Engineering Mathematics: YouTube Workbook

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Acknowledgments

1. Partial derivatives & applications
   1. Partial derivatives & partial differential equations
   2. Partial derivatives & chain rule
   3. Taylor polynomial approximations: two variables
   4. Error estimation
   5. Differentiate under integral signs: Leibniz rule
2. Some max/min problems for multivariable functions
   1. How to determine & classify critical points
   2. More on determining & classifying critical points
   3. The method of Lagrange multipliers
   4. Another example on Lagrange multipliers
   5. More on Lagrange multipliers: 2 constraints
3. A glimpse at vector calculus
   1. Vector functions of one variable
   2. The gradient field of a function
   3. The divergence of a vector field
   4. The curl of a vector field
   5. Introduction to line integrals
   6. More on line integrals
   7. Fundamental theorem of line integrals
   8. Flux in the plane + line integrals
4. Double integrals and applications
   1. How to integrate over rectangles
   2. Double integrals over general regions
   3. How to reverse the order of integration
   4. How to determine area of 2D shapes
   5. Double integrals in polar co-ordinates
   6. More on integration & polar co-ordinates
5. Ordinary differential equations
   1. Separable differential equations
   2. Linear, first–order differential equations
   3. Homogeneous, first–order ODEs
   4. 2nd–order linear ordinary differential equations
   5. Nonhomogeneous differential equations
   6. Variation of constants / parameters
6. Laplace transforms and applications
   1. Introduction to the Laplace transform
   2. Laplace transforms + the first shifting theorem
   3. Laplace transforms + the 2nd shifting theorem
   4. Laplace transforms + differential equations
7. Fourier series
   1. Introduction to Fourier series
   2. Odd + even functions + Fourier series
   3. More on Fourier series
   4. Applications of Fourier series to ODEs
8. PDEs & separation of variables
   1. Deriving the heat equation
   2. Heat equation & separation of variables
   3. Heat equation & Fourier series
   4. Wave equation and Fourier series
9. Bibliography