M450

M450 Advanced Mathematics for Engineers I 
Fall 2018

 

Instructor: Dr. Shixu Meng
Office: East Hall 4827
When: TuTh 8:30-10:30 am
Where: 2166 DOW
Office Hours: TuWeTh 11:00 am-12:00 pm

 

Course Description: This course is an introduction to some of the main mathematical techniques in engineering and physics. It is intended to provide some background for courses in those disciplines with a mathematical requirement that goes beyond calculus. Model problems in mathematical physics are studied in detail and applications emphasized throughout. Topics include Fourier series and integrals, the classical partial differential equations (heat, wave and Laplace equation) solved by separation of variables and an introduction to complex analysis with applications to potential theory. See more details in Advanced Mathematics for Engineers I Syllabus.

 

Schedule Notes
Lecture 1: Review of ODEs Lecture 1
Lecture 2: Review of Series and Series Solution to ODE Lecture 2
Lecture 3: Complex Numbers Lecture 3
Lecture 4: Fourier Series Lecture 4
Lecture 5: Half- and Quarter- Range Expansions Lecture 5
Lecture 6: Manipulation of Fourier Series and Vector Spaces
Lecture 6
Lecture 7: Sturm-Liouville Theory
Lecture 7
Lecture 8: Diffusion (heat) Equation Lecture 8
Lecture 9: Wave Equation Lecture 9
Lecture 10: Multidimensional Wave Equation Lecture 10
Lecture 11: D’Alembert’s Solution and Laplace Equation Lecture 11
Midterm Exam Midterm Exam
Lecture 12: Laplace Equation Lecture 12
Lecture 13: Laplace Equation in Polar Coordinates Lecture 13
Lecture 14: Fourier transform Lecture 14
Lecture 15: Applications of Fourier Transform Lecture 15
Lecture 16: Polar Representation of Complex Numbers and Analyticity Lecture 16
Lecture 17: Analyticity Lecture 17
Lecture 18: Conformal Mapping Lecture 18
Lecture 19: The Bilinear Transformation Lecture 19
Lecture 20: The Bilinear Transformation II Lecture 20
Lecture 21: Complex Integration Lecture 21
Lecture 22: Cauchy Theorem and Fundamental Theorem of Complex Integral Calculus Lecture 22
Lecture 23: Cauchy Integral Formula Lecture 23
Lecture 24: Residue Theorem and Applications Lecture 24
Lecture 25: Laurent Series Lecture 25
Final Exam Final Exam

 

Homework and Solutions

HW 1 Solution 1
HW 2 Solution 2
HW 3 Solution 3
HW 4 Solution 4
HW 5 Solution 5
HW 6 Solution 6
HW 7 Solution 7
HW 8 Solution 8
HW 9 Solution 9
HW 10 Solution 10