620-141 Intermediate Mathematics A

Note

1. Students enrolling in this subject are expected to have completed VCE Specialist Mathematics 3/4 (or an equivalent subject). Students who have completed VCE Mathematical Methods 3/4 but not VCE Specialist Mathematics 3/4 should discuss their suitability for this subject with the Department's Director of First-year Studies.
2. Students may only gain credit for one of 620-141, 620-162 (1997 Handbook 618-141, 618-162). Passing 620-141 excludes subsequent credit for 620-161. Furthermore, credit cannot be obtained for 620-141 if any of 620-111, 620-121, 620-200, 620-211 (1997 Handbook 618-111, 618-121, 618-200, 618-211) has already been passed.

Credit Points

Coordinator

Semester

Contact

Subject Description

Students completing this subject should comprehend

• the manipulation of vectors, matrices, and systems of linear equations;
• the concepts of solid geometry;
• the properties of basic functions of calculus;

have developed the ability to

• solve systems of linear equations;
• employ vector methods in geometrical problems;
• differentiate and integrate the basic functions of calculus;
• use differential calculus to solve extremal problems;
• compute a wide range of integrals;
• use integration to compute area, length and volume;

and appreciate fundamental concepts in linear algebra and calculus necessary for further serious studies in mathematics.

Vectors and matrices: vectors in three-dimensional space, dot and cross products, triple products, determinants; equations of lines and planes, geometrical applications; matrices, row operations, inverses; solution of linear equations, row-reduction, rank. Calculus: functions of one real variable, 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; applications of integration, areas, arc length, surface areas and volumes of solids of revolution.

Assessment

Up to 26 pages of written assignments, a three-hour end-of-semester written examination and class tests totalling not more than 1.5 hours.