Definite integrals of functions of a single variable. Fundamental Theorem of Calculus. Indefinite integrals. Applications of the definite integral to area, volume, arc length and surface of revolution. Integral of trigonometric and hyperbolic functions and their inverses, techniques of integrations, improper integrals. Infinite sequences and series, converging tests, alternating series, absolute and conditional convergence. Power series, Taylor and Maclaurin series, convergence of Taylor series. The Binomial Series and applications of Taylor series.
Course Objectives & Outcomes
- Equip the student with necessary knowledge and skills to enable them to find the integral of different kinds of single valued functions.
- Use integrals in different kinds of applications.
- Unable the student to use different convergence tests to determine the convergence or the divergence of series.
- Use power series in some applications.
At the end of this course, the student will be able to:
- Identify the fundamental theory of calculus.
- Use different technics to find integrals.
- Calculate trigonometric and improper integrals.
- Apply integration in solving geometric applications.
- Select the best convergent test to determine the convergence or divergence of series.
- Use power series in some mathematical applications.
- Draw graphs for specific problems and identify initial condition.
- Thomas, Weir and Hass (2010) Thomas Calculus, Early Transcendental, 12th edition, Addison-Wesley, ISBN-13: 978-0321730787, ISBN-10: 032173078X.
- Anton, Bivens and Davis (2013) Calculus Late Transcendentals, 〖10〗^thEdition, John Wiley & Sons, INC, ISBN-13: 978-1-11809248-4 ISBN-10: 1118092481.
- R. Ellis, D. Gulick (2000) Calculus with Analytic Geometry, 5^th edition, Academic Press. 5th edition, ISBN-13: 978-0030968006, ISBN-10: 0030968003
Course ID: MATH 205
|Credit hours||Theory||Practical||Laboratory||Lecture||Studio||Contact hours||Pre-requisite||4||4||4||MATH 201|