Handbook 1996 : Faculty of Science (Volume 4 page 206)
Mathematics subject : Next:618-122 | Prev:618-112 | Search | Help
618-121 "Mathematics 1A" appears differently in several places - choose the one you want:
1. Mathematics, Faculty of Science (v4, p206) : Next:618-122 | Prev:618-112
3. First Year Engineering, Faculty of Engineering (v4, p85) : Next:618-122 | Prev:610-172
Note: Credit cannot be obtained for both 618-121 and any of 618-101 (1995 Handbook), 618-111 or 618-142, nor for both of 618-121 and any of 618-141, 618-161 or 618-162 if 618-121 has already been passed.
Credit points: 12.5
Coordinator: Dr J J Cross
Prerequisite: 618-141; or both of 618-161, 618-162; or satisfactory performance in the Exemption Test.
Contact: 39 lectures (three a week), 13 x 1-hour tutorials and 39 hours problem solving
Timetable: Semester 1
Objectives:
On completion of this subject, students should:Comprehend:
- some of the nature of the different types of numbers they use;
- the intuitive notion of limits as used in continuity, differentiation and integration;
- the notion of integral as area;
- the extension of the notion of vectors in two or three dimensions to any finite number of dimensions;
- the theoretical treatment of systems of simultaneous linear equations.
Have developed:
- an ability to manipulate complex numbers and to use them to solve problems;
- an ability to use differential calculus to solve extremal problems;
- an ability to compute a wide range of integrals;
- an ability to use integration to compute area, length and volume;
- an ability to solve arbitrary systems of simultaneous linear equations.
Appreciate:
- the role of proof and logical reasoning in mathematics;
- the use of complex numbers; the role of limits in both the differential and integral calculus;
- the practical uses of calculus; the use of the ideas of linear algebra in dealing with the solution of simultaneous linear equations.
Content:
Foundations: sets, integers, mathematical induction; real numbers; complex numbers, polar form, de Moivre's theorem, complex exponential. Calculus: functions of one real variable (including limits and continuity), derivatives; curve sketching; maxima and minima, curvature; antiderivatives and the definite integral; trigonometric functions and their inverses, logarithm, exponential function, hyperbolic functions and their inverses; systematic integration; approximate integration; applications of integration, areas, arc length, surface areas and volumes of solids of revolution. Vectors and linear equations: vectors in three-dimensional space, dot and cross products, triple products, determinants; linear dependence; equations of lines and planes, geometrical applications; bases and coordinates, dimension; row-reduction, rank, inverse, solution of linear equations, geometrical interpretation.
Assessment:
Up to 26 pages of written assignments, up to three hours of end-of-semester written examination and class tests totalling not more than 1.5 hours.
1. Mathematics, Faculty of Science (v4, p206) : Next:618-122 | Prev:618-112
3. First Year Engineering, Faculty of Engineering (v4, p85) : Next:618-122 | Prev:610-172
2. Math. & Stats., Faculty of Educ(Parkville) (v5, p144) : Next:618-122
Note: Credit cannot be obtained for both 618-121 and any of 618-101 (1995 Handbook), 618-111 or 618-142, nor for both of 618-121 and any of 618-141, 618-161 or 618-162 if 618-121 has already been passed.
Credit points: 12.5
Coordinator: Dr J J Cross.
Prerequisite: 618-141; or both of 618-161, 618-162; or satisfactory performance in the Exemption Test.
Contact: 39 lectures (three a week), 13 1-hour tutorials and 39 hours problem solving
Timetable: First semester.
Objectives:
On completion of this subject, students should:Comprehend:
- some of the nature of the different types of numbers they use;
- the intuitive notion of limits as used in continuity, differentiation and integration;
- the notion of integral as area;
- the extension of the notion of vectors in two or three dimensions to any finite number of dimensions;
- the theoretical treatment of systems of simultaneous linear equations.
Have developed:
- an ability to manipulate complex numbers and to use them to solve problems;
- an ability to use differential calculus to solve extremal problems;
- an ability to compute a wide range of integrals;
- an ability to use integration to compute area, length and volume;
- an ability to solve arbitrary systems of simultaneous linear equations.
