite papers: Either ((MATH101 or MATHS101) and (MATH102 or MATHS102)) or minnimum B grade in ENGEN102.

#### Restriction(s)

Restricted papers: ENGG284, ENGEN201, MATH255 and MATH259