Engineering Mathematics I (010.140)

 

Fall 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 2:30-3:45pm

Classroom

Building 302, Room 209

Teaching Assistants

Eunjung Ju and Jongmin Kim, Building 302, Room 312-1, Phone 1864

Pre-Requisites

Elementary Calculus

Grading policy

Midterm and final exams: 70%

Homework & Course participation: 30%

Textbook

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

Outline

  • Chap 7. Linear Algebra

  • Chap 8. Linear Algebra: Matrix Eigenvalue Problems

  • Chap 1. First Order ODEs

  • Chap 2. Second Order Linear ODEs

  • Midterm exam

  • Chap 3. Higher-Order Linear ODEs

  • Chap 4. Systems of ODEs

  • Chap 5. Series Solutions of ODEs

  • Chap 6. Laplace Transforms

  • Final exam

Schedule

Week 1

9 / 3

Chap 7. Linear Algebra: Matrices, Vectors, Determinants.

  • 7.1 Matrices, Vectors

  • 7.2 Matrix Multiplication

9 / 5

  • 7.3 Linear Systems of Equations. Gauss Elimination

  • 7.4 Linear Independence. Rank of a Matrix. Vector Space

Homework #1

  • Chap 7.2: 1, 19, 21
  • Chap 7.3: 4, 7
  • Chap 7.4: 2, 7, 13, 14, 22, 23

Week 2

9 / 10

  • 7.5 Solutions of Linear Systems

  • 7.6 Second- and Third Order Determinants

  • 7.7 Determinants. Cramer's Rule

9 / 12

  • 7.8 Inverse of a Matrix. Gauss-Jordan Elimination

Chap 8. Linear Algebra: Matrix Eigenvalue Problems

  • 8.1 Eigenvalues, Eigenvectors

Homework #2

  • Chap 7.4: 27, 30
  • Chap 7.7: 8, 9, 19, 22
  • Chap 7.8: 5, 7, 13, 15, 17
  • Chap 8.1: 2, 4, 8, 14, 15

Week 3

9 / 17

  • 8.2 Applications

  • 8.3 Symmetic, Skew-Symmetric, and Orthogonal Matrices

  • 8.4 Eigenbases. Diagonalization. Quadratic Forms

 

9 / 19

Chap 1. First Order ODEs

  • 1.1 Basic concepts.

  • 1.2 Geometric meaning of direction fields

  • 1.3 Separable ODEs

Homework #3

  • Chap 8.1: 30
  • Chap 8.2: 1, 3, 5, 18
  • Chap 8.3: 3, 5, 7, 14, 15
  • Chap 8.4: 1, 2, 7, 13, 19
  • Chap 1.3: 4, 7, 9, 14, 15

Week 4

9 / 24

No Class

9 / 26

No Class

Week 5

10 / 1

  • 1.4 Exact ODEs. Integrating factors

  • 1.5 Linear ODEs. Bernoulli equation

10 / 3

No Class

Week 6

10 / 8

  • 1.6 Orthogonal trajectories

  • 1.7 Existence and uniqueness

 Chap 2. Second Order Linear ODEs

  • 2.1 Homogeneous linear ODEs of second order

10 / 10

  • 2.2 Homogeneous linear ODEs with constant coefficients

  • 2.3 Differential operator

  • 2.4 Modeling: Free Oscillations

Homework #4

  • Chap 1.4: 1, 4, 9, 13
  • Chap 1.5: 2, 6, 7, 8,18, 20
  • Chap 1.6: 3, 4
  • Chap 2.1: 8, 10, 11, 20
  • Chap 2.2: 1, 4, 6
  • Chap 2.4: 2, 3

Week 7

10 / 15

  • 2.5 Euler-Cauchy equation

  • 2.6 Existence and uniqueness: Wronskian

10 / 17

  • 2.7 Nonhomogeneous ODEs

  • 2.8 Modeling: Forced Oscillations

  • 2.9 Modeling: Electric circuits

  • 2.10 Solution by variation of parameters

Week 8

10 / 22

Chap 3. Higher-Order Linear ODEs

  • 3.1 Homogeneous linear ODEs

  • 3.2 Homogeneous linear ODEs with constant coefficients

  • 3.3 Nonhomogeneous linear ODEs

10 / 24

Midterm exam (6pm-8pm, bld. 302, room 105)

Week 9

10 / 29

No Class

10 / 31

No Class

Week 10

11 / 5

Chap 4. Systems of ODEs

  • 4.1 Systems of ODEs as models

  • 4.2 Basic theory of systems of ODEs

11 / 7

  • 4.3 Constant-coefficient systems.

  • 4.6 Nonhomogeneous linear systems of ODEs

Homework #5

  • Chap 3.3: 3, 7
  • Chap 4.1: 12, 16
  • Chap 4.3: 3, 7, 18
  • Chap 4.6: 4, 5, 15, 19

Week 11

11 / 12

Chap 5. Series Solutions of ODEs

  • 5.1 Power series method

  • 5.2 Theory of the power series method

11 / 14

  • 5.3 Legendre's equation

  • 5.4 Frobenius method

Homework #6

  • Chap 5.1: 2, 4, 5
  • Chap 5.2: 1, 2, 8, 16, 17
  • Chap 5.3: 5, 6, 7
  • Chap 5.4: 1, 2, 10

Week 12

11 / 19

  • 5.5 Bessel's Equation

  • 5.6 Bessel's functions of the second kind

11 / 21

  • 5.7 Sturm-Liouville problems. Orthogonal functions

  • 5.8 Orthogonal eigenfunction expansions

Week 13

11 / 26

Chap 6. Laplace Transforms

  • 6.1 Laplace transform. Inverse transform

  • 6.2 Transforms of derivatives and integrals

 

Homework #7

  • Chap 5.5: 1, 8, 9, 21, 25
  • Chap 5.6: 2
  • Chap 5.8: 2, 11

11 / 28

  • 6.2 (continued)

  • 6.3 Unit step function. t-shifting

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

Week 14

12 / 3

  • 6.5 Convolution. Integral equations

  • 6.6 Differentiation and integration of transforms

12 / 5

  • 6.6 (continued)

  • 6.7 Systems of ODEs

Week 15

12 / 10

No Class

12 / 12

Final exam (6pm-8pm)