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1. Demonstrate understanding of basic concepts in linear algebra, relating to matrices, vector spaces and eigenvectors.
2. Demonstrate understanding of basic concepts in calculus, relating to functions, differentiation and integration.
3. Employ methods related to these concepts in a variety of applications.
4. Apply logical thinking to problem-solving in context.
5. Use appropriate technology to aid problem-solving.
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

• Matrices and Linear Equations (8 lectures)
  • Algebraic properties of matrices.
  • Systems of linear equations, coefficient and augmented matrices. Row operations.
  • Gauss-Jordan reduction. Solution set.
  • Linear combnations of vectors. Inverse matrix, elementary matrices, application to linear systems.
• Determinants (2 lectures)
  • Definition and properties. Computation. Adjoint.
• Optimisation and Convex Sets (4 lectures)
  • Convex sets, systems of linear inequalities.
  • Optimization of a linear functional on a convex set: geometric and algebraic methods.
  • Applications.
• The Vector Space R^n (4 lectures)
  • Definition. Linear independence, subspaces, basis.
• Eigenvalues and Eigenvectors (5 lectures)
  • Definitions and calculation: characteristic equation, trace, determinant, multiplicity.
  • Similar matrices, diagonalization. Applications.

• Functions (6 lectures)
  • Real and irrational numbers. Decimal expansions, intervals.
  • Domain, range, graph of a function. Polynomial, rational, modulus, step, trig functions, odd and even functions.
  • Combining functions, 1-1 and monotonic functions, inverse functions including inverse trig functions.
  Integration (5 lectures)
  • Areas, summation notation. Upper and lower sums, area under a curve.
  • Properties of the definite integral. Fundamental Theorem of Calculus.
  Revision of Differentiation (2 lectures)
  • Revision of differentiation, derivatives of inverse functions.
  Logarithmic and Exponential Functions (3 lectures)
  • Logarithm as area under a curve. Properties.
  • Exponential function as inverse of logarithm, properties. Other exponential and log functions. Hyperbolic functions.
  Techniques of Integration (6 lectures)
  • Substitution, integration by parts, partial fractions.
  • Trig integrals, reduction formulae. Use of Matlab in evaluation of integrals.
  Numerical Integration (2 lectures)
  • Riemann sums, trapezoidal and Simpson's rules.

Tutorial 2: Gauss-Jordan elimination. Linear combinations of vectors. Composition of functions, 1-1 functions.
Tutorial 3: Systems of equations. Inverse functions. Exponential functions.
Tutorial 4: Inverse matrices. Summation, upper and lower sums.
Tutorial 5: Determinants. Definite integrals, average value.
Tutorial 6: Convex sets, optimization. Antiderivatives, Fundamental Theorem of Calculus.
Tutorial 7: Optimization. Linear dependence and independence. Differentiation of inverse functions.
Tutorial 8: Linear dependence, span, subspace. Log, exponential and hyperbolic functions.
Tutorial 9: Basis and dimension. Integration.
Tutorial 10: Eigenvalues and eigenvectors. Integration by parts, reduction formulae.
Tutorial 11: Eigenvalues and eigenvectors. Tirigonometric integrals.
Tutorial 12: Diagonalization, Markov processes. Numerical integration.
(Note: This tutorial is not an actual class, but is a set of typical problems with solutions provided.)

Note: Precise tutorial content may vary due to the vagaries of public holidays.

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 6.

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

1. All written assignments are to be submitted at the designated time and place with a signed cover sheet attached.
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.