MATH103-18S1 (C) Semester One 2018

Mathematics 1B

15 points

Start Date: Monday, 19 February 2018
End Date: Sunday, 24 June 2018
Withdrawal Dates
Last Day to withdraw from this course:
  • Without financial penalty (full fee refund): Friday, 2 March 2018
  • Without academic penalty (including no fee refund): Friday, 18 May 2018


A consolidation of concepts from MATH102 and introduction to more advanced ideas in calculus and linear algebra. It is a prerequisite for many courses in mathematics and other subjects at 200-level.

MATH103 deals with techniques and ideas in algebra, calculus and statistics. It is designed mainly for students who have passed MATH102, and who need at least 30 points of Mathematics at the 100 level. After passing MATH103, you will be able to enrol in any 200-level mathematics course.

Topics: vectors and geometry, eigenvalues and eigenvectors, sequences and mathematical induction, series and approximation, techniques and applications of integration, differential equations, probability.

Learning Outcomes

  • Learning Outcomes for Topic 1: Differential equations
  • Identifying the type of a given differential equation (DE).
  • Identify and apply an appropriate solution method for 1st and 2nd order DEs
  • Use a numerical method to approximate the solution to a DE
  • Describe and interpret important features of a DE
  • Modelling problems that are solved by a DE
  • The difference between an analytical and numerical solution

    Learning Outcomes for Topic 2: Sequences and series
    Use mathematical language to:
  • demonstrate understanding of what a sequence is and that it may be defined explicitly, or by a recurrence relation, or as a series
  • explain what it means for a sequence to converge, and different failures thereof
  • describe an application of recurrence relation
  • Calculate Taylor series of a function, and determine convergence (or not)
  • Identify and apply an appropriate method for analyzing a sequence
  • Use techniques from the course to prove given statements about sequences by natural induction

    Learning Outcomes for Topic 3: Linear algebra and vector geometry
  • Represent and interpret matrices as linear transformations.
  • Evaluate determinants by cofactor expansion and by elementary row operations.
  • Describe and apply properties of determinants.
  • Calculate vector addition, scalar multiplication and dot products.
  • Interpret and describe orthogonality, and compute angles, distances and projections.
  • Compute cross products and calculate areas and volumes.
  • Use vectors to represent lines and planes.
  • Solve intersection and distance problems involving lines and planes.
  • Calculate and interpret eigenvalues and eigenvectors for 2 x 2 and simple 3 x 3 matrices.
  • Calculate characteristic polynomials.

    Learning Outcomes for Topic 4: Curves and Surfaces
    Define the key concepts in curves and vector valued functions and two-variable functions.
    Describe and interpret:
  • curves using parametric and polar equations
  • vector valued functions and their derivatives
  • a two-variable function from its level curves

    Use techniques from the course to:
  • sketch curves from their parametric and polar descriptions
  • find derivatives of vector valued functions
  • find partial derivatives and interpret these geometrically and physically
  • find critical values of functions of two variables and determine their nature
    • University Graduate Attributes

      This course will provide students with an opportunity to develop the Graduate Attributes specified below:

      Critically competent in a core academic discipline of their award

      Students know and can critically evaluate and, where applicable, apply this knowledge to topics/issues within their majoring subject.



MATH109, MATH199, EMTH119

Course Coordinator

For further information see Mathematics and Statistics Head of Department


Assessment Due Date Percentage 
Tutorials 10%
Two assignments and TA quizzes 24%
Test 20%
Final Examination 46%

To obtain a clear pass in this course, you must both pass the course as a whole (≥ 50%) and also obtain at least 40% in the final examination.

Textbooks / Resources

Recommended reading:
Stewart, James: Calculus Early Transcendentals. 8th edition. ISBN: 9781305272378

Indicative Fees

Domestic fee $749.00

International fee $3,788.00

* All fees are inclusive of NZ GST or any equivalent overseas tax, and do not include any programme level discount or additional course-related expenses.

For further information see Mathematics and Statistics .

All MATH103 Occurrences