- Permutations, combinations and elementary probabilities.

- Mathematical induction.

- Exponential and logarithmic functions.

- Trigonometric functions, trigonometric formulae.

- Limits of algebraic, exponential and logarithmic functions.

- Derivatives of algebraic, exponential and logarithmic functions.

- Differentiation rules: addition, product, quotient and chain rule.

- Maxima and minima.

- Indefinite and definite integrals.

- Area.

- Integration by substitution.

- Trapezoidal rule with error estimation. Course Learning Outcomes

CLO 1 | use the set notations; calculate probabilities; and prove by induction |

CLO 2 | solve problems involving exponential, logarithmic and trigonometric functions |

CLO 3 | evaluate limits and derivatives |

CLO 4 | compute simple definite and indefinite integrals |

CLO 5 | solve practical problems such as determining maxima and minima; finding area |

(and Co-requisites and

Impermissible combinations) Not for students: (a) with Level 2 or above in M1 or M2 of HKDSE Math or equivalent; (b) have passed or already enrolled in any of following courses: MATH1009, 1013, 1821, 1851, PHYS1150, CHEM1044, level 2 or above math courses; (c) have passed MATH1853. Course Status with Related Major/Minor /Professional Core 2021 Major in Chemistry (Intensive) ( Disciplinary Elective )

2021 Major in Molecular Biology & Biotechnology (Intensive) ( Disciplinary Elective )

2020 Major in Chemistry (Intensive) ( Disciplinary Elective )

2020 Major in Molecular Biology & Biotechnology (Intensive) ( Disciplinary Elective )

2019 Major in Chemistry (Intensive) ( Disciplinary Elective )

2019 Major in Molecular Biology & Biotechnology (Intensive) ( Disciplinary Elective )

2018 Major in Chemistry (Intensive) ( Disciplinary Elective )

2018 Major in Molecular Biology & Biotechnology (Intensive) ( Disciplinary Elective )

2017 Major in Chemistry (Intensive) ( Disciplinary Elective )

2017 Major in Molecular Biology & Biotechnology (Intensive) ( Disciplinary Elective )

Course to PLO Mapping 2021 Major in Chemistry (Intensive) < PLO 4,5 >

2021 Major in Molecular Biology & Biotechnology (Intensive) < PLO 3,4 >

2020 Major in Chemistry (Intensive) < PLO 4,5 >

2020 Major in Molecular Biology & Biotechnology (Intensive) < PLO 3,4 >

2019 Major in Chemistry (Intensive) < PLO 4,5 >

2019 Major in Molecular Biology & Biotechnology (Intensive) < PLO 3,4 >

2018 Major in Chemistry (Intensive) < PLO 4,5 >

2018 Major in Molecular Biology & Biotechnology (Intensive) < PLO 3,4 >

2017 Major in Chemistry (Intensive) < PLO 4,5 >

2017 Major in Molecular Biology & Biotechnology (Intensive) < PLO 3,4 >

Offer in 2021 - 2022 Y 1st sem 2nd sem Examination Dec May Offer in 2022 - 2023 Y Course Grade A+ to F Grade Descriptors

A | Demonstrate an excellent understanding of key concepts and ideas by being able to identify the appropriate theorems and their applications through correctly analysing problems, clearly and elegantly presenting correct logical reasoning and argumentation and being able to carry out computations carefully and correctly, and with some innovative approaches to solving problems. |
---|---|

B | Demonstrate a good understanding of key concepts and ideas by being able to identify the appropriate theorems and their applications through correctly analysing problems, but with some minor inadequacies in arguments, identifying the appropriate theorems or their applications and presentation or with some minor computational errors. |

C | Demonstrate an acceptable understanding of key concepts and ideas by being able to correctly identify appropriate theorems, but with some inadequacies in applying the theorems through incorrectly analysing problems with poor argument and presentation or a number of minor computational errors. |

D | Demonstrate some understanding of key concepts and ideas by being able to correctly identify appropriate theorems, but with substantial inadequacies in applying the theorems through incorrectly analysing problems with poor argument or presentation or with substantial computational errors. |

Fail | Demonstrate poor and inadequate understanding by not being able to identify appropriate theorems or their applications, or not being able to complete the solution. |

& Learning Activities

Activities | Details | No. of Hours |
---|---|---|

Lectures | 36 |

Rectangle1. Calculate 15% of 723.

