MAT 222

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This course covers more complex topics in differential and integral calculus. ... Form and solve first and second order differential equations. 4. Solve problems containing implicit, ... Hanrahan V., Secker P., Porkess R., Pure Mathematics 1 ( MEI Structured ... Bostock, L. and Chandler, S., Core Mathematics, Stanley Thornes ...
Community College of the Cayman Islands

ASSOCIATE DEGREE SYLLABUS

COURSE NAME:

CALCULUS II

COURSE #: MAT 222

COURSE DESCRIPTION This course covers more complex topics in differential and integral calculus. These include: trigonometric, implicit and parametric functions; further techniques of integration; first and second order differential equations; hyperbolic functions: their inverses, derivatives and integrals; polar coordinates, and power series. Credits: 3 Prerequisite:

MA 221

COURSE OBJECTIVES This course is intended to enable the student to: 1. Differentiate and integrate trigonometric functions 2. Classify a function and integrate it appropriately. 3. Form and solve first and second order differential equations. 4. Solve problems containing implicit, parametric and hyperbolic functions and power series.

COURSE OUTLINE I

DIFFERENTIATION AND INTEGRATION TRIGONOMETRIC FUNCTIONS Sin x, cos x, tan x, sin–1x, cos–1x, tan–1x. Trig. Identities in integration.

II

FURTHER TECHNIQUES OF INTEGRATION Integration by parts. Integration using partial fractions. Standard integrals. Systematic integration.

OF

1

Reduction methods. III

IMPLICIT AND PARAMETRIC FUNCTIONS

IV

DIFFERENTIAL EQUATIONS Forming differential equations. First order – variable separable, first order exact, integrating factor. Second order linear, particular integral, complementary functions

V

POLAR COORDINATES Polar curve sketching (recap). Area.

VI

HYPERBOLIC FUNCTIONS The hyperbolic functions, their inverses, derivatives and integrals.

VII

POWER SERIES MacLaurin’s series. Expansions of ex, ln(1 +/- x), cos x, sin x. Taylor’s expansion.

ASSESSMENT Quiz, Course Assignments/Project Mid-Semester Examination Final Examination Total

-

40% 20% 40% 100%

REQUIRED TEXT Stewart, James, Calculus Early Transcendentals, Brooks/ Cole Publishing Company Ltd., 2 nd Edition, 1991

References 2

The following textbook(s) will be used for this course: Finney, Demana, Waits, Kennedy, Calculus A Complete Course (2nd Edition), Addison-Wesley, Longman, 2000. Backhouse, Houldsworth, Horril, Wood, Essential Pure Mathematics , Longman, 1991. Hanrahan V., Secker P., Porkess R., Pure Mathematics 1 (MEI Structured Mathematics), Hodder and Stoughton. Hanrahan V., Secker P., Porkess R., Pure Mathematics 2 (MEI Structured Mathematics), Hodder and Stoughton. Berry C., Hanrahan V., Porkess R., Pure Mathematics 3 (MEI Structured Mathematics), Hodder and Stoughton. Bostock, L. and Chandler, S., Core Mathematics, Stanley Thornes (Publishing) Ltd., 1996 Bostock, L., Chandler, S., Rourke, C., Further Pure Mathematics, Stanley Thornes (Publishing) Ltd., 1982 May-12

3