Engineering Mathematics (400.001)

Fall  2005

 


 

Description

 

This course is intended to introduce basic concepts of differential equations and solution techniques.

 

Instructor

Jehee Lee

Building 302, Room 325, Phone 1845

 

Class hours

Monday and Wednesday 4:00-5:15pm

 

Classroom Building 302, Room 308

 

Teaching Assistants

Manmyung Kim

Building 302, Room 312-1, Phone 1864

 

Pre-Requisites

Elementary Calculus

 

Grading policy

1st midterm: 25%

2nd midterm: 25%

Final: 25%

Homework & Course participation: 25%

 

Textbook

Erwin Kreyszig, Advanced Engineering Mathematics 8th Ed., John Wiley & Sons.

 

Outline
  • Chap 1. First-Order Differential Equations

  • Chap 2. Linear Differential Equations of Second and High-Order

  • Chap 3. Systems of Differential Equations

  • Midterm

  • Chap 5. Laplace Transforms

  • Chap 10. Fourier Series, Integrals, and Transforms

  • Midterm

  • Chap 11. Partial Differential Equations

  • Chap 17. Numerical Methods in General

  • Chap 19. Numerical Methods for Differential Equations

  • Final

Announcement

Old midterms are available for study purposes.

Schedule

Week 1

9 / 5

 Chap 1. Differential Equations of the First Order

  • 1.1 Basic concepts and ideas

  • 1.2 Geometric interpretation

  • 1.3 Separable differential equations

  • 1.4 Modeling: Separable equations

9 / 7

  • 1.5 Exact differential equations

  • 1.6 Linear differential equations

  • Reading assignment: 6.1 and 6.2

  • Homework #1

    • Chap 1.3: 4, 9, 10, 14, 15, 17, 21, 22

    • Chap 1.4: 17. 18

    • Chap 1.5: 8, 9, 14, 17, 19, 31, 32

    • Chap 1.6: 9, 11, 17, 18, 20, 26, 27, 28, 29, 33, 35

 

9 / 12

  • 1.7 Modeling of electric circuits

  • 1.8 Orthogonal trajectories

  • 1.9 Existence and Uniqueness

  • Picard iteration

9 / 14

 Chap 2. Linear Differential Equations of Second and Higher Order

  • 2.1 Homogeneous linear equations of 2nd order

  • 2.2 Second order homogeneous equations with constant coefficients

  • 2.3 Case of complex roots

  • 2.4 Differential operator

  • Reading assignment: 6.3 and 6.4

  • Homework #2

    • Chap 1.8: 12, 15, 18

    • Chap 1.9: 13, 18

    • Chap 2.1: 7

    • Chap 2.2: 11, 16, 18, 19, 20, 21, 22, 23

    • Chap 2.3: 1, 7, 16, 20

Week 3

9 / 19

 No class (추석)

9 / 21

  • 2.6 Euler-Cauchy equation

  • 2.7 Existence and uniqueness: Wronskian

  • Reading assignment: 6.5 and 6.6

  • Homework #3

    • Chap 2.6: 12, 17

    • Chap 2.7: 11, 17

Week 4

9 / 26

  • 2.8 Nonhomogeneous equations

  • 2.9 Solution by undetermined coefficients

  • 2.10 Solution by variation of parameters

  • 2.12 Modeling of electric circuits

9 / 28

  • 2.13 Higher order linear differential equations

  • 2.14 Higher order homogeneous equations with constant coefficients

  • 2.15 Higher order nonhomogeneous equations

  • Reading assignment: 6.7 and 6.8

  • Homework #4

    • Chap 2.8: 3, 8, 13

    • Chap 2.9: 1, 8, 13

    • Chap 2.10: 6, 9, 14

    • Chap 2.14: 7

    • Chap2.15: 6, 13

    • Compute the integral of (x^n ln x)

Week 5

10 / 3

 No class (개천절)

10 / 5

 Chap 3. Systems of Differential Equations

  • 3.0 Vectors, matrices, eigenvalues

  • 3.1 Introductory examples

  • 3.2 Basic concepts and theory