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On successful completion of this course students will be able to:

1. Demonstrate understanding of concepts in linear algebra, relating to vector spaces, linear transformations, orthogonality, eigenvalues and eigenvectors and diagonalisation.
2. Demonstrate understanding of concepts in calculus, relating to differential equations, sequences, series and convergence and multivariable calculus.
3. Employ methods related to these concepts in a variety of applications.
4. Apply logical thinking to problem-solving in context.
5. Demonstrate an understanding of the role of proof in mathematics.
6. Use appropriate technology to aid problem-solving.
7. Demonstrate skills in writing mathematics.

A set of Course Notes are available as a PDF on the MyUni site for this course. (More specific details will be provided on MyUni.)

1. Poole, D., Linear Algebra: a Modern Introduction 4th edition (Cengage Learning)
2. Stewart, J., Calculus 8th edition (metric version) (Cengage Learning)

While it is not compulsory to buy the texts, they are recommended, especially for students who want extra support in this course. Copies of these text books may be purchased from the Co-op bookshop on campus or from the publisher and electronic versions are also available for purchase from the publisher. Copies of both books are available in the Barr Smith Library for short term borrowing and reference.

This course uses MyUni extensively and exclusively for providing electronic resources, such as lecture notes and videos, assignment and tutorial questions, and worked solutions. Students should make appropriate use of these resources. MyUni can be accessed here:

This course also makes use of online assessment software for mathematics called Mobius, which we use to provide students with instantaneous formative feedback. Further details about using Mobius will be provided on MyUni.

Students are also reminded that they need to check their University email on a daily basis. Sometimes important and time-critical information might be sent by email and students are expected to have read it. Any problems with accessing or managing student email accounts should be directed to Technology Services.

This course relies on lectures to guide students through the material, tutorial classes to provide students with small group and individual assistance and a sequence of written and online assignments to provide formative assessment opportunities for students to practise techniques and develop their understanding of the course.

For additional support we also run a drop-in service called First Year Maths Help on the ground floor of Ingkarni Wardli. This is staffed with tutors Monday to Friday 10am-4pm. Just drop in whenever!

Activity	Quantity	Workload hours
Lectures	48	72
Tutorials	11	22
Assignments	11	55
Mid Semester Test	1	7
Total		156

In Mathematics IB the two topics of algebra and calculus detailed below are taught in parallel, with two lectures a week on each. The tutorials are a combination of algebra and calculus topics, pertaining to the previous week's lectures.

Lecture Outline

Algebra

• Further Results on R^n (7 lectures)
  • Revision of subspaces, linear independence, basis, dimension.
  • Row and column space, null space of a matrix. Rank and rank theorem.
  • Scalar product, distance. Length and angle. Orthogonality, Gram-Schmidt process.
• Linear Transformations (4 lectures)
  • Kernel and range, the matrix of a linear transformation.
  • Dimension theorem.
• Symmetric Matrices (4 lectures)
  • General quadratic equation in 2 variables, conics.
  • Revision of eigenvalues, eigenvectors and diagonalization.
  • Orthogonal diagonalization of real symmetric matrix. Applications.

Calculus

• Differential Equations (5 lectures)
  • First order DE's: separable, linear.
  • Linear second order DE's with constant coefficients. Applications.
  • Modelling. The logistic equation.
• Limits (5 lectures)
  • Definition and uniquess of limit, limit laws.
  • Squeeze Theorem, trigonometric limits, one-sided limits, limits at infinity, unbounded functions.
  • Improper integrals. Linear approximation. L'Hopital's rule.
• Continuity (2 lectures)
  • Continuity, classification of discontinuities, continuity and differentiation.
  • Intermediate Value Theorem. Newton's Method.
• Applications of the Derivative (5 lectures)
  • Extrema of continuous functions, applied max-min problems.
  • Rolle's Theorem, Mean Value Theorem and consequences.
  • Graphing: First and second derivative tests, concavity and inflection points.
• Taylor Series (6 lectures)
  • Taylor and Maclaurin polynomials, Taylor's Theorem, error terms.
  • Power series, geometric series, convergence of power series, interval and radius of convergence.
  • Taylor and Maclaurin series, binomial series, differentiation and integration of power series.
• Calculus of More than One Variable (8 lectures)
  • Surfaces: planes, cylinders, quadric surfaces.
  • Functions of more than one variable, limits and continuity.
  • Partial derivatives, derivatives of higher order. Chain rules, directional derivative, gradient.
  • Tangent planes, local maxima and minima. Second derivative test for functions of 2 variables.

Assessment Task	Task Type	Weighting	Learning Outcomes
Written Assignments	Formative	7.5%	all
MapleTA Assignments	Formative	7.5%	all
Tutorial Participation	Formative	5%	all
Mid Semester Test	Summative and Formative	10%	1,2,4,5
Exam	Summative	70%	1,2,3,4,5,6,8

Due to the current COVID-19 situation modified arrangements have been made to assessments to facilitate remote learning and teaching. Assessment details provided here reflect recent updates.

Assignments - 35% weighting
Mid Semester Test - 15% weighting
Final Examination - 50% weighting

Assignments (both Written and Mobius) continue as before. Note that for Written and Mobius 1, 2 and 3, either the original weighting or the amended weighting will be applied, whichever gives you the higher overall assignment mark at the end of semester.

The Mid Semester Test will take place in one of the lecture times in Week 7, Monday 27th April - Friday 1st of May. The Test will be
conducted online via Mobius. Further details about the test will be provided closer to the date.

The final Examination will take place in the usual exam period at the end of semester. This exam will be administered online via MyUni. Further details about the exam will be provided closer to the date.

An aggregate score of 50% is required to pass the course. Furthermore students must achieve at least 45% on the final examination to pass the course.

Hand-in (written) assignments are due every fortnight, the first is released in Week 1 and due in Week 3.

Maple TA (online) assignments are due every week, the first is released in Week 1 and due in Week 3.

Tutorials are weekly beginning in Week 2.

The Mid Semester Test occurs in your enrolled computer lab in Week 7.

Precise details of all of these will be provided on the MyUni site for this course.

1. All written assignments are to be e-submitted following the instructions on MyUni.
2. Late assignments will not be accepted without a medical certificate.
3. Written assignments will have a one week turn-around time for feedback to students.
4. Online Maple TA assignments provide instantaneous feedback to students.

See MyUni for more comprehensive details regarding assignment submission, our late policy etc.

Replacement and Additional Assessment Examinations (R/AA Exams)

Students are encouraged to read the University's R/AA exam information on the University’s Examinations webpage here:


In this course Additional (Academic) exams will be granted to those students who have obtained a final mark
of 40–49%.