
Course Category: 
Mathematics 
Course Level: 
Undergraduate 
Credit Hours: 
3 
Prerequisites: 
MTH101 

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, Fourier series and Laplace transformations.
Course Learning Outcomes
Upon successful completion of this course, you should be able to:
 Determine Limits and Continuity of multivariable function
 Evaluate Partial Differentiation and will know the related techniques
 Apply the concept of ExtremeValues of multivariable functions to real world problems
 Solve Double Integral for Cartesian and Polar coordinates and can do their interconversions
 Find Triple Integrals in rectangular, spherical and cylindrical coordinates
 Apply Multiple Integrals for area and volume problems
 Apply elementary operations on VectorValued function
 Compute arclength 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
Course Contents
Introduction to three dimensional geometry. Limits, continuity and Partial Derivatives of Multivariable Function. Vectors. Directional derivative. Tangent Planes and Normal Lines to the Surfaces. Maxima And Minima of Functions of two variables. Applications of Extrema of Functions. Double Integration in rectangular and polar coordinates. Vector Valued Functions. Integration of Exact differentials. Line integrals. Greens Theorem and its application. Divergence and Curl of a vector. Scalar Fields, Vector fields, Volume and Surface integrals. Conservative Fields. Divergence Theorem. Fourier Series. Laplace Transforms.
Course Related Links
For basic rules of differentiation and their proofs
You can find useful material related to function of one variable on this site
You can find the topics related to integration, application of integration, geometry , curves and polar coordinates
Anitmated Description of topics
Online notes on Multivariable Calculus
A very valuable link containing online lectures being delivered by electronic pen 


