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Calculus Revisited: Complex Variables, Differential Equations, and Linear Algebra

Mathematics MIT CC BY-NC-SA 4.0 20 lectures

Calculus Revisited is a series of videos and related resources that covers the materials normally found in freshman- and sophomore-level introductory mathematics courses. _Complex Variables, Differential Equations, and Linear Algebra_ is the third course in the series, consisting of 20 Videos, 3 Study Guides, and a set of Supplementary Notes. Students should have mastered the first two courses in the series ([Single Variable Calculus](/resources/res-18-006-calculus-revisited-single-variable-calculus-fall-2010/index.htm) and [Multivariable Calculus](/resources/res-18-007-calculus-revisited-multivariable-calculus-fall-2011/index.htm)) before taking this course. The series was first released in 1972, but equally valuable today for students who are learning these topics for the first time. About the Instructor Herb Gross has taught math as senior lecturer at MIT and was the founding math department chair at Bunker Hill Community College. He is the developer of the {{% resource_link "0c9b64dd-6f41-4cc8-ae48-7d8d4b750efb" "Mathematics As A Second Language" %}} website, providing arithmetic and algebra materials to elementary and middle school teachers. Acknowledgements Funding for this resource was provided by the {{% resource_link "1afa4fb6-6d61-45ed-8718-5d53c56e1bdf" "Gabriella and Paul Rosenbaum Foundation" %}}. _Other Resources by Herb Gross_ [Calculus Revisited: Single Variable Calculus](/courses/res-18-006-calculus-revisited-single-variable-calculus-fall-2010/)  [Calculus Revisited: Multivariable Calculus](/courses/res-18-007-calculus-revisited-multivariable-calculus-fall-2011/)

Syllabus

  1. 1 Lecture 1: The Complex Numbers
  2. 2 Lecture 2: Functions of a Complex Variable
  3. 3 Lecture 3: Conformal Mappings
  4. 4 Lecture 4: Sequences and Series
  5. 5 Lecture 5: Integrating Complex Functions
  6. 6 Lecture 1: The Concept of a General Solution
  7. 7 Lecture 2: Linear Differential Equations
  8. 8 Lecture 3: Solving the Linear Equations L(y) = 0; Constant Coefficients
  9. 9 Lecture 4: Undetermined Coefficients
  10. 10 Lecture 5: Variations of Parameters
  11. 11 Lecture 6: Power Series Solutions
  12. 12 Lecture 7: Laplace Transforms
  13. 13 Lecture 1: Vector Spaces
  14. 14 Lecture 2: Spanning Vectors
  15. 15 Lecture 3: Constructing Bases
  16. 16 Lecture 4: Linear Transformations
  17. 17 Lecture 5: Determinants
  18. 18 Lecture 6: Eigenvectors
  19. 19 Lecture 7: Dot Products
  20. 20 Lecture 8: Orthogonal Functions

Course materials