2. If 9.8 is 12% of your grade, find your grade.

3. Find the height in meters of a person 5’6″ tall.Group ProjectAre irrationals rational?after 1.2Group ProjectCalculate your BMIafter1.4Group ProjectAnalyze newspaper circulationIf time permitsChapter 22.1Linear equations in one variablepage 57-58: 1,11,13,17,23,26,35,432.2Introduction to problem solvingpage 65-70: 1,5,11,132.3Formulas and problem solvingpage 75-78: 1,5,532.4Linear inequalities and problem solvingpage 87-90: 1,3,7,11,43,45,59,632.6Absolute value equationspage 102-103: 5,9,15,21,53,57Group ProjectAlgebraic poetry — Lilavati’s swarmafter 2.2Group ProjectAlgebraic poetry — The rose-red cityIf time permitsGroup ProjectCalculate your incomeafter 2.4Exam 1Chapter 33.1Graphing equations (include material from 3.3)page 129-131: 1,3,5,7,9,17,19,27,33,373.2Introduction to functionspage 142-146: 1,3,11,23,25,29,35,37,53,55,57,593.4The slope of a linepage 164-168: 5,23,29,31,41,43,64,69,71,953.5Equations of linespage 175-178: 1,13,25,41,42,44,47Group ProjectHurricane season (and Tracking Chart)If time permitsGroup ProjectThree swimmersafter 3.1Group ProjectCigarette adsafter 3.4Group ProjectLife expectancyafter 3.5Chapter 44.1Linear equations in two variablespage 216-218: 1,3,9,17,21,77Group ProjectWhich Honda should you buy?If time PermitsGroup ProjectPhotos of all sizesafter 4.1Exam 2Chapter 55.1Exponentspage 267-268: 7,13,19,25,33,49,695.2More exponentspage 273-274: 1,5,7,21,24,555.3Polynomials and polynomial functionspage 284-287: 17,23,35,45,475.4Multiplying polynomialspage 293-295: 1,7,23,25,295.5The greatest common factorpage 299-301: 3,9,11,135.6Factoring trinomials (use quadratic formula for roots from 8.2)page 308-309: 15,25,27,475.7Factoring special productspage 314-315: 1,13,41,455.8 (partial)Solving quadratic equations (via quadratic formula and roots)page 327-331: 5,9,13Group ProjectThe largest boxA Special Largest Box (Spring 2006) (after 5.4) Group ProjectFactoring trinomials completelyafter 5.7Group ProjectFree falling from bridgesIf time permitsExam 3Chapter 66.1Multiplying and dividing rational expressionspage 351-354: 1,17,37,41,47,636.2Adding and subtracting rational expressionspage 359-361: 7,21,30,31,33Group ProjectCalculate your areasIf time permitsGroup ProjectCalculate your lottery winningafter 6.2Chapter 77.1Radicals and radical functionspage 423-425: 3,9,19,25,39,43,45,53,757.2Rational exponentspage 431-433: 1,11,19,29,39,41,47,51,61,657.6 (partial)Radical equationspage 460-463: 1,9,11,13 (with 7.2),53,59 (with 7.1)Group ProjectSkid marksafter 7.6Group ProjectRun Fido, Run!If time permitsChapter 99.3Exponential functionspage 567-569: 2,5,18,20,21,27,35,379.5Logarithmic functionspage 581-582: 29,31,41,45,51,699.6Properties of logarithmspage 587-589: 1,9,17,21,35,43,53,55,579.8 (partial)Exponential and logarithmic equationspage 599-601: 11,27, 28 (with 9.5),31,32,33 (with 9.6)Group ProjectThe black bear populationafter 9.5Group ProjectPuzzled by Logs?after 9.8Optional Topics5.1Scientific notationpage 267-268: 102,104,109,125, 1285.2More scientific notationpage 273-274: 69,73Group ProjectVery large and very small numbers4.2Linear Equations in Three variablespage 224-225: 5,7,9,13Group ProjectTacos anyone?9.7Logarithms and Change of Basepage 594-595: 15,21,27,39,45,47Group ProjectHow long it takes to double your money?If time permitsFinal Exam

