MATHS 1011 - Mathematics IA
North Terrace Campus - Semester 2 - 2018
This course, together with MATHS 1012 Mathematics IB, provides an introduction to the basic concepts and techniques of calculus and linear algebra, emphasising their inter-relationships and applications to engineering, the sciences and financial areas, introduces students to the use of computers in mathematics, and develops problem solving skills with both theoretical and practical problems. Topics covered are: Calculus: Functions of one variable, differentiation and its applications, the definite integral, techniques of integration. Algebra: Systems of linear equations, subspaces, matrices, optimisation, determinants, applications of linear algebra.
- General Course Information
Course Code MATHS 1011 Course Mathematics IA Coordinating Unit School of Mathematical Sciences Term Semester 2 Level Undergraduate Location/s North Terrace Campus Units 3 Contact Up to 5 hours per week Available for Study Abroad and Exchange Y Prerequisites At least a C- in both SACE Stage 2 Mathematical Methods (formerly Mathematical Studies) and SACE Stage 2 Specialist Mathematics; or a 3 in International Baccalaureate Mathematics HL; or MATHS 1013. Incompatible ECON 1005, ECON 1010, MATHS 1009, MATHS 1010 Assumed Knowledge At least B in both SACE Stage 2 Mathematical Methods (formerly Mathematical Studies) and SACE Stage 2 Specialist Mathematics. Students who have not achieved this standard are strongly advised to take MATHS 1013 before attempting MATHS 1011. Course Description This course, together with MATHS 1012 Mathematics IB, provides an introduction to the basic concepts and techniques of calculus and linear algebra, emphasising their inter-relationships and applications to engineering, the sciences and financial areas, introduces students to the use of computers in mathematics, and develops problem solving skills with both theoretical and practical problems. Topics covered are: Calculus: Functions of one variable, differentiation and its applications, the definite integral, techniques of integration. Algebra: Systems of linear equations, subspaces, matrices, optimisation, determinants, applications of linear algebra.
Course Coordinator:Dr Adrian Koerber
The full timetable of all activities for this course can be accessed from Course Planner.
- Learning Outcomes
Course Learning Outcomes
University Graduate Attributes
This course will provide students with an opportunity to develop the Graduate Attribute(s) specified below:
University Graduate Attribute Course Learning Outcome(s) Deep discipline knowledge
- informed and infused by cutting edge research, scaffolded throughout their program of studies
- acquired from personal interaction with research active educators, from year 1
- accredited or validated against national or international standards (for relevant programs)
all Critical thinking and problem solving
- steeped in research methods and rigor
- based on empirical evidence and the scientific approach to knowledge development
- demonstrated through appropriate and relevant assessment
3,4,5On successful completion of this course students will be able to:
- Demonstrate understanding of and proficiency with basic concepts in linear algebra: systems of linear equations, subspaces, matrices, optimisation, determinants.
- Demonstrate understanding of and proficiency with basic concepts in calculus: functions of one variable, differentiation and its applications, the definite integral, techniques of integration.
- Employ methods related to these concepts in a variety of applications.
- Apply logical thinking to problem-solving in context.
- Use appropriate technology to aid problem-solving.
- Demonstrate skills in writing mathematics.
- Learning Resources
A set of Course Notes should be purchased from the Online Shop and picked up from the Image and Copy centre, Level 1 in the Hughes Building. Alternatively these will be available as a pdf on the MyUni site for this course. (More specific details will be provided on MyUni.)
- Poole, D., Linear Algebra: a Modern Introduction 4th edition (Cengage Learning)
- 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: https://myuni.adelaide.edu.au/
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.
- Learning & Teaching Activities
Learning & Teaching Modes
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!
The information below is provided as a guide to assist students in engaging appropriately with the course requirements.
Activity Quantity Workload hours Lectures 48 72 Tutorials 11 22 Assignments 11 55 Mid Semester Test 1 7 Total 156
Learning Activities Summary
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.
- 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.
- 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.
- Areas, summation notation. Upper and lower sums, area under a curve.
- Properties of the definite integral. Fundamental Theorem of Calculus.
- Revision of differentiation, derivatives of inverse functions.
- Logarithm as area under a curve. Properties.
- Exponential function as inverse of logarithm, properties. Other exponential and log functions. Hyperbolic functions.
- Substitution, integration by parts, partial fractions.
- Trig integrals, reduction formulae. Use of Matlab in evaluation of integrals.
