# Virtual University of Pakistan

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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

 Topic Lecture Resource Page Introduction 1 Handout 1-4 Values of Functions 2 Handout 5-8 Elements of three dimensional geometry 3 Handout 9-14 Polar co-ordinates 4 Handout 15-21 Limit of Multivariable Function 5 Handout 22-28 Geometry of continuous functions 6 Handout 29-35 Geometric meaning of partial derivative 7 Handout 36-39 Quiz-01 Euler theorem, Chain Rule 8 Handout 40-45 Examples about Chain Rule 9 Handout 46-50 Introduction to Vectors 10 Handout 51-59 The Triple Scalar or Box Product 11 Handout 60-66 Tangent planes to the surfaces 12 Handout 67-73 Assignment-01 Orthogonal Surface 13 Handout 74-80 Extrema of Functions of Two Variables 14 Handout 81-84 Examples of Extrema of Functions 15 Handout 85-90 Extreme Valued Theorem 16 Handout 91-95 Examples of Extreme Valued Theorem 17 Handouts 96-102 Quiz-02 Revision of Integration 18 Handout 103-106 Use Of Integrals 19 Handout 107-110 Double integral for non-rectangular region 20 Handout 111-114 Examples of double integrals 21 Handout 115-118 Examples of volume and area 22 Handout 119-121 MID TERM EXAMINATION Polar Coordinate Systems 23 Handout 122-125 Sketching in polar co-ordinates 24 Handout 126-130 Double integrals in polar co-ordinates 25 Handout 131-134 Examples of Double integrals in polar co-ordinates 26 Handout 135-137 Vector valued functions 27 Handout 138-141 Limits of vector valued function 28 Handout 142-147 Quiz-03 Change of Parameter 29 Handout 148-152 First Fundamental Theorem of Calculus 30 Handout 200-205 Exact Differentials 30 Handout 153-158 Line Integral 31 Handout 159-163 Examples of line integral 32 Handout 164-167 Examples of line integral 33 Handout 168-171 Assignment#2 Examples of line integral 34 Handout 172-178 Definite Integrals 35 Handout 179-181 Scalar Field 36 Handout 182-185 GDB Higher Order Derivative & Leibniz Theorem 37 Handout 186-195 Taylor and Maclaurin Series 38 Handout 196-204 Numerical Integration 39 Handout 205-215 FINAL EXAMINATIONS