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

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.

Mathematics IA Student Notes.

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

This course uses MyUni exclusively for providing electronic resources, such as lecture notes, assignment papers, and sample solutions. Students should make appropriate use of these resources. Link to MyUni login page: https://myuni.adelaide.edu.au/webapps/login/

This course also makes use of online assessment software for mathematics called Maple TA, which we use to provide students with instantaneous formative feedback.

This course relies on lectures to guide students through the material, tutorial classes to provide students with class/small group/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.

Activity	Quantity	Workload hours
Lectures	48	72
Tutorials	11	22
Assignments	11	62
Total		156

In Mathematics IA 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

• 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.

Calculus

• 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 Outline

Tutorial 1: Matrices and linear equations. Real numbers, domain and range of functions.
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.

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.

Tutorials 1-11 have a participation mark worth a total of 10%.

Assignments 1-11 are made up of a written component, worth a total of 10%, and an online (Maple TA) component, worth 10%.

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.