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
Taught by
School of Mathematics and Statistics—Faculty of Engineering
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:
Demonstrate correct use of mathematical notation in calculus.
Set out logical mathematical arguments.
Understand the definition of area as a limit and use it to solve problems.
Use the Fundamental Theorem of Calculus to evaluate integrals.
Apply the theory of calculus to solve real world problems.
Decide if series converge or diverge using tests.
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
Once you've signed up to this course, you can use to see due dates for assessments and information about extensions.
Mandatory requirements
Find out what you must do to pass this course.
In addition to achieving an overall pass mark of at least 50% students must:
- 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
Who to contact


Selected offering
MATH 142
7 Jul–9 Nov 2025
Trimester 2 · CRN 17160