Course Overview
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Course Synopsis
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This course focuses on two basic applications Differential Calculus and Integral Calculus. Under these we will study different techniques and some Fundamental theorems of calculus in multiple dimensions for examplernStokes theorem Divergence theorem Greens theoremrnOther topics of discussion are Limits and Continuity Extreme values Taylor and Maclaurin Series.
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Course Learning Outcomes
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Upon successful completion of this course you should be able to
- Evaluate limits and establish continuity in multivariable functions demonstrating a profound understanding of mathematical precision.
- Compute partial derivatives adeptly and apply a variety of techniques showcasing a nuanced understanding of multivariable calculus.
- Employ the concept of extreme values in multivariable functions to solve realworld problems demonstrating advanced problemsolving skills.
- Compute double integrals in Cartesian and Polar coordinates as well as triple integrals in rectangular spherical and cylindrical coordinates showcasing versatility in integration methods.
- Apply multiple integrals effectively to solve problems related to area and volume demonstrating practical proficiency in geometric applications.
- Execute elementary operations on vectorvalued functions illustrating a comprehensive mastery of vector calculus.
- State and apply Greens Theorem Divergence Theorem and Stokes Theorem and demonstrate the ability to find Taylor and Maclaurin series for given functions showcasing mastery of advanced calculus concepts.
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Course Calendar
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1
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Introduction to Calculus and Functions(Lecture # 1)
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2
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Values of functions (Lecture # 2)
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3
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Elements of three dimensional geometry (Lecture 3)
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4
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Polar co-ordinates ( Lecture 4)
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5
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Limit of Multivariable Function ( Lecture 5 )
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6
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Geometry of Continuous Functions ( Lecture 6 )
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7
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Geometric meaning of partial derivative ( Lecture 7 )
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Assignment 1
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8
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More About Euler Theorem Chain Rule ( Lecture 8 )
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9
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Examples about Chain Rule
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10
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Introduction to vectors ( Lecture 10 )
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11
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The Triple Scalar or Box Product (Lecture 11)
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12
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Tangent planes to the surfaces ( Lecture 12 )
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Quiz 1
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13
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Orthogonal Surface (Lecture 13)
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14
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Extrema of Functions of Two Variables ( Lecture 14 )
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15
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Examples of Extrema of Functions
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16
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Extreme Valued Theorem ( Lecture 16 )
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17
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Examples of Extreme Valued Theorem
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18
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Revision of Integration ( Lecture 18 )
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19
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Use Of Integrals ( Lecture 19 )
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Quiz 2
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20
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Double integral for non-rectangular region ( Lecture 20 )
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21
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Examples of Double Integrals
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22
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Examples of Volume and Area
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Mid Term
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23
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Polar Coordinate Systems ( Lecture 23 )
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24
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Sketching ( Lecture 24 )
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25
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Double integrals in polar co-ordinates (Lecture 25)
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26
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Examples of Double Integrals in Polar Co-ordinates
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27
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Vector Valued Functions (Lecture 27)
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28
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Limits of Vector Valued Functions (Lecture 28)
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Assignment 2
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29
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Change of parameter (Lecture 29)
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30
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Exact Differential (Lecture 30)
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31
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Line Integral (Lecture 31)
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32
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Examples of Line Integral
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35
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Definite Integrals (Lecture 35)
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Quiz 3
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36
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Scalar Field (Lecture 36)
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37
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Higher Order Derivative and Leibniz Theorem
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38
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Taylor and Maclaurin Series
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Final Term
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