## MATH1011 Applications of Calculus

### General Information

MATH1011 is a Junior (or first-year) unit forming part of the Fundamental Mathematics stream.

- Credit point value: 3CP.
- Classes per week: Two lectures and one tutorial.
- Lecturer(s) in 2021: Clio Cresswell
- Email contact address: [email protected]
Students: please check if your question can be answered by referring to the FAQ page before emailing us. If you decide to email us please include your name and SID.

Students have the right to appeal any academic decision made by the School or Faculty: see sydney.edu.au/students/academic-appeals.html.

You may also view the description of MATH1011 in the University's course search database.

### Answers to frequently asked questions

See the main junior mathematics page for information relating to all junior mathematics units, and see in particular the Junior Maths FAQ page.

### Diagnostic Quizzes

Students enrolled in MATH1011 should find both of these diagnostic quizzes straightforward and be able to obtain correct answers to most of the questions on the first attempt, without help and without using a calculator.

Students who find either of these quizzes difficult should contact the First Year Director (office Carslaw 525) immediately for advice.

### Online Resources

For enrolled students or other authorized people only, here is a link to the Canvas page for MATH1011.

* The teaching material appearing on this web site is intended for the use of enrolled students of the University of Sydney, and (unless otherwise specified) the University of Sydney holds copyright. Any other person or institution wishing to use any of this material must contact the university to make appropriate arrangements.*

### Useful Links

### Timetable

Show timetable / Hide timetable.

## MATH1011 Fundamentals of Mathematics

MATH1011 is a Level I Mathematics course intended for students who are in specific programs (such as Industrial Design), or who do not have sufficient Assumed Knowledge for direct entry into MATH1131, Mathematics 1A. See the course overview below. This course is not available as a General Education course or as a free elective.

**Units of credit:** 6

**Assumed knowledge:** A level of knowledge equivalent to achieving a mark of at least 60 in HSC Mathematics is assumed; students who have taken HSC General Mathematics will not have achieved this level. Students who have completed HSC Mathematics, but have not achieved a mark of at least 60 are advised to complete an appropriate Bridging Course before the commencement of semester. Otherwise, they are advised to seek help from the Director of First Year Mathematics.

**Exclusions:** DPST1013, MATH1031, ECON1202 or not enrolled in 3991 or any UNSW Business Program.

**Cycle of offering:** Terms 1 & 3

**Graduate attributes:** The course will enhance your research, inquiry and analytical thinking abilities.

**More information:**

The Online Handbook entry contains up-to-date timetabling information.

If you are currently enrolled in MATH1011, you can log into UNSW Moodle for this course.

For general advice, see advice on choosing first-year courses.

#### Course Overview

MATH1011 has two lecture strands, one in Calculus and one in Algebra, and introduces students to MAPLE, a computer based mathematical software package.

The Calculus strand emphasises curve sketching and develops the basic theory of differentiation, which can be thought of as the mathematical study of change, and of integration, which can be thought of as the mathematical study of area. One of the most practical results in mathematics, the Fundamental Theorem of the Calculus, states the surprising result that these theories are intimately connected. Modelling with the exponential function and the study of separable differential equations are given prominence in this strand.

The Algebra strand revises the theory of the trigonometric functions, and begins the study of vectors and matrices: with these two tools we can cope with simultaneous equations involving many variables. Complex numbers are also studied as they are needed when solving polynomial equations.

