What You’ll Discover in TTC Video Understanding Multi-Variable Calculus
Understanding Multivariable CalculusTeaching Award: Problems, Solutions and Tips-The University of Florida’s Professor Bruce H. Edwards won the award. He brings together the fundamental concepts of calculus in a deeper and more powerful manner.
File size: 13.03GB
TTC Video – Understanding Multi-Variable Calculus
Calculating the volume of odd is possible-We depend on three-dimensional calculus to shape objects, predict the outcome of large numbers of trials in statistics, and even forecast the weather. Once we understand the fundamentals and application of multivariable calculus we can see how these concepts lead to new laws, whole new fields of Physics, and new ways of approaching one.-impossible problems.
 We can use multivariable calculus to calculate the ge
- Optimization tools that can take into account as many variables and factors as necessary;
- These vector fields give us an insight into the workings fluids from hydraulic pistons to ocean currents or weather.
- New coordinate systems are available that allow us to solve integrals with Cartesian coordinates.
- Mathematics can be described as the mathematical definition of planes and surfaces in spaces. This is how many mathematics fields such as topology or differential geometry are created.
 Understanding Multivariable CalculusTeaching Award: Problems, Solutions and Tips-Professor Bruce H. Edwards, University of Florida winner, brings together basic concepts of calculus in an even deeper and stronger way. For professionals and students, this course will help them to increase their quantitative knowledge.-Open intellectual exercise for retired professionals and teachers who want to learn about the incredible applications of 3-D calculus.
 This book is intended for people who know basic calculus. Understanding Multivariable Calculus It is not necessary to be familiar with the following, but it does allow you to follow. Calculus II. II. Calculus II that does carry over, such vector calculus is briefly reintroduced here, with a new emphasis placed on three dimensions.
 The 36 comprehensive lectures will focus on the development and generalization of fundamental tools for integration/differentiation to functions of more that one variable. Under the expert guidance of Professor Edwards, you’ll embark on an exhilarating journey through the concepts of multivariable calculus, enlivened with real-Beautiful animated graphics and world examples that take calculus beyond the textbook to our three-dimensional world of mathematics-Dimensional world.
 A New Approach to Old Problems
 How can you integrate in a particular region? xy plane that can’t be defined by just one standard y = (x) function? Multivariable calculus contains many surprises and answers. In Understanding Multivariable CalculusProfessor Edwards reveals powerful new tools in each lecture to solve difficult problems in just a few steps. He turns complex integrals into simple ones and gives exact answers that even calculators cannot.
 These new tools will allow you to
- Use double or triple integrals to directly integrate volumes with surface areas.
- Use vectors to define parametric equations that are easily differentiateable for a function;
- Use polar, cylindrical and spherical coordinates for double and triple integrals evaluations. These solutions are more difficult than in standard Cartesian coordinates.
 With a passion for the subject and clarity, Professor Edwards guides you through these new techniques. This makes even the most difficult material easy to understand and enjoyable. With animated graphics featuring state-Of-The-Software that creates art from three-This course will bring dimensional surfaces and volumes alive, as well an accompanying illustrated book. It will allow anyone with an interest in math to gain a better understanding of one of the most important mathematical achievements of all time.
 About Your Professor
 Dr. Bruce H. Edwards holds the position of Professor of Mathematics in University of Florida. Dartmouth College is where he earned his Ph.D. He was awarded numerous Teacher of Year awards and awards for his contributions to mathematics education in Florida.
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1A Visual Introduction to the 3-D Calculus
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2Functions for Several Variables
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3Limits, Partial Derivatives and Continuity
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4Partial Derivatives—One Variable at a Time
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Chain Rules and 5Total Differentials
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6Extrema Functions of Two Variables
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7Applications to Optimization Issues
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8Linear Models & Least Squares Regression
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9Vectors in Space and the Dot Product
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10The Cross Product between Two Vectors in Space
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Space 11Lines & Planes
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Space 12Curved Surfaces
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13Vector-Space-Valuable Functions
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14Kepler’s Laws—The Calculus The Orbits
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15-Directional Derivatives & Gradients
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16Tangent Planes & Normal Vectors to a Surface
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17Lagrange Multipliers—Constrained Optimization
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18Applications for Lagrange Multipliers
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19Iterated integrals & Area in the plane
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Volume and 20Double IntegralsIn taking the next step in learning to integrate multivariable functions, you’ll find that the double integral has many of the same properties as its one-Dimensional counterpart. These integrals are evaluated in a region R bound by variable constraints. You can extrapolate the single variable formula to determine the average value of a given function to multiple variables.
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21Double Integrals for Polar Coordinates
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22Centers for Mass Variable Density
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23Surface Area of Solid
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24Triple Integrations and Applications
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25Triple Integrals in Cylindrical Coordinates
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26Triple Integrals in Spherical Coordinates
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27Vector Fields—Velocity, Gravity, Electricity
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28Curl, Divergence, Line Integrals
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29More Line Integrals & Work by a Force Field
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30Fundamental Theory of Line Integrals
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31Green’s Theorem—Boundaries and Regions
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32Applications of Green’s Theorem
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33Parametric Surfaces for Space
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Flux Integrals and 34Surface Integrals
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35Divergence Theorem—Boundaries and Solids
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36Stokes’s Theorem and Maxwell’s Equations
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