Gold Coast, Australia
Area of Study
Taught In English
Prerequisite : A grade of SA over 4 semesters in Mathematics B (Qld high school subject) or equivalent study over 4 semesters of a high school subject that includes the study of differential and integral calculus.
Students that do not have this prerequisite should consider studying the course 1013SCG that does not assume a knowledge of Mathematics B or equivalent.
Course Level Recommendations
ISA offers course level recommendations in an effort to facilitate the determination of course levels by credential evaluators.We advice each institution to have their own credentials evaluator make the final decision regrading course levels.
Recommended U.S. Semester Credits3 - 4
Recommended U.S. Quarter Units4 - 6
Hours & Credits
The course revises and extends basic integral and differential calculus of one variable, introduces partial derivatives and basic vector algebra in two and three dimensions. It provides a foundation for later studies in mathematics and science.
This course acts as a bridge between the students' previous experience in mathematics and further tertiary study in mathematics. It provides the basis for the acquisition of the basic computational and theoretical skills necessary for the practising scientist, mathematician, engineer or pilot and introduces students to the mathematical and logical way of thinking desirable in the training of these professionals.
This course acts as a bridge between the students' previous experience in mathematics and further tertiary study in mathematics. It provides the basis for the acquisition of the basic computational and theoretical skills necessary for the practising scientist, mathematician, engineer and pilot and introduces students to the mathematical and logical way of thinking desirable in the training of these professionals.
The course revises and extends basic integral and differential calculus of one variable, introduces partial derivatives and basic vectors in three dimensions. It provides a mathematical foundation for later studies in mathematics and science.
After successfully completing this course you should be able to:
1 Manipulate 2D and 3D vectors and use vector addition and subtraction as well as the dot and cross product of vectors. Use these ideas in problems involving geometric, force and velocity vectors.
2 Know and use the standard addition formulas for sin, cos and tan. Be able to prove some of the simpler trig addition formulas. Understand and use the inverse trigonometric functions.
3 Define and evaluate reasonably straightforward limits and be able to use and interpret the limit definition of the derivative.
4 Calculate derivatives using the sum, product, quotient and chain rule. Know the derivatives of basic functions.
5 Identify the local maxima, minima and points of inflection of straightforward functions and use this information to sketch the graphs of these functions.
6 State and use the small change formula appropriately.
7 Convert word problems into mathematics and analyze them using calculus.
8 State and calculate Taylor approximations to standard functions.
9 State and use l'Hopital's rule to evaluate 0/0 limits.
10 Understand the definition of integrals using Riemann sums and be able to provide a variety of situations in which the integral is used besides areas under curves.
11 State the Fundamental Theorem of Calculus and be able to evaluate simple definite and indefinite integrals.
12 Be able to use straightforward substitutions to evaluate integrals.
13 Use definite integrals to calculate areas.
14 Understand the geometric meaning and the analytic definition of partial derivatives. Calculate the first and second derivatives of straightforward functions and be able to apply the small change formula for functions of several variables.
Test or quiz - Algebra quiz 5%/5
Log of Learning Activities - Tutorials (11) 11%/33
Assignment - Problem Solving Assignment - Assignments (2) 10%/10
Exam - selected and constructed responses - Mid-semester exam 20%/90
Exam - selected and constructed responses - Final Examination 54%/90
Courses and course hours of instruction are subject to change.
Eligibility for courses may be subject to a placement exam and/or pre-requisites.
Credits earned vary according to the policies of the students' home institutions. According to ISA policy and possible visa requirements, students must maintain full-time enrollment status, as determined by their home institutions, for the duration of the program.