M450 Advanced Mathematics for Engineers I
Fall 2018
Instructor:  Dr. Shixu Meng 
Office:  East Hall 4827 
When:  TuTh 8:3010:30 am 
Where:  2166 DOW 
Office Hours:  TuWeTh 11:00 am12:00 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: SturmLiouville 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
