620-162 Introductory Mathematics B

Note

1. 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.
2. This subject is normally taken after 620-161, but may also be taken by students who would otherwise have selected 620-141 in first semester.

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 the 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

• the 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 row 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 24 pages of written assignments, a three-hour end-of-semester written examination and class tests totalling not more than 1.5 hours.