Engineering Mathematics I (010.140.005)

 

Spring  2007

 

 

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.

 

http://mrl.snu.ac.kr/courses/courses.html

 

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

Sohmin Ahn

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

Course Evaluation (code: 6138)

 

 

Schedule

Week 1

3 / 5

 Chap 1. First Order ODEs

  • 1.1 Basic concepts.

  • 1.2 Geometric meaning of direction fields

  • 1.3 Separable ODEs

3 / 7

  • 1.4 Exact ODEs. Integrating factors

  • 1.5 Linear ODEs. Bernoulli equation.

  • Homework #1

    • Chap 1.3: 2, 3, 10, 14, 27

    • Chap 1.4: 1, 3, 8,

    • Chap 1.5: 6, 7, 8, 27, 28

Week 2

3 / 12

 Electric Theater

3 / 14

 No class

Week 3

3 / 19

  • 1.6 Orthogonal trajectories

  • 1.7 Existence and uniqueness

 Chap 2. Second Order Linear ODEs

  • 2.1 Homogeneous linear ODEs of second order

3 / 21

  • 2.2 Homogeneous linear ODEs with constant coefficients

  • 2.3 Differential operator

  • 2.4 Modeling: Free Oscillations

  • Homework #2

    • Chap 1.6: 3, 6, 14, 18

    • Chap 1.7: 2, 6

    • Chap 2.1: 7, 8, 9, 15, 16, 20

    • Chap 2.2:1, 4, 21

    • Chap 2.3: 7

    • Chap 2.4: 2, 14

Week 4

3 / 26

  • 2.5 Euler-Cauchy equation

  • 2.6 Existence and uniqueness: Wronskian

3 / 28

  • 2.7 Nonhomogeneous ODEs

  • 2.9 Modeling: Electric circuits

  • 2.10 Solution by variation of parameters

  • Homework #3

    • Chap 2.5: 3, 12

    • Chap 2.6: 3, 11

    • Chap 2.7: 4, 5, 6

    • Chap 2.8: 2, 15

    • Chap 2.9: 4, 10

    • Chap 2.10: 2, 3, 5

Week 5

4 / 2

 Chap 3. Higher-Order Linear ODEs

  • 3.1 Homogeneous linear ODEs

  • 3.2 Homogeneous linear ODEs with constant coefficients

  • 3.3 Nonhomogeneous linear ODEs

4 / 4

 Chap 4. Systems of ODEs

  • 4.0 Basics of matrices and vectors

  • 4.1 Systems of ODEs as models

  • 4.2 Basic theory of systems of ODEs

  • Homework #4

    • Chap 3.1: 9, 10

    • Chap 3.3: 1, 2, 3, 11

Week 6

4 / 9

  • 4.3 Constant-coefficient systems.

  • 4.6 Nonhomogeneous linear systems of ODEs

4 / 11

 Chap 19. Numerics in General

  • 19.1 Introduction

  • Homework #5

    • Chap 4.1: 1, 11, 16

    • Chap 4.3: 6, 7

    • Chap 4.6: 3, 8, 18

Week 7

4 / 16

  • 19.2 Solution of equations by iteration

4 / 18

  • 19.3 Interpolation

  • 19.4 Spline interpolation

Week 8

4 / 23

  • 19.5 Numeric integration and differentiation

  • 21.1 Methods for first-order ODEs

4 / 25

 Midterm exam

Week 9

4 / 30

 Chap 21. Numerics for ODEs

  • 22.3 Methods for systems and higher order ODEs

Chap 6. Laplace Transforms

  • 6.1 Laplace transform. Inverse transform

  • 6.2 Transforms of derivatives and integrals

5 / 2

  • 6.2 (continued)

  • 6.3 Unit step function. t-shifting

  • 6.4 Short Impulses. Dirac's delta function. Partial fractions

  • Homework #6

    • Chap 6.1: 2, 6, 7, 22, 30, 31, 32, 48, 51

    • Chap 6.2: 3, 6, 7, 11, 21, 27

    • Chap 6.3: 7, 8, 16, 17, 25, 28

    • Chap 6.4: 3, 8

Week 10

5 / 7

  • 6.4 (continued)

  • 6.5 Convolution. Integral equations

  • 6.6 Differentiation and integration of transforms

5 / 9

  • 6.6 (continued)

  • 6.7 Systems of ODEs

 Chap 11. Fourier Series, Integrals, and Transforms

  • 11.1 Fourier series

Week 11

5 / 14

  • 11.1 (continued)

  • 11.2 Functions of any period

  • 11.3 Even and odd functions. Half-range expansions

5 / 16

  • 11.4 Complex Fourier series

  • 11.5 Forced oscillations

  • 11.6 Approximation by trigonometric polynomials

Week 12

5 / 21

  • 11.7 Fourier integrals

  • 11.8 Fourier cosine and sine transforms

5 / 23

  • 11.9 Fourier transform. Discrete and fast transforms

Week 13

5 / 28

 Chap 12. Partial Differential Equations

  • 12.1 Basic concepts

  • 12.2 Modeling: Vibrating string, Wave equation

  • 12.3 Solution by separating variables

5 / 30

  • 12.4 D'Alembert's solution of the wave equation

  • 12.5 Heat equation: Solution by Fourier series

  • 12.6 Heat equation: Solution by Fourier integrals and transforms

Week 14

6 / 4

  • 12.7 Modeling Membrane, Two-dimensional wave equation

  • 12.8 Rectangular membrane. Double Fourier series

  • 12.12 Solution by Laplace transforms

6 / 6

 No class (현충일)

Week 15

6 / 12

 Final exam