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CourseRES.18-00820 lectures11 h 29 min

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

Prof. Herbert Gross · Massachusetts Institute of Technology

Start with lecture 1 At MIT OpenCourseWare

About

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

Part I: Complex Variables

  1. Lecture 1: The Complex Numbers 44 min · Video
  2. Lecture 2: Functions of a Complex Variable 36 min · Video
  3. Lecture 3: Conformal Mappings 36 min · Video
  4. Lecture 4: Sequences and Series 34 min · Video
  5. Lecture 5: Integrating Complex Functions 35 min · Video

Part II: Differential Equations

  1. Lecture 1: The Concept of a General Solution 35 min · Video
  2. Lecture 2: Linear Differential Equations 36 min · Video
  3. Lecture 3: Solving the Linear Equations L(y) = 0; Constant Coefficients 20 min · Video
  4. Lecture 4: Undetermined Coefficients 30 min · Video
  5. Lecture 5: Variations of Parameters 25 min · Video
  6. Lecture 6: Power Series Solutions 34 min · Video
  7. Lecture 7: Laplace Transforms 39 min · Video

Part III: Linear Algebra

  1. Lecture 1: Vector Spaces 32 min · Video
  2. Lecture 2: Spanning Vectors 28 min · Video
  3. Lecture 3: Constructing Bases 41 min · Video
  4. Lecture 4: Linear Transformations 37 min · Video
  5. Lecture 5: Determinants 40 min · Video
  6. Lecture 6: Eigenvectors 39 min · Video
  7. Lecture 7: Dot Products 42 min · Video
  8. Lecture 8: Orthogonal Functions 35 min · Video

Syllabus and materials

At MIT OpenCourseWare, as the course publishes them.

Credits and licence

Institution
Massachusetts Institute of Technology
Department
Mathematics
Teacher
Prof. Herbert Gross
Term
Fall 2011
Level
Undergraduate
Language
English
Subjects
Mathematics
Source
MIT OpenCourseWare
Licence
CC BY-NC-SA 4.0, as MIT OpenCourseWare states it. Non-commercial use only. MIT OpenCourseWare's terms
Attribution
Prof. Herbert Gross. Calculus Revisited: Complex Variables, Differential Equations, and Linear Algebra. Fall 2011. Massachusetts Institute of Technology: MIT OpenCourseWare, https://ocw.mit.edu/. License: Creative Commons BY-NC-SA.
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