618-162 Introductory Mathematics B

Note:

1. Students may not gain credit for both Mathematics 618-162 and any of 618-100 (1995 Handbook), 618-141 or 618-151 (1955 Handbook). Furthermore, credit cannot be obtained for 618-162 if any of 618-101 (1995 Handbook), 618-111, 618-121 or 618-141 has already been passed.

2. This subject is normally taken after 618-161, but may also be taken by students who would otherwise have selected 618-141 in first semester.

Credit Points:

Coordinator:

Timetable:

Contact:

Objectives:

On completion of this subject, students 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 skills required to solve systems of linear equations;

• the skills to employ vector methods in geometrical problems;

• the skills required to differentiate the integrate the basic functions of calculus;

• 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.

Appreciate:

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

Content:

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: