Engineering Mathematics I (010.140.005)

 

Spring  2006

 


 

Description

 

Most practical problems involved in engineering can be formulated and solved mathematically. Engineering Mathematics I, II, and III introduce undergraduate students to those areas of mathematics which, from a modern point of view, are most important in connection with such engineering problems. In particular, this course, Engineering Mathematics I, emphasizes the ordinary differential equations which are used to describe the physical situations of such engineering problems. This course is also required for Engineering Mathematics II and III.

 

Instructor

Jehee Lee

Building 302, Room 325, Phone 1845

 

Class hours

Monday and Wednesday 1:00-2:15pm

 

Classroom

Building 302, Room 309

 

Teaching Assistants

Jong Pil Park

Building 302, Room 312-1, Phone 1864

 

Pre-Requisites

Elementary Calculus

 

Grading policy

Midterm: 40%

Final: 40%

Homework & Course participation: 20%

 

Textbook

Erwin Kreyszig, Advanced Engineering Mathematics 9th Ed., John Wiley & Sons.

 

Outline

  • Chap 1. First Order ODEs

  • Chap 2. Second Order Linear ODEs

  • Chap 3. Higher-Order Linear ODEs

  • Chap 4. Systems of ODEs

  • Chap 19. Numerics in General

  • Midterm

  • Chap 21. Numerics for ODEs

  • Chap 6. Laplace Transforms

  • Chap 11. Fourier Series, Integrals, and Transforms

  • Chap 12. Partial Differential Equations

  • Final

Notification

 We will have a class on 4/26.

 

 Midterm schedule

  • 4/29 Saturday 10:00am to Noon

  • Building 301, Room 301

 Final exam schedule

  • 6/13 Tuesday 6pm to 8pm

  • Building 301, Room 301

Schedule

Week 1

3 / 6

 Chap 1. First Order ODEs

  • 1.1 Basic concepts.

  • 1.2 Geometric meaning of direction fields

  • 1.3 Separable ODEs

3 / 8

  • 1.4 Exact ODEs. Integrating factors

  • 1.5 Linear ODEs. Bernoulli equation.

  • Reading assignment: 7.1 and 7.2

Week 2

3 / 13

  • 1.6 Orthogonal trajectories

  • 1.7 Existence and uniqueness

 Chap 2. Second Order Linear ODEs

  • 2.1 Homogeneous linear ODEs of second order

  • Homework #1

    • Chap 1.3: 2, 3, 9, 14, 15, 29

    • Chap 1.4: 3, 4, 12, 21

    • Chap 1.5: 7, 8, 15, 20, 21

3 / 15

  • 2.2 Homogeneous linear ODEs with constant coefficients

  • 2.3 Differential operator

  • 2.4 Modeling: Free Oscillations

  • Reading assignment: 7.3 and 7.4

Week 3

3 / 20

  • 2.5 Euler-Cauchy equation

  • 2.6 Existence and uniqueness: Wronskian

  • Homework #2

    • Chap 1.6: 4, 7

    • Chap 1.7: 5, 10

    • Chap 2.1: 7, 8, 9, 15, 16

    • Chap 2.2: 2, 30

    • Chap 2.3: 14

    • Chap 2.4: 6

    • Chap 2.5: 8, 11

3 / 22

  • 2.7 Nonhomogeneous ODEs

  • 2.9 Modeling: Electric circuits

  • 2.10 Solution by variation of parameters

  • Reading assignment: 7.5 and 7.6

Week 4

3 / 27

 Chap 3. Higher-Order Linear ODEs

  • 3.1 Homogeneous linear ODEs

  • 3.2 Homogeneous linear ODEs with constant coefficients

  • 3.3 Nonhomogeneous linear ODEs

  • Homework #3

    • Chap 2.7: 1, 3, 15

    • Chap 2.9: 7, 11, 14

    • Chap 2.10: 7, 8, 10, 13, 14

    • Chap 3.1: 3, 4, 9, 10

    • Chap 3.2: 9, 10

    • Chap 3.3: 3, 6, 7

    • find the integral of (x^n ln x)

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