Course Description
Vectors in 3-dimensional space: geometry of the three dimensional space and vectors, parametric equations of lines and planes in space, quadratic surfaces. Partial derivative: domain and the range of functions of several variables , limit and continuity of function of several variable, partial derivatives, the chain rule, directional derivatives and gradient , the extreme values of function of several variables, Lagrange multipliers
Multiple integral: double integral, Polar coordinates, polar curves, double integrals and area in polar coordinates , triple integral, triple integral in cylindrical and spherical coordinates
Line integral: line integral on parameterized two or three dimensional curve of scalar functions and vector valued functions. Green's theorems.
Course Objectives & Outcomes
Objectives:
- Equip student with necessary knowledge and skills to enable them to find all operations on three dimensional vectors and find equation of line and plane.
- Enable the student to find limits, partial derivatives, directional derivatives and the extreme values of functions of several variables.
- Equip student with necessary skills to apply the double and triple integrals to find the area, the volume, the work, the flow, and the flux.
Outcomes: Upon successful completion of this course, the student will be able to:
- Calculate all operations on three dimensional vectors and the equation of line, the plane in space and find the distance between point and line or plane.
- Calculate the limits, the partial derivatives, the total derivatives, the directional derivatives and the extreme values of functions of two variables.
- Evaluate the double and triple integrals using polar, cylindrical or spherical coordinates.
- Apply multiple integrals to find the area, the volume, work, the flow, and the flux. Apply Green's theorems.
References
- 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 301
Credit hours | Theory | Practical | Laboratory | Lecture | Studio | Contact hours | Pre-requisite | 4 | 4 | 4 | MATH 203 |
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