Calculus Revisited Videos Part 3

Calculus is, in many ways, the gateway to more advanced mathematical topics.  For that reason Part 3 of our Calculus Revisited course gives an introduction to three of those areas that are often of great concern to people whose work involves more advanced mathematics.  The three topics we chose are: Complex Variables, Ordinary Differential Equations and Linear Algebra.

Block 1: Complex Variables

1) Complex Numbers

2) Derivatives of Complex Valued Functions

3) Conformal Mapping

4) Infinite Series of Complex Numbers

5) Integrating Complex Functions

Block 2: Ordinary Differential Equations


1) Solutions of Differential Equations

2) Linear Differential Equations of Order 2

3) Linear Homogeneous Differential Equations of Order 2

4) Undetermined Coefficients

5) Variation of Parameters

6) Power Series Solutions

7) LaPlace Transforms

Block 3: Linear Algebra

1) Vector Spaces - A Structural (Axiomatic) Definition

2) Spanning Vectors

3) Constructing Bases

4) Linear Transformations

5) Determinants

6) Eigenvectors

Block 3: Enrichment Topics

1) The Dot Product Revisited

2) Orthogonal Functions (Fourier Series)

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We wish to acknowledge the support of the Gabriella and Paul Rosenbaum Foundation in helping us develop the content on this website.  Without the support of the Foundation and its president, Madge Goldman, much of the material that will be posted here would not have existed.

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