Math 421:10, TTh, 2-3:20pm, BE--253 (LIV), Spring 2024

Syllabus and General Information 

• Lecturer : Dr. Vladimir Shtelen
• Office and Office Hours: HLL- 203, Tuesadays & Thursdays 12:30-1:30pm
• e-mail address: shtelen@math.rutgers.edu
• web site: http://www.math.rutgers.edu/~shtelen
• Departmental web page for Math 421
• Textbook: Dennis G. Zill, Advanced Engineering Mathematics, 7th ed., 2022, Jones&Barlett Learning
• Grading: Midterm exams - 20% each, Final exam - 40%,  Quizzes - 15%  Homework - 5%
  
  

  Lecture	Date	Sections covered	Suggested Homework problems
  1	01/16	4.1 Definition of the Laplace transform	1, 3, 5, 7, 13, 24, 31, 35
  2	01/18	4.2 The Inverse Transform and Derivatives	5, 7, 11, 15, 17, 18, 23, 33, 34, 35, 38
  3	01/23	4.3 Translation Theorems    Quiz 1	3, 7, 11, 16, 19, 28, 44, 29, 49, 59, 60, 74
  4	01/25	4.4 Additional Operational Properties	3, 8, 11, 13, 14, 26, 31, 37, 41, 48, 67
  5	01/30	4.5 Dirac Delta Function 4.6 Systems of Linear Differential Equations    Quiz 2	4.5: 1, 3, 8, 10 4.6: 1, 3, 5, 7
  6	02/01	7.6 Vector Spaces 8.1 Matrix Algebra	7.6: 11, 13, 17, 27, 28 8.1: 13, 17, 42
  7	02/06	8.2 Systems of Linear Algebraic Equations 8.3 Rank of a Matrix     Quiz 3	8.2: 3, 10, 11, 15 8.3: 4, 7, 9, 13, 15, 17
  8	02/08	8.4 Determinants 8.5 Properties of Determinants	8.4: 15, 19, 21, 24, 27 8.5: 25, 26, 29
  9	02/13	8.6 Inverse of a Matrix 8.7 Cramer's Rule	8.6: 7, 15, 21, 27, 31, 47, 53 8.7: 1, 7, 8
  10	02/15	Exam 1 (on topics covered in Lectures 1-8)
  11	02/20	8.8: The Eigenvalue Problem	3, 5, 13, 14, 21
  12	02/22	7.7 Gram-Schmidt Process	2, 3, 5, 9, 15, 17
  13	02/27	8.10 Orthogonal Matrices          Quiz 4	1, 5, 7, 13, 15, 16
  14	02/29	8.12 Diagonalization	3, 5, 13, 21, 27
  15	03/05	12.1 Orthogonal Functions    Quiz 5	1, 3, 5, 9, 11
  16	03/07	12.2 Fourier Series	1, 5, 9, 15
  17	03/19	12.3 Fourier Sine and Cosine Series 12.4 Complex Fourier Series       Quiz 6	12.3: 3, 5, 8, 13, 20, 23, 29, 36 12.4: 1, 3, 5, 6
  18	03/21	3.9 Linear Models: BVPs 12.5 Sturm-Liouville Problem	3.9: 11, 16 12.5: 1, 5
  19	03/26	13.1 Separable Partial Differential Equations	3, 9, 15, 17, 21, 23
  20	03/28	Exam 2 (on topics covered in Lectures 9-18)
  21	04/02	13.2 Classical PDEs and BVPs 13.3 Heat Equation	13.2:1, 3, 5, 7, 8, 11 13.3: 2, 5, 6
  22	04/04	13.4 Wave Equation	13.4: 1, 3, 5, 8
  23	04/09	13.5 Laplace's Equation        Quiz 7 13.6 Nonhomogeneous BVPs	13.5: 3, 4, 5, 15 13.6: 1, 3, 5, 9, 10, 11
  24	04/11	13.7 Orthogonal Series Expansions	1, 2, 3, 5, 7
  25	04/16	13.8 Fourier Series in Two Variables   Quiz 8	1, 3, 5
  26	04/18	14.1 Laplace's Equation in Polar Coordinates	1, 3, 7, 10
  27	04/23	15.3 Fourier Integral	1, 3, 7, 9
  28	04/25	Review for the Final Exam