MATHS101-22A (HAM)

Introduction to Calculus

15 Points

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


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Paper Description

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To give students in mathematics, or in subjects that use mathematical methods, a comprehensive foundation in differential and integral calculus, and examples of its applications.

Students who enroll in MATHS101 have until Thursday 14 April to determine if they wish to change down to a lower level mathematics paper (MATHS165, MATHS168, ENGEN101) without any fees loss. See section 12.2 and 13.2 of the change of enrollment section of the calendar.

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Paper Structure

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This is a lecture/tutorial-based paper with five contact hours per week -- four lectures and one tutorial per week.

Lectures will be available as recordings. You are strongly encouraged to attend class in person.
There are weekly assignments with questions set from the required textbook.

If COVID restrictions necessitate, the paper will probably become online only and assessment procedures may change. More details will be provided as necessary.

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Learning Outcomes

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Students who successfully complete the course should be able to:

  • .

    Understand what a limit is. Be able to calculate limits.

    Understand the definition of the derivative. Calculate derivatives using the definition.

    Differentiate elementary functions using rules like sum, product, quotient, chain.

    Apply the derivative to find maximum and minimum of functions.

    Calculate the indefinite and definite integral of a function.

    Apply methods of substitution and integration by parts and applications.

    Use the logarithm and exponential function.

    Understand limits of sequences, series and functions and be able to apply those definitions.

    Apply tests for convergence.

    Linked to the following assessments:
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The internal assessment mark will consist of TWO Tests (held in the evenings on campus) plus the total tutorial component (including weekly assignments).

Assignment sheets will be available each week, via moodle.

See the table below for Test dates.

For identification purposes you must take your student ID Card to both tests. If you do not, your test mark will not be counted until we cannot verify that it was you who sat the test.

The D rule: An UNRESTRICTED pass (i.e. C- or better) will only be awarded to students who achieve both a final overall mark of at least 50% and an Examination mark of at least 40%.

Calculators will NOT be permitted in Tests or the Final Examination.

COPYING of other students’ Assignments/Tests will receive zero (this will include all students involved) and be reported to the Disciplinary Committee. See the ACADEMIC INTEGRITY/CHEATING sections below.

A final overall grade of RP (Restricted pass) will NOT be accepted as a prerequisite for entry into any higher level Maths paper.

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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. 11x Assignments (best 9 out of 11 marks counted)
  • Other: Hand-in box located in FG link, ground floor
2. Test 1: probably in S.1.04
11 Apr 2022
6:00 PM
3. Test 2: probably in S.1.04
30 May 2022
6:00 PM
4. Exam: D-rule applies
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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Required Readings

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Schaum’s Outlines ‘Calculus’ (6th Edn), Ayres & Mendelson, McGraw-Hill. (Soft cover).

Assignments will be set from this textbook so you will need to purchase a copy (eg,from the bookshop at the university).
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Recommended Readings

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The library has many different calculus textbooks. They all cover the same material. The trick is to find one or two that you find clear/easy-to-read. You are advised to look at a few.

Calculus by James Stewart (Highly recommended)

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

Calculus and analytic geometry by George B. Thomas, Jr.

Calculus with analytic geometry by G.F. Simmons

Calculus with analytic geometry by Howard Anton

Calculus: single variable by Deborah Hughes-Hallett

Calculus by Ron Larson

Calculus by Frank Morgan

Calculus I and II by Jerrold E. Marsden

A first course in calculus by Serge Lang

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Other Resources

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Calculus gems by G.F. Simmons

The cartoon guide to calculus by Larry Gonick

How to think like a mathematician by Kevin Houston

How to study as a mathematics major by Lara Alcock

How to study by Ronald Fry

How to study by Allan Mundsack et al

The secrets of college success by Lynn Jacobs and Jeremy Hyman

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Online Support

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All information relating to this paper including your internal assessment marks will be posted on Moodle.
It is your responsibility to check your marks are entered correctly.
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Four lectures and one tutorial per week. Plus you are expected to spend another 5 hours per week doing work for the paper (reading, assignments, study,...).

For each test, we recommend doing at least 10 hours of study. And much more for the final exam.

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Linkages to Other Papers

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More calculus is taught in MATHS201 Continuing calculus, which covers multivariable and vector calculus, and in MATHS301 Real and complex analysis. Calculus is applied in MATHS203 Differential equations and modelling, MATHS304 Computational mathematics, and MATHS303 Applied mathematics.

Maths majors/double majors, etc usually also take MATHS102 Introduction to Algebra and MATHS135 Discrete Structures in their first year.

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Prerequisite papers: At least a minimum B- grade in MATHS165, MATHS166, or FOUND007; or MATHS102; or 14 credits in NCEA Level 3 Calculus including at least 11 credits from AS91577, AS91578 and AS91579; or equivalent.




Restricted papers: ENGEN184, ENGEN101, ENGEN102, RPLCR103

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