MATH 142Calculus 1B

Integration looks at summing continuous variables, providing a way to define and compute areas and volumes, which are essential for many applications. This course develops integral calculus, including the view of integration as anti-differentiation, leading to the Fundamental Theorem of Calculus. Sequences and series are introduced, and functions are approximated using their Taylor polynomials. Techniques of integration are developed, including substitution and integration by parts. Differential equations are introduced, many of which arise from physical systems, and the course also introduces basic methods for solving them.

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Course details

Dates
7 Jul 2025 to 9 Nov 2025
Starts
Trimester 2
Fees
NZ$899.40 for
International fees
NZ$4,771.80
Lecture start times
  • Monday 12.00pm
  • Wednesday 12.00pm
  • Thursday 12.00pm
Campus
Kelburn
Estimated workload
Approximately 150 hours or 8.8 hours per week for 17 weeks
Points
15

Entry restrictions

Prerequisites
Corequisites
None
Restrictions
None

Taught by

School of Mathematics and StatisticsFaculty of Engineering

Key dates

Find important dates—including mid-trimester teaching breaks—on the University's key dates calendar.

You'll be told about assessment dates once the course has begun.

Key dates

About this course

The course will cover the following topics:

  • Integration: definition, properties, the Fundamental Theorem of Calculus
  • Methods of integration, applications, improper integrals
  • Differential equations
  • Sequences and series
  • Maclaurin and Taylor polynomials

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To enrol in MATH 142 you need one of MATH 141, QUAN 111 or PHYS 101, or ALL of the following NCEA Level 3 achievement standards: 

  • 3.6 (Differentiation, AS91578) achieved with Excellence 
  • 3.7 (Integration, AS91579), and 
  • one of 3.1 (Conics, AS91573), 3.3 (Trigonometry, AS91575), or 3.5 (Complex numbers, AS91577).
  • You need a Merit or Excellence grade in at least one of 3.1, 3.3, 3.5, or 3.7. 

Course learning objectives

Students who pass this course should be able to:

  1. Demonstrate correct use of mathematical notation in calculus.

  2. Set out logical mathematical arguments.

  3. Understand the definition of area as a limit and use it to solve problems.

  4. Use the Fundamental Theorem of Calculus to evaluate integrals.

  5. Apply the theory of calculus to solve real world problems.

  6. Decide if series converge or diverge using tests.

  7. Find Taylor polynomials of suitable functions.

How this course is taught

During the trimester, there will be three lectures per week. These will be live-streamed and recorded for students to view subsequently. Students are required to sign up for a tutorial (available in person) and attendance is strongly recommended. Tutorials are weekly and start in week two.

Note: The single best predictor we have of final outcome for the course is your level of engagement with the course - attendance at lectures and completing tutorials, assignments and reading your notes and the textbook.

Assessment

  • Final test (centrally managed exam) Type: IndividualMark: 40%
  • 6 Assignments Mark: 30%
  • Test 1 Mark: 30%

Assessment dates and extensions

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Mandatory requirements

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In addition to achieving an overall pass mark of at least 50% students must:

  1. Achieve a mark of at least 40% in either the mid-term test or the final test (exam).

If you believe that exceptional circumstances may prevent you from meeting the mandatory course requirements, contact the course coordinator for advice as soon as possible.

Lecture times and rooms

What you’ll need to get

Recommended texts

Recommended texts add to your understanding of the course.

Title: Calculus Early Transcendentals

Edition: 12th

Authors: Howard Anton, Irl C. Bivens, Stephen Davis

Publisher: Wiley

ISBN: 9781119820482

Chapters: 5-8,10

Past versions of this course

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Selected offering

MATH 142

7 Jul–9 Nov 2025

Trimester 2 · CRN 17160

2025 course optionsOptions (1)