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††††††††††††††††††††††††††††††††††† Math 209 (XO1)

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††††††††††††††††† Final Exam Information

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††††††††††††††††††††† Solutions for Midterm Exam Practice Questions

††††††††††††††††††††† Midterm Solutions Version I

††††††††††††††††††††Midterm Solutions Version II

 

Solutions for Final Exam Practice Questions ( LA Questions)††††††††† ††††††††††††††††††††††††††††††††††††††††††††††††Solutions for Final Exam Practice Questions ( MC Questions)

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†††††††††††††††† Course Outline

 

†††††††††††††††† Lecture Notes

†††††††††††††††† 14.1- Functions of Two Variables

†††† ††††††††††††14.2-Limits and Continuity

 

†††††††††††††††† 14.5- The Chain Rule

†† ††††††††††††††14.6- Directional Derivatives and Gradient Vectors

†††††††††††††††† 14.7- Maximum and Minimum Values

†††††††††††††††† 14.8- Lagrange Multipliers

†††††††††††††††† 15.1- Double Integrals

†††††††††††††††† 15.2- Iterated Integrals

†††††††††††††††† 15.3- Double Integrals over General Regions

†††††††††††††††† 15.4- Double Integrals in Polar Coordinates†††††††

†††††††††††††††† 15.5- Applications of Double Integrals

†††††††††††††††† 15-6- Surface Area

†††††††††††††††† 15.7- Triple Integrals in Rectangular Coordinates

†††††††††††††††† 15.8- Triple Integrals in Cylindrical Coordinates

†††††††††††††††† 15.9- Triple Integrals in Spherical Coordinates

†††††††††††††††† 15.10- Change of Variables in Triple Integrals

†††††††††††††††† 16.1- Vector Fields

†††††††††††††††† 16.2- Line Integrals

†††††††††††††††† 16.3- The Fundamental Theorem for Line Integrals

†††††††††††††††† 16.4- Greenís Theorem

†††††††††††††††† 16.5- Curl and Divergence

†††††††††††††††† 16.6- Parametric Surfaces and Their Areas

†††††††††††††††† 16.7- Surface Integrals

†††††††††††††††† Application of Surface Integrals: Flux

†††††††††††††††† 16.8- Stokesí Theorem

†††††††††††††††† 16.9- The Divergence Theorem

 

 

 

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