## 1011 maths

### MATHS 1011 - Mathematics IA

### North Terrace Campus - Semester 2 - 2021

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.

Open All

- General Course Information
##### Course Details

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 Staff

**Course Coordinator:**Dr Adrian Koerber##### 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:- 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.
- Demonstrate an understanding of the role of proof in mathematics.
- Demonstrate skills in writing mathematics.

##### 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

3,4,5 - Learning Resources
##### Required Resources

A comprehensive set of Course Notes will be available as a PDF on the MyUni site for this course. (More specific details will be provided on MyUni.)

##### Recommended Resources

- Poole, D.,
*Linear Algebra: a Modern Introduction*4th edition (Cengage Learning) - Stewart, J.,
*Calculus*9th edition (metric version) (Cengage Learning)

##### Online Learning

This course uses MyUni extensively and exclusively for providing electronic resources, such as lecture notes and videos, 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 Mobius, which we use to provide students with instantaneous formative feedback. Further details about using Mobius 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. - Poole, D.,
- Learning & Teaching Activities
##### Learning & Teaching Modes

This course relies on lecture videos 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.

We provide additional support via discussions on MyUni and via "drop-in" help.##### Workload

The information below is provided as a guide to assist students in engaging appropriately with the course requirements.

**Activity****Quantity****Workload hours**Course Notes & Videos 1 set 72 Lectures 12 12 Tutorials 11 11 Assignments & Practice 11 55 Mid Semester Test 1 6 **Total****156**##### Learning Activities Summary

In Mathematics IA the two topics of algebra and calculus detailed below are taught in parallel. The tutorials are a combination of algebra and calculus topics, pertaining to the previous week's lectures.**Topic Outline****Algebra****Linear systems and Gauss-Jordan elimination**- 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**- Linear combinations of vectors
- Homogeneous linear systems
- Linearly independent sets of vectors
- Subspaces and bases

**Matrix algebra**- Addition of matrices
- Multiplication of matrices
- Applications
- Elementary matrices
- The inverse of a matrix

**Optimisation**- Introduction, definitions
- Convex sets and vertices
- The method of slack variables

**Determinants**- Definition of the determinant
- Determinants and elementary row operations

**Calculus****Functions**- Definition, domain and range. Examples of functions.
- Inverses, inverse trigonometric functions.
- Zeros of functions.
- Limits, continuity.
- Interval bisection method.

**Differentiation and its applications**- Definition, interpretation, concavity.
- Rules for differentiation (product, quotient, chain).
- Implicit differentiation, derivatives of inverses.
- Related rates.
- Maxima and minima of functions and applications

**Integration**- Summation notation, definition of definite integral.
- Antiderivatives and The Fundamental Theorem of Calculus.
- Techniques of integration: substitution, parts, partial fractions.
- Applications.
- Improper integrals.

- Assessment
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 Summary

**Assessment Task****Task Type****Weighting****Learning Outcomes**Written Assignments Formative and Summative 12.5% all Mobius Assignments Formative and Summative 12.5% all Mid Semester Test Summative and Formative 15% 1,2,3,4 Final Exam Summative 60% 1,2,3,4,5,6 ##### Assessment Related Requirements

An aggregate score of 50% is required to pass the course.

##### Assessment Detail

Precise details of the nature and timing of all assessment components will be provided on the MyUni site for this course.

##### Submission

See MyUni for more comprehensive details regarding assignment submission, our late policy etc.

##### Course Grading

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:

https://www.adelaide.edu.au/student/exams/modified-arrangements-for-coursework-assessment/replacement-examinations-and-additional-assessment - 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.

MATHS 1011 is rated by StudentVIP members:

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### Reviews

Great overview of concepts in lectures with tutorials each week backing up these concepts. Staff in this course are always willing to help students with great explanations of any misconceptions. Enough support given without giving away answers.

Anonymous, Semester 1, 2019Has good, passionate lecturers. The lecture notes are amazing.

Anonymous, Semester 1, 2014Has good lecturers for Calculus and Algebra.

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