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 example
Stokes theorem, Divergence theorem, Greens theorem,
Other topics of discussion are Limits and Continuity, Extreme values, Fourier series and Laplace transformations.
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Course Learning Outcomes
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Upon successful completion of this course, you should be able to:
- Determine Limits and Continuity of multi-variable function
- Evaluate Partial Differentiation and will know the related techniques.
- Apply the concept of Extreme-Values of multi-variable functions to real world problems.
- Solve Double Integral for Cartesian and Polar co-ordinates and can do their inter-conversions
- Find Triple Integrals in rectangular, spherical and cylindrical co-ordinates.
- Apply Multiple Integrals for area and volume problems.
- Apply elementary operations on Vector-Valued function
- Compute arc-length and solve problems regarding change of parameter.
- Evaluate Line, Surface and Volume integral.
- State Green’s Theorem, Divergence Theorem and Stoke’s Theorem and show how these theorems are applied.
- Find Fourier Series of given periodic function.
- Solve problems related to Laplace Transformation.
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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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Introduction to Two Dimensional Geometry (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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Coordinate systems(Lecture # 4)
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5
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Limit of functions of Two variables.(Lecture # 5)
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6
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Partial derivatives.(Lecture # 6)
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7
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Geometrical Meaning of Partial derivative.(Lecture # 7)
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8
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Chain Rule.(Lecture # 8)
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9
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More about Chain Rule.(Lecture # 9)
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Assignment No. 1
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10
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Introduction to vectors and their Product.(Lecture # 10)
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11
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Scalar triple product and Directional Derivative.(Lecture # 11)
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12
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Tangent Planes to the surfaces.(Lecture # 12)
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13
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Normal Lines and Differentail of a function.(Lecture # 13)
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14
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Absolute and relative Extrema.(Lecture # 14)
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15
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Second Partial Derivative Tests for Extrema.(Lecture # 15 )
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16
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Extreme Value Theorm And Examples.(Lecture # 16)
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Quiz No. 1
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17
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Worked example of extrema of functions.(Lecture # 17)
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18
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Introduction to double integral.(Lecture # 18)
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Quiz No. 2
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19
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Area as Anti derivative.(Lecture # 19)
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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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Worked Examples.(Lecture # 21)
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22
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Volume as duoble integral.(Lecture # 22)
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Mid Term Exam
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23
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Introduction to polar coordinates.(Lecture # 23)
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24
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Curve Sketching In Polar Coordinates.(Lecture # 24)
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25
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Double integration in Polar coordinates.(Lecture # 25)
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26
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Examples of Double Integrals in Polar coordinates.(Lecture # 26)
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27
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Interoduction to vector valued functions.(Lecture # 27)
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28
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Continuty , Derivative and Integrals of Vector Valued Functions.(Lecture # 28)
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Assignment No. 2
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29
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Change of parameter and chain rule.(Lecture # 29)
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30
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Integration of exact Differentials.(Lecture # 30)
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31
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Line integrals along a curve.(Lecture # 31)
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32
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Examples of Line integrals ( Along Prametric Curves)(Lecture # 32)
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33
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Exact differentials and line integrals.(Lecture # 33)
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34
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Greens Theorem and its application (Lecture # 34)
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35
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Definate integrals for the powers of sine and cosine functions(Lecture # 35)
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36
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Line integrals over the Saclar and vector fields(Lecture # 36)
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Quiz No. 3
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37
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Volume and Surface integrals(Lecture # 37)
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38
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Conservative vector fields and Divergence Theorem.(Lecture # 38)
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39
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Periodic Functions.(Lecture # 39)
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40
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Fourier Series.(Lecture # 40)
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41
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Examples of Fourier Series, Even and Odd functions.(Lecture # 41)
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42
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Fourier Series(Contd) and Half Range Series.(Lecture # 42)
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43
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Fourier Series of Functions other then period 2pi.(Lecture # 43)
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44
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Laplace Transform.(Lecture # 44)
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45
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Inverse Laplace Transforms.(Lecture # 45)
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Final Term Exam
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