Calculus 3

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

1. Thomas, Weir and Hass (2010) Thomas Calculus, Early Transcendental, 12th edition, Addison-Wesley, ISBN-13: 978-0321730787, ISBN-10: 032173078X.
2. Anton, Bivens and Davis (2013) Calculus Late Transcendentals, 〖10〗^thEdition, John Wiley & Sons , INC,ISBN-13: 978-1-11809248-4 ISBN-10: 1118092481.
3. 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