Engineering Mathematics: YouTube Workbook
Publisher: Bookboon.com
Published: 2013
ISBN-13: 9788740305227
Table of contents: title: Content; title: How to use this workbook; title: About the author; title: Acknowledgments; title: 1. Partial derivatives & applications; title: 1.1. Partial derivatives & partial differential equations; title: 1.2. Partial derivatives & chain rule; title: 1.3. Taylor polynomial approximations: two variables; title: 1.4. Error estimation; title: 1.5. Differentiate under integral signs: Leibniz rule; title: 2. Some max/min problems for multivariable functions; title: 2.1. How to determine & classify critical points; title: 2.2. More on determining & classifying critical points; title: 2.3. The method of Lagrange multipliers; title: 2.4. Another example on Lagrange multipliers; title: 2.5. More on Lagrange multipliers: 2 constraints; title: 3. A glimpse at vector calculus; title: 3.1. Vector functions of one variable; title: 3.2. The gradient field of a function; title: 3.3. The divergence of a vector field; title: 3.4. The curl of a vector field; title: 3.5. Introduction to line integrals; title: 3.6. More on line integrals; title: 3.7. Fundamental theorem of line integrals; title: 3.8. Flux in the plane + line integrals; title: 4. Double integrals and applications; title: 4.1. How to integrate over rectangles; title: 4.2. Double integrals over general regions; title: 4.3. How to reverse the order of integration; title: 4.4. How to determine area of 2D shapes; title: 4.5. Double integrals in polar co-ordinates; title: 4.6. More on integration & polar co-ordinates; title: 5. Ordinary differential equations; title: 5.1. Separable differential equations; title: 5.2. Linear, first–order differential equations; title: 5.3. Homogeneous, first–order ODEs; title: 5.4. 2nd–order linear ordinary differential equations; title: 5.5. Nonhomogeneous differential equations; title: 5.6. Variation of constants / parameters; title: 6. Laplace transforms and applications; title: 6.1. Introduction to the Laplace transform; title: 6.2. Laplace transforms + the first shifting theorem; title: 6.3. Laplace transforms + the 2nd shifting theorem; title: 6.4. Laplace transforms + differential equations; title: 7. Fourier series; title: 7.1. Introduction to Fourier series; title: 7.2. Odd + even functions + Fourier series; title: 7.3. More on Fourier series; title: 7.4. Applications of Fourier series to ODEs; title: 8. PDEs & separation of variables; title: 8.1. Deriving the heat equation; title: 8.2. Heat equation & separation of variables; title: 8.3. Heat equation & Fourier series; title: 8.4. Wave equation and Fourier series; title: 9. Bibliography