- Riemann sums, trapezoidal and Simpson's rules.
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.
- Matrices and Linear Equations (8 lectures)
The University's policy on Assessment for Coursework Programs is based on the following four principles:
- Assessment must encourage and reinforce learning.
- Assessment must enable robust and fair judgements about student performance.
- Assessment practices must be fair and equitable to students and give them the opportunity to demonstrate what they have learned.
- Assessment must maintain academic standards.
Assessment Related Requirements
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.
Grades for your performance in this course will be awarded in accordance with the following scheme:
Grade Mark Description FNS Fail No Submission F 1-49 Fail P 50-64 Pass C 65-74 Credit D 75-84 Distinction HD 85-100 High Distinction CN Continuing NFE No Formal Examination RP Result Pending
Further details of the grades/results can be obtained from Examinations.
Grade Descriptors are available which provide a general guide to the standard of work that is expected at each grade level. More information at Assessment for Coursework Programs.
Final results for this course will be made available through Access Adelaide.
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
Assessment Task Task Type Weighting Learning Outcomes Hand-in Assignments Formative 7.5% all MapleTA Assignments Formative 7.5% all Tutorial Participation Formative 5% all Mid Semester Test Summative and Formative 10% 1,2,3,4 Exam Summative 70% 1,2,3,4,6
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.
- All written assignments are to be submitted at the designated time and place with a signed cover sheet attached.
- Late assignments will not be accepted without a medical certificate.
- Written assignments will have a one week turn-around time for feedback to students.
- Online Maple TA assignments provide instantaneous feedback to students.
- Student Feedback
The University places a high priority on approaches to learning and teaching that enhance the student experience. Feedback is sought from students in a variety of ways including on-going engagement with staff, the use of online discussion boards and the use of Student Experience of Learning and Teaching (SELT) surveys as well as GOS surveys and Program reviews.
SELTs are an important source of information to inform individual teaching practice, decisions about teaching duties, and course and program curriculum design. They enable the University to assess how effectively its learning environments and teaching practices facilitate student engagement and learning outcomes. Under the current SELT Policy (http://www.adelaide.edu.au/policies/101/) course SELTs are mandated and must be conducted at the conclusion of each term/semester/trimester for every course offering. Feedback on issues raised through course SELT surveys is made available to enrolled students through various resources (e.g. MyUni). In addition aggregated course SELT data is available.
- Student Support
- Policies & Guidelines
This section contains links to relevant assessment-related policies and guidelines - all university policies.
- Fraud Awareness
Students are reminded that in order to maintain the academic integrity of all programs and courses, the university has a zero-tolerance approach to students offering money or significant value goods or services to any staff member who is involved in their teaching or assessment. Students offering lecturers or tutors or professional staff anything more than a small token of appreciation is totally unacceptable, in any circumstances. Staff members are obliged to report all such incidents to their supervisor/manager, who will refer them for action under the university's student’s disciplinary procedures.
The University of Adelaide is committed to regular reviews of the courses and programs it offers to students. The University of Adelaide therefore reserves the right to discontinue or vary programs and courses without notice. Please read the important information contained in the disclaimer.
- 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.
- 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.
Tutorial 1: Subspaces, linear independence. First order DEs.
Tutorial 2: Row, column and null space. Second order DEs.
Tutorial 3: Rank theorem. Distance, angle and orthogonality. Logistic equation. Orthogonality.
Tutorial 4: Gram-Schmidt process, projections, linear transformations. Limits, Squeeze Theorem.
Tutorial 5: Linear transformations: kernel, range, standard matrix. Limits, improper integrals.
Tutorial 6: Composition of linear transformations, conic sections.L'Hopital's rule. Discontinuities.
Tutorial 7: Eigenvalues, eigenvectors, diagonalisation. Newton's Method. Intermediate Value Theorem.
Tutorial 8: Standard form for conics and quadrics. Max-min problems. Mean Value Theorem.
Tutorial 9: Functions of 2 variables, limits and continuity. Mean Value Theorems, graph sketching.
Tutorial 10: Limits, continuity, partial derivatives of functions of 2 variables. Taylor and Maclaurin polynomials.
Tutorial 11: Tangent planes to surfaces. Chain rule. Directional derivatives. Series, convergence.
Tutorial 12: Maximum rate of change. Classification of critical points. Taylor and Maclaurin series.
(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.