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MTH201 : Multivariable Calculus

Course Overview

Course Synopsis

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, Green's theorem, Other topics of discussion are Limits and Continuity, Extreme values, Taylor and Maclaurin Series.

Course Learning Outcomes

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 Taylor and Maclaurin series of given function.

Course Calendar

Values of Functions2Handout5-8
Elements of three dimensional geometry3Handout9-14
Polar co-ordinates4Handout15-21
Limit of Multivariable Function5Handout22-28
Geometry of continuous functions6Handout29-35
Geometric meaning of partial derivative7Handout36-39
Euler theorem, Chain Rule8Handout40-45
Examples about Chain Rule9Handout46-50
Introduction to Vectors10Handout51-59
The Triple Scalar or Box Product11Handout60-66
Tangent planes to the surfaces12Handout67-73
Orthogonal Surface13Handout74-80
Extrema of Functions of Two Variables14Handout81-84
Examples of Extrema of Functions15Handout85-90
Extreme Valued Theorem16Handout91-95
Examples of Extreme Valued Theorem17Handouts96-102
Revision of Integration18Handout103-106
Use Of Integrals19Handout107-110
Double integral for non-rectangular region20Handout111-114
Examples of double integrals21Handout115-118
Examples of volume and area22Handout119-121
Polar Coordinate Systems23Handout122-125
Sketching in polar co-ordinates24Handout126-130
Double integrals in polar co-ordinates25Handout131-134
Examples of Double integrals in polar co-ordinates26Handout135-137
Vector valued functions27Handout138-141
Limits of vector valued function28Handout142-147
Change of Parameter29Handout148-152
First Fundamental Theorem of Calculus30Handout200-205
Exact Differentials30Handout153-158
Line Integral31Handout159-163
Examples of line integral32Handout164-167
Examples of line integral33Handout168-171
Examples of line integral34Handout172-178
Definite Integrals35Handout179-181
Scalar Field36Handout182-185
Higher Order Derivative & Leibniz Theorem37Handout186-195
Taylor and Maclaurin Series38Handout196-204
Numerical Integration39Handout205-215
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