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1. Demonstrate understanding of and proficiency with basic concepts in linear algebra: systems of linear equations, subspaces, matrices, optimisation, determinants.
2. Demonstrate understanding of and proficiency with basic concepts in calculus: functions of one variable, differentiation and its applications, the definite integral, techniques of integration.
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. Demonstrate skills in writing mathematics.

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

This course uses MyUni extensively and exclusively for providing electronic resources, such as lecture notes, 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 Maple TA, which we use to provide students with instantaneous formative feedback. Further details about using Maple TA 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.

Algebra

• Linear systems and Gauss-Jordan elimination (5 lectures)
  • Systems of linear equations and elementary operations
  • Reduced row echelon form
  • The three possible outcomes of Gauss-Jordan elimination
  • Applications
• Spanning sets and linearly independent sets (4 lectures)
  • Linear combinations of vectors
  • Homogeneous linear systems
  • Linearly independent sets of vectors
  • Subspaces and bases
• Matrix algebra (5 lectures)
  • Addition of matrices
  • Multiplication of matrices
  • Applications
  • Elementary matrices
  • The inverse of a matrix
• Optimisation (6 lectures)
  • Introduction, definitions
  • Convex sets and vertices
  • The method of slack variables
• Determinants (3 lectures)
  • Definition of the determinant
  • Determinants and elementary row operations

Calculus

• Functions (5 lectures)
  • Definition, domain and range. Examples of functions.
  • Inverses, inverse trigonometric functions.
  • Zeros of functions.
  • Limits, continuity.
  • Interval bisection method.
• Differentiation and its applications (7 lectures)
  • Definition, interpretation, concavity.
  • Rules for differentiation (product, quotient, chain).
  • Implicit differentiation, derivatives of inverses.
  • Related rates.
  • Maxima and minima of functions and applications
• Integration (10 lectures)
  • Summation notation, definition of definite integral.
  • Antiderivatives and The Fundamental Theorem of Calculus.
  • Techniques of integration: substitution, parts, partial fractions.
  • Applications.
  • Improper integrals.

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 6.

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.