Jordan University of Science and Technology

Department of Mathematics and Statistics
 

Math 201 (Intermediate Analysis)         Semester: First         Year:0000 /0000

Course Objectives:

The objectives of this course is to let the students analyze and apply several types of functions: Vector valued functions, functions of several variables, and vector fields. By the end of this course the student should be able to:
  1. Recognize the several types of coordinate systems.
  2. Analyze vector valued functions and their applications.
  3. Analyze real valued functions of several variables and evaluate partial derivatives and multiple integrals.
  4. Solve optimization problems involving 2 or 3 variables.
  5. Analyze vector fields and evaluate several types of integrations: Line and surface integrals.
  6. Recognize and apply Green's, Divergence, and Stokes' Theorems.

Text Book:

Anton, Howard. Calculus, sixth edition. Wiley, New York, 1999.

References:

  1. Salas and Hille's. Calculus, One and Several Variables, seventh edition. Wiley, New York, 1995.
  2. Thomas and Finney. Calculus, ninth edition. Addison Wesley, Reading, Massachussets, 1996.

    3.  

Grading Policy:

First Exam 
30%
Second Exam 
30%
Final Exam 
40%

Schedule:

Week  Subject 
1 Rectangular coordinate systems in 3-space, spheres, 
cylindrical surfaces, applications. 
2 Vectors, dot products, cross products 
3 Prametric equations of lines in 3-space, planes in 3-space, 
Applications of Lines and Planes. 
4 Introduction to vector valued functions, 
Calculus of vector-valued functions, arc length. 
5 Unit tangent and normal vectors, curvature, motion along a curve.
6 Solving problems about vector-valued functions. 
Functions of several variables, quadratic surfaces.
7 Limits and continuity, partial derivatives, gradients. 
8 Differentiability, chain rule, directional derivative.
9 Tangent planes, total differentials, functions of n variables. 
10 Maxima and minima, Lagrange multipliers. 
Applications to maxima and minima problems.
11 Double integrals, double integrals in polar coordinates. surface area. 
12 Triple integrals, cylindrical and spherical coordinates,
Triple integrals in cylindrical and spherical coordinates.
13 Introduction to vector fields: line integrals, independent of path,
14 Green's Theorem, surface integral, surface integral of vector fields; Flux.
15 Divergence Theorem, Stokes' Theorem. Applications. 

File translated from TEX by TTH, version 2.51.
On 9 Oct 1999, 15:30.