MATHS 1012 - Mathematics IB

North Terrace Campus - Semester 2 - 2016

This course, together with MATHS 1011 Mathematics IA, 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: Applications of the derivative; functions of two variables; Taylor series; differential equations. Algebra: The real vector space, eigenvalues and eigenvectors, linear transformations and applications of linear algebra.

• General Course Information
Course Details
Course Code MATHS 1012 Mathematics IB School of Mathematical Sciences Semester 2 Undergraduate North Terrace Campus 3 Up to 5.5 hours per week Y MATHS 1011 ECON 1005, ECON 1010, MATHS 1009, MATHS 1010 This course, together with MATHS 1011 Mathematics IA, 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: Applications of the derivative; functions of two variables; Taylor series; differential equations. Algebra: The real vector space, eigenvalues and eigenvectors, linear transformations and applications of linear algebra.

Course Timetable

The full timetable of all activities for this course can be accessed from Course Planner.

• Learning Outcomes
Course Learning Outcomes
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 and symmetric matrices.
2. Demonstrate understanding of concepts in calculus, relating to differential equations, limits and continuity, and Taylor series.
3. Demonstrate understanding of introductory concepts in two-variable calculus.
4. Employ methods related to these concepts in a variety of applications.
5. Apply logical thinking to problem-solving in context.
6. Demonstrate an understanding of the role of proof in mathematics.
7. Use appropriate technology to aid problem-solving.
8. Demonstrate skills in writing mathematics.

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
4,5,6,7
• Learning Resources
Required Resources
Mathematics IB Student Notes.
Recommended Resources
1. Poole: Linear Algebra a Modern Introduction 4th ed. (Cengage Learning)
2. Stewart: Calculus 7th ed. (international ed.) (Brooks/Cole)
Online 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.

• Learning & Teaching Activities
Learning & Teaching Modes
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 assessmentopportunities for students to practice techniques and develop their understanding of the course.

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 62 Total 156
Learning Activities Summary
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.
Tutorial Outline

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.

• Assessment

The University's policy on Assessment for Coursework Programs is based on the following four principles:

1. Assessment must encourage and reinforce learning.
2. Assessment must enable robust and fair judgements about student performance.
3. Assessment practices must be fair and equitable to students and give them the opportunity to demonstrate what they have learned.
4. Assessment must maintain academic standards.

Assessment Summary
 Assessment Task Task Type Weighting Learning Outcomes Tutorials Formative 10% all Assignments Formative 20% all Exam Summative 70% 1,2,3,4,5,6,8
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.
Assessment Detail

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%.

Submission
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.

Grades for your performance in this course will be awarded in accordance with the following scheme:

M10 (Coursework Mark Scheme)
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.

• 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
• 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.

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