Calculus Revisited: Complex Variables, Differential Equations, and Linear Algebra
Massachusetts Institute of Technology via MIT OpenCourseWare
-
35
-
- Write review
Learn AI, Data Science & Business — Earn Certificates That Get You Hired, 50% Off
Learn Generative AI, Prompt Engineering, and LLMs for Free
Overview
AI, Data Science & Cloud Certificates from Google, IBM & Meta — 50% Off
One plan covers every Professional Certificate on Coursera. 50% off Coursera Plus Annual for 10 days only — price increases June 17.
Unlock All Certificates
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/)Â
[Calculus Revisited: Multivariable Calculus](/courses/res-18-007-calculus-revisited-multivariable-calculus-fall-2011/)
Syllabus
- Lecture 1: The Complex Numbers
- Lecture 1: The Concept of a General Solution
- Lecture 1: Vector Spaces
- Lecture 2: Functions of a Complex Variable
- Lecture 2: Linear Differential Equations
- Lecture 2: Spanning Vectors
- Lecture 3: Conformal Mappings
- Lecture 3: Constructing Bases
- Lecture 3: Solving the Linear Equations L(y) = 0; Constant Coefficients
- Lecture 4: Linear Transformations
- Lecture 4: Sequences and Series
- Lecture 4: Undetermined Coefficients
- Lecture 5: Determinants
- Lecture 5: Integrating Complex Functions
- Lecture 5: Variations of Parameters
- Lecture 6: Eigenvectors
- Lecture 6: Power Series Solutions
- Lecture 7: Dot Products
- Lecture 7: Laplace Transforms
- Lecture 8: Orthogonal Functions
Taught by
Prof. Herbert Gross