MATH 6702 Math Methods in Applied Sciences II
Spring 2013
MW 4:30-6:00
Sustainable Education 110.
Office Hours: MW 6-7, classroom.
Review of vector calculus and and its application to partial
differential equations.
The text that will be used is:
Advanced
Engineering Mathematics by Dennis G. Zill,
Warren S.
Wright, Jones & Bartlett Learning.
The syllabus can be found here.
There will be two midterm.
The exercise listed are for HW collection. I will collect them
every
two weeks and grade 2 or 3 exercises among the one assigned. In the
list of assigned problems below the number in square braskets refer to
the 4th and 3rd editions of the textbook.
The final grade will be based on the following rules: 45%
final, 35%
midterms, 20% HW. Curving will be done on the final result.
Arguments covered.
- Multidimensional Calculus
- Curves and surfaces, gradients, divergence and curl
- Taylor expansions in IR3
- Divergence and Stokes theorem
- Classification of partial differential equations
- The concept of well-posed problems
- Potential Problems
- Derivation of Laplace's equation; Dirichlet and Neumann
problems
- The maximum principle and uniqueness of solutions
- Green's identities and Green's functions for selected
domains
- Connections to variational problems and complex
variables
- Parabolic Problems
- Derivation of the heat equation in IR3; discussion of
boundary and initial conditions; the maximum principle for the heat
equation and uniqueness of solutions; fundamental solution for pure
initial value problems; Duhamel's principle for inhomogeneous equations
- Hyperbolic Problems
- The concept of characteristics for a single first order
equation
- Solution of initial value problems; the concept of a
shock
- D'Alembert solution of the wave equation; Huyghen's
principle
and the solution of the wave equation in IR3
First week
Material covered:
- 9.1 Vector Function
- 9.2 Motion on a curve
- 9.3 Curvature and component of the acceleration
Exercises:
- (9.1): 19, 26, 31, 36
- (9.2): 6, 8, 21 [17], 26 [22]
- (9.3): 4, 21, 22
Second week
Material covered:
- 9.4 Partial Derivatives
- 9.5 Directional Derivative
- 9.6 Tangent Planes and Normal Lines
Exercises:
- (9.4): 33, 43, 55
- (9.5): 29, 39, 40
- (9.6): 21, 22, 38
Third week
Material covered:
Exercises:
Fourth week
Material covered:
- 9.8 Line Integrals
- 9.9 Independence of the Path
Exercises:
- (9.8): 30, 37, 39
- (9.9): 17, 18, 21
Fifth week
Material covered:
- 9.10 Double Integrals
- 9.11 Double Integrals in Polar Coordinates
Exercises:
- (9.10): 19, 23, 61
- (9.11): 15, 29, 34
Sixth week
Material covered:
- 9.12 Green’s Theorem
- 9.13 Surface Integrals
- 9.14 Stokes’ Theorem
Exercises:
- (9.12): 8, 12, 28
- (9.13): 13, 18, 43
- (9.14): 8, 15, 18
The first midterm will be on Wednesday Febraury 20. Here is the solution set.
Seventh week
- Review class and midterm.
Eighth week
Material covered:
- Midterm solution set.
- 9.15 Triple Integrals
Exercises:
Nineth week
Material covered:
- 9.16 Divergence Theorem
- 9.17 Change of Variables in Multiple Integrals
- Review.
Exercises:
- (9.16): 11, 15, 22
- (9.17): 10, 16,27
The second midterm will be on Wednesday April 3. Here is the solution set.
Tenth week
Material covered:
- 12.1 Orthogonal function.
- 12.2 Fourier Series.
- 12.3 Fourier Cosine and Sine Series.
Exercises:
- (12.1): 11, 21, 22
- (12.2): 5, 12, 17
- (12.3): 30, 32, 49
Eleventh week
Spring Break.
Twelfth week
Material covered:
- 13.5 Laplace's Equation.
- The Maximum Principle and Green Functions.
Exercises:
Projects for extra credit. Please, if you decide to turn in extra credit, choose one of this problems or let me know one of you choice.
Thirteenth week
Material covered:
- 13.3 Heat Equation.
- 14.1 Problems in Polar Coordinates.
Exercises:
- (13.3): 3, 5, 6
- (14.1): 2, 7, 13
Fourteenth week
Material covered:
- 13.4 Wave Equation.
- 14.2 Problems in Cylindrical Coordinates
Exercises:
- (13.4): 2, 4, 12
- (14.2): 9, 17