Appreciate:
- the role of proof and logical reasoning in mathematics;
- the use of complex numbers; the role of limits in both the differential and integral calculus;
- the practical uses of calculus; the use of the ideas of linear algebra in dealing with the solution of simultaneous linear equations.
Content:
Foundations Sets, integers, mathematical induction; real numbers; complex numbers, polar form, de Moivre's theorem, complex exponential. Calculus Functions of one real variable (including limits and continuity), derivatives; curve sketching; maxima and minima, curvature; antiderivatives and the definite integral; trigonometric functions and their inverses, logarithm, exponential function, hyperbolic functions and their inverses; systematic integration; approximate integration; applications of integration, areas, arc length, surface areas and volumes of solids of revolution. Vectors and linear equations Vectors in three- dimensional space, dot and cross products, triple products, determinants; linear dependence; equations of lines and planes, geometrical applications; bases and coordinates, dimension; row- reduction, rank, inverse, solution of linear equations, geometrical interpretation.
Assessment:
Up to 26 pages of written assignments, up to three hours of end-of-semester written examination and class tests totalling not more than 1.5 hours.
* Note that CONTACT, CONTENT, SEMESTER differs from the maintainer's version above. A log of variations is available.
2. Math. & Stats., Faculty of Educ(Parkville) (v5, p144) : Next:618-122
4. Mathematical Sciences, Faculty of Eco & Comm (v3, p208) : Next:618-122 | Prev:617-141
Note: Credit cannot be obtained for both 618-121 and any of 618-101 (1995 Handbook), 618-111 or 618-142, nor for both of 618-121 and any of 618-141, 618-161 or 618-162 if 618-121 has already been passed.
Credit points: 12.5
Coordinator: Dr J J Cross
Prerequisite: 618-141; or both of 618-161, 618-162; or satisfactory performance in the Exemption Test.
Contact: 39 lectures (three a week), 13 x 1-hour tutorials and 39 hours problem solving
Timetable: Semester 1
Objectives:
On completion of this subject, students should:Comprehend:
- some of the nature of the different types of numbers they use;
- the intuitive notion of limits as used in continuity, differentiation and integration;
- the notion of integral as area;
- the extension of the notion of vectors in two or three dimensions to any finite number of dimensions;
- the theoretical treatment of systems of simultaneous linear equations.
Have developed:
- an ability to manipulate complex numbers and to use them to solve problems;
- an ability to use differential calculus to solve extremal problems;
- an ability to compute a wide range of integrals;
- an ability to use integration to compute area, length and volume;
- an ability to solve arbitrary systems of simultaneous linear equations.
Appreciate:
- the role of proof and logical reasoning in mathematics;
- the use of complex numbers; the role of limits in both the differential and integral calculus;
- the practical uses of calculus; the use of the ideas of linear algebra in dealing with the solution of simultaneous linear equations.
Content:
Foundations Sets, integers, mathematical induction; real numbers; complex numbers, polar form, de Moivre's theorem, complex exponential. Calculus Functions of one real variable (including limits and continuity), derivatives; curve sketching; maxima and minima, curvature; antiderivatives and the definite integral; trigonometric functions and their inverses, logarithm, exponential function, hyperbolic functions and their inverses; systematic integration; approximate integration; applications of integration, areas, arc length, surface areas and volumes of solids of revolution. Vectors and linear equations Vectors in threedimensional space, dot and cross products, triple products, determinants; linear dependence; equations of lines and planes, geometrical applications; bases and coordinates, dimension; rowreduction, rank, inverse, solution of linear equations, geometrical interpretation.
Assessment:
Up to 26 pages of written assignments, up to three hours of end-of-semester written exam-ination and class tests totalling not more than 1.5 hours.
* Note that ASSESSMENT, CONTENT, OBJECTIVES differs from the maintainer's version above. A log of variations is available.
4. Mathematical Sciences, Faculty of Eco & Comm (v3, p208) : Next:618-122 | Prev:617-141
Status: Official 1996 Date created: Oct 9 1995 Last modified: Oct 9 1995 Authorised by: Academic Registrar Email enquiries: Course_Information@registrar.unimelb.edu.au
Maintained by: Dept. of Mathematics, Faculty of Science.
Copyright © University of Melbourne 1995,1996.