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

- Institution: Massachusetts Institute of Technology
- Department: Mathematics
- Teacher: Prof. Herbert Gross
- Term: Fall 2011
- Level: Undergraduate
- Language: English
- Subjects: Mathematics
- Source: [MIT OpenCourseWare](https://ocw.mit.edu/courses/res-18-008-calculus-revisited-complex-variables-differential-equations-and-linear-algebra-fall-2011/)
- Licence: [CC BY-NC-SA 4.0](https://creativecommons.org/licenses/by-nc-sa/4.0/) (Non-commercial use only.)
- Who can watch: Tweens profiles and older (sources give no ratings; placed by Invisible Network from the source's own words)

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 and Multivariable Calculus) 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 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 Gabriella and Paul Rosenbaum Foundation.

Other Resources by Herb Gross

Calculus Revisited: Single Variable Calculus

Calculus Revisited: Multivariable Calculus

## Lectures

1. [Lecture 1: The Complex Numbers](https://invisiblenetwork.ai/learn/mit/res-18-008-calculus-revisited-complex-variables-differential-equations-and-linear-algebra-fall-2011/c4514e2c6206), 44 min (Video)
2. [Lecture 2: Functions of a Complex Variable](https://invisiblenetwork.ai/learn/mit/res-18-008-calculus-revisited-complex-variables-differential-equations-and-linear-algebra-fall-2011/ecd163929b87), 36 min (Video)
3. [Lecture 3: Conformal Mappings](https://invisiblenetwork.ai/learn/mit/res-18-008-calculus-revisited-complex-variables-differential-equations-and-linear-algebra-fall-2011/99cd874e7e33), 36 min (Video)
4. [Lecture 4: Sequences and Series](https://invisiblenetwork.ai/learn/mit/res-18-008-calculus-revisited-complex-variables-differential-equations-and-linear-algebra-fall-2011/bdd2e7e888f5), 34 min (Video)
5. [Lecture 5: Integrating Complex Functions](https://invisiblenetwork.ai/learn/mit/res-18-008-calculus-revisited-complex-variables-differential-equations-and-linear-algebra-fall-2011/13addc7b6683), 35 min (Video)
6. [Lecture 1: The Concept of a General Solution](https://invisiblenetwork.ai/learn/mit/res-18-008-calculus-revisited-complex-variables-differential-equations-and-linear-algebra-fall-2011/9e11ff51eb64), 35 min (Video)
7. [Lecture 2: Linear Differential Equations](https://invisiblenetwork.ai/learn/mit/res-18-008-calculus-revisited-complex-variables-differential-equations-and-linear-algebra-fall-2011/0a2305f8dc8c), 36 min (Video)
8. [Lecture 3: Solving the Linear Equations L(y) = 0; Constant Coefficients](https://invisiblenetwork.ai/learn/mit/res-18-008-calculus-revisited-complex-variables-differential-equations-and-linear-algebra-fall-2011/02a902edb2f1), 20 min (Video)
9. [Lecture 4: Undetermined Coefficients](https://invisiblenetwork.ai/learn/mit/res-18-008-calculus-revisited-complex-variables-differential-equations-and-linear-algebra-fall-2011/76a54c2cea85), 30 min (Video)
10. [Lecture 5: Variations of Parameters](https://invisiblenetwork.ai/learn/mit/res-18-008-calculus-revisited-complex-variables-differential-equations-and-linear-algebra-fall-2011/25f7de0cc4f7), 25 min (Video)
11. [Lecture 6: Power Series Solutions](https://invisiblenetwork.ai/learn/mit/res-18-008-calculus-revisited-complex-variables-differential-equations-and-linear-algebra-fall-2011/9526437c75c7), 34 min (Video)
12. [Lecture 7: Laplace Transforms](https://invisiblenetwork.ai/learn/mit/res-18-008-calculus-revisited-complex-variables-differential-equations-and-linear-algebra-fall-2011/0fe60ef51bc1), 39 min (Video)
13. [Lecture 1: Vector Spaces](https://invisiblenetwork.ai/learn/mit/res-18-008-calculus-revisited-complex-variables-differential-equations-and-linear-algebra-fall-2011/1851de59a050), 32 min (Video)
14. [Lecture 2: Spanning Vectors](https://invisiblenetwork.ai/learn/mit/res-18-008-calculus-revisited-complex-variables-differential-equations-and-linear-algebra-fall-2011/13da8fbbd8c9), 28 min (Video)
15. [Lecture 3: Constructing Bases](https://invisiblenetwork.ai/learn/mit/res-18-008-calculus-revisited-complex-variables-differential-equations-and-linear-algebra-fall-2011/c2d19ba50021), 41 min (Video)
16. [Lecture 4: Linear Transformations](https://invisiblenetwork.ai/learn/mit/res-18-008-calculus-revisited-complex-variables-differential-equations-and-linear-algebra-fall-2011/5a3b1d05684a), 37 min (Video)
17. [Lecture 5: Determinants](https://invisiblenetwork.ai/learn/mit/res-18-008-calculus-revisited-complex-variables-differential-equations-and-linear-algebra-fall-2011/dea4efd93260), 40 min (Video)
18. [Lecture 6: Eigenvectors](https://invisiblenetwork.ai/learn/mit/res-18-008-calculus-revisited-complex-variables-differential-equations-and-linear-algebra-fall-2011/4be3c844b6cb), 39 min (Video)
19. [Lecture 7: Dot Products](https://invisiblenetwork.ai/learn/mit/res-18-008-calculus-revisited-complex-variables-differential-equations-and-linear-algebra-fall-2011/19372871ab86), 42 min (Video)
20. [Lecture 8: Orthogonal Functions](https://invisiblenetwork.ai/learn/mit/res-18-008-calculus-revisited-complex-variables-differential-equations-and-linear-algebra-fall-2011/91ad39eb9361), 35 